diff --git a/.github/workflows/pr.yml b/.github/workflows/pr.yml
index 6068d6e3e..06d34a0c9 100644
--- a/.github/workflows/pr.yml
+++ b/.github/workflows/pr.yml
@@ -8,14 +8,14 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: install Go
-      uses: actions/setup-go@v2
+      uses: actions/setup-go@v3
       with:
         go-version: 1.20.x
     - name: checkout code
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3
       with:
         fetch-depth: 0
-    - uses: actions/cache@v2
+    - uses: actions/cache@v3
       with:
         path: |
           ~/go/pkg/mod
@@ -50,12 +50,12 @@ jobs:
       - staticcheck
     steps:
     - name: install Go
-      uses: actions/setup-go@v2
+      uses: actions/setup-go@v3
       with:
         go-version: ${{ matrix.go-version }}
     - name: checkout code
-      uses: actions/checkout@v2
-    - uses: actions/cache@v2
+      uses: actions/checkout@v3
+    - uses: actions/cache@v3
       with:
         path: |
           ~/go/pkg/mod
@@ -72,7 +72,7 @@ jobs:
         go test -p=1 -v -timeout=30m ./...
         go test -p=1 -tags=purego -v -timeout=30m ./...
     - name: Test (32 bits & race)
-      if: (matrix.os == 'ubuntu-latest') && (matrix.go-version == '1.19.x')
+      if: (matrix.os == 'ubuntu-latest') && (matrix.go-version == '1.20.x')
       run: |
           go test -p=1 -v -timeout=30m -short -race  ./ecc/bn254/...
           go test -p=1 -v -timeout=30m -short -tags=noadx  ./ecc/bn254/...
@@ -88,7 +88,7 @@ jobs:
     steps:
       - name: Notify slack -- workflow failed
         id: slack
-        uses: slackapi/slack-github-action@v1.19.0
+        uses: slackapi/slack-github-action@v1.23.0
         with:
           payload: |
             {
@@ -111,7 +111,7 @@ jobs:
     steps:
       - name: Notify slack -- workflow succeeded
         id: slack
-        uses: slackapi/slack-github-action@v1.19.0
+        uses: slackapi/slack-github-action@v1.23.0
         with:
           payload: |
             {
diff --git a/ecc/bls12-377/fr/kzg/kzg.go b/ecc/bls12-377/fr/kzg/kzg.go
index a1b3a7690..3c139caf9 100644
--- a/ecc/bls12-377/fr/kzg/kzg.go
+++ b/ecc/bls12-377/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bls12377.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bls12377.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bls12377.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bls12377.G2Affine // [G₂, [α]G₂ ]
+	G1 bls12377.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bls12377.G1Affine, size)
+	srs.Pk.G1 = make([]bls12377.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bls12377.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bls12377.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bls12377.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bls12377.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bls12377.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bls12377.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bls12377.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bls12377.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bls12377.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bls12377.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bls12377.PairingCheck(
-		[]bls12377.G1Affine{fminusfaG1Aff, negH},
-		[]bls12377.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bls12377.G1Affine{totalG1Aff, negH},
+		[]bls12377.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bls12377.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bls12377.PairingCheck(
 		[]bls12377.G1Affine{foldedDigests, foldedQuotients},
-		[]bls12377.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bls12377.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bls12-377/fr/kzg/kzg_test.go b/ecc/bls12-377/fr/kzg/kzg_test.go
index 0836edb7c..15fd138c8 100644
--- a/ecc/bls12-377/fr/kzg/kzg_test.go
+++ b/ecc/bls12-377/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bls12377.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bls12-377/fr/kzg/marshal.go b/ecc/bls12-377/fr/kzg/marshal.go
index 0c6e43cfc..404191685 100644
--- a/ecc/bls12-377/fr/kzg/marshal.go
+++ b/ecc/bls12-377/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bls12377.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bls12377.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bls12377.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bls12377.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bls12377.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bls12377.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bls12377.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bls12377.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bls12-377/fr/pedersen/pedersen.go b/ecc/bls12-377/fr/pedersen/pedersen.go
index 18c130742..cee17840b 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bls12-377"
+	curve "github.com/consensys/gnark-crypto/ecc/bls12-377"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bls12377.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bls12377.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bls12377.G1Affine
-	basisExpSigma []bls12377.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bls12377.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls12377.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bls12377.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bls12377.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bls12377.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bls12377.G1Affine, knowledgeProof bls12377.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bls12377.G1Affine, knowled
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bls12377.G1Affine, knowledgeProof bls12377.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bls12377.Pair([]bls12377.G1Affine{commitment, knowledgeProof}, []bls12377.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bls12377.G1Affine, knowledgeProof
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bls12-377/fr/pedersen/pedersen_test.go b/ecc/bls12-377/fr/pedersen/pedersen_test.go
index 51a14eef4..939642488 100644
--- a/ecc/bls12-377/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-377/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bls12-377"
+	curve "github.com/consensys/gnark-crypto/ecc/bls12-377"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bls12377.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls12377.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bls12377.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bls12377.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bls12377.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bls12-377/fr/permutation/permutation.go b/ecc/bls12-377/fr/permutation/permutation.go
index 7031fd3b5..b2168ce47 100644
--- a/ecc/bls12-377/fr/permutation/permutation.go
+++ b/ecc/bls12-377/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bls12-377/fr/permutation/permutation_test.go b/ecc/bls12-377/fr/permutation/permutation_test.go
index 01d093445..8d527af95 100644
--- a/ecc/bls12-377/fr/permutation/permutation_test.go
+++ b/ecc/bls12-377/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bls12-377/fr/plookup/plookup_test.go b/ecc/bls12-377/fr/plookup/plookup_test.go
index 6a32ff6fe..90e44b7e1 100644
--- a/ecc/bls12-377/fr/plookup/plookup_test.go
+++ b/ecc/bls12-377/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bls12-377/fr/plookup/table.go b/ecc/bls12-377/fr/plookup/table.go
index 65844d345..b8bbbd6fc 100644
--- a/ecc/bls12-377/fr/plookup/table.go
+++ b/ecc/bls12-377/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bls12-377/fr/plookup/vector.go b/ecc/bls12-377/fr/plookup/vector.go
index 36c4ad776..9633f589b 100644
--- a/ecc/bls12-377/fr/plookup/vector.go
+++ b/ecc/bls12-377/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bls12-377/g1.go b/ecc/bls12-377/g1.go
index b5b6f65e6..54b590234 100644
--- a/ecc/bls12-377/g1.go
+++ b/ecc/bls12-377/g1.go
@@ -92,6 +92,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bls12-377/g2.go b/ecc/bls12-377/g2.go
index c2155c8dc..bb8e3e5a6 100644
--- a/ecc/bls12-377/g2.go
+++ b/ecc/bls12-377/g2.go
@@ -81,6 +81,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bls12-377/hash_to_g1.go b/ecc/bls12-377/hash_to_g1.go
index 6d5762e3a..85a19e73b 100644
--- a/ecc/bls12-377/hash_to_g1.go
+++ b/ecc/bls12-377/hash_to_g1.go
@@ -166,9 +166,9 @@ func g1MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve1 implements the SSWU map
+// MapToCurve1 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{17252667382019449424, 8408110001211059699, 18415587021986261264, 10797086888535946954, 9462758283094809199, 54995354010328751}
 	var sswuIsoCurveCoeffB = fp.Element{11130294635325289193, 6502679372128844082, 15863297759487624914, 16270683149854112145, 3560014356538878812, 27923742146399959}
@@ -268,7 +268,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SSWU map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	//this is in an isogenous curve
 	g1Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -287,7 +287,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	//this is in an isogenous curve
 	g1Isogeny(&res)
@@ -305,8 +305,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g1Isogeny(&Q0)
diff --git a/ecc/bls12-377/hash_to_g1_test.go b/ecc/bls12-377/hash_to_g1_test.go
index 00ec21465..a5a45d5f0 100644
--- a/ecc/bls12-377/hash_to_g1_test.go
+++ b/ecc/bls12-377/hash_to_g1_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !isOnE1Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bls12-377/hash_to_g2.go b/ecc/bls12-377/hash_to_g2.go
index 03f649caa..9ae6997be 100644
--- a/ecc/bls12-377/hash_to_g2.go
+++ b/ecc/bls12-377/hash_to_g2.go
@@ -613,9 +613,9 @@ func g2MulByZ(z *fptower.E2, x *fptower.E2) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve2 implements the SSWU map
+// MapToCurve2 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve2(u *fptower.E2) G2Affine {
+func MapToCurve2(u *fptower.E2) G2Affine {
 
 	var sswuIsoCurveCoeffA = fptower.E2{
 		A0: fp.Element{4274545572028848265, 14157081418478689358, 13123833976752631407, 4466041663276938746, 9062541850312583986, 90030181981586611},
@@ -739,7 +739,7 @@ func g2Sgn0(z *fptower.E2) uint64 {
 
 // MapToG2 invokes the SSWU map, and guarantees that the result is in g2
 func MapToG2(u fptower.E2) G2Affine {
-	res := mapToCurve2(&u)
+	res := MapToCurve2(&u)
 	//this is in an isogenous curve
 	g2Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -758,7 +758,7 @@ func EncodeToG2(msg, dst []byte) (G2Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve2(&fptower.E2{
+	res = MapToCurve2(&fptower.E2{
 		A0: u[0],
 		A1: u[1],
 	})
@@ -779,11 +779,11 @@ func HashToG2(msg, dst []byte) (G2Affine, error) {
 		return G2Affine{}, err
 	}
 
-	Q0 := mapToCurve2(&fptower.E2{
+	Q0 := MapToCurve2(&fptower.E2{
 		A0: u[0],
 		A1: u[1],
 	})
-	Q1 := mapToCurve2(&fptower.E2{
+	Q1 := MapToCurve2(&fptower.E2{
 		A0: u[2+0],
 		A1: u[2+1],
 	})
diff --git a/ecc/bls12-377/hash_to_g2_test.go b/ecc/bls12-377/hash_to_g2_test.go
index f3b31b8a8..79a9e8979 100644
--- a/ecc/bls12-377/hash_to_g2_test.go
+++ b/ecc/bls12-377/hash_to_g2_test.go
@@ -95,7 +95,7 @@ func TestMapToCurve2(t *testing.T) {
 	properties.Property("[G2] mapping output must be on curve", prop.ForAll(
 		func(a fptower.E2) bool {
 
-			g := mapToCurve2(&a)
+			g := MapToCurve2(&a)
 
 			if !isOnE2Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -118,7 +118,7 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range encodeToG2Vector.cases {
 		var u fptower.E2
 		g2CoordSetString(&u, c.u)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -126,12 +126,12 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range hashToG2Vector.cases {
 		var u fptower.E2
 		g2CoordSetString(&u, c.u0)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g2CoordSetString(&u, c.u1)
-		q = mapToCurve2(&u)
+		q = MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bls12-377/internal/fptower/e12.go b/ecc/bls12-377/internal/fptower/e12.go
index de9c52aa9..0d5d2b553 100644
--- a/ecc/bls12-377/internal/fptower/e12.go
+++ b/ecc/bls12-377/internal/fptower/e12.go
@@ -230,15 +230,17 @@ func (z *E12) DecompressKarabina(x *E12) *E12 {
 	var one E2
 	one.SetOne()
 
-	// g3 == 0
-	if x.C1.B2.IsZero() {
+	if x.C1.B2.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.C0.B1, &x.C1.B2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.C0.B2)
 
-		// g3 != 0
-	} else {
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
+
 		// t0 = g1^2
 		t[0].Square(&x.C0.B1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -302,20 +304,24 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t0 := make([]E2, n)
 	t1 := make([]E2, n)
 	t2 := make([]E2, n)
+	zeroes := make([]bool, n)
 
 	var one E2
 	one.SetOne()
 
 	for i := 0; i < n; i++ {
-		// g3 == 0
-		if x[i].C1.B2.IsZero() {
+		if x[i].C1.B2.IsZero() /* g3 == 0 */ {
 			t0[i].Mul(&x[i].C0.B1, &x[i].C1.B2).
 				Double(&t0[i])
 			// t1 = g2
 			t1[i].Set(&x[i].C0.B2)
 
-			// g3 != 0
-		} else {
+			if t1[i].IsZero() /* g3 == g2 == 0 */ {
+				x[i].SetOne()
+				zeroes[i] = true
+				continue
+			}
+		} else /* g3 != 0 */ {
 			// t0 = g1^2
 			t0[i].Square(&x[i].C0.B1)
 			// t1 = 3 * g1^2 - 2 * g2
@@ -335,6 +341,10 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t1 = BatchInvertE2(t1) // costs 1 inverse
 
 	for i := 0; i < n; i++ {
+		if zeroes[i] {
+			continue
+		}
+
 		// z4 = g4
 		x[i].C1.B1.Mul(&t0[i], &t1[i])
 
@@ -717,7 +727,7 @@ func (z *E12) SetBytes(e []byte) error {
 func (z *E12) IsInSubGroup() bool {
 	var a, b E12
 
-	// check z^(Phi_k(p)) == 1
+	// check z^(phi_k(p)) == 1
 	a.FrobeniusSquare(z)
 	b.FrobeniusSquare(&a).Mul(&b, z)
 
diff --git a/ecc/bls12-377/marshal.go b/ecc/bls12-377/marshal.go
index 6140b863d..7912f7f1d 100644
--- a/ecc/bls12-377/marshal.go
+++ b/ecc/bls12-377/marshal.go
@@ -32,25 +32,27 @@ import (
 // To encode G1Affine and G2Affine points, we mask the most significant bits with these bits to specify without ambiguity
 // metadata needed for point (de)compression
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
 	mUncompressed         byte = 0b000 << 5
+	_                     byte = 0b001 << 5 // invalid
 	mUncompressedInfinity byte = 0b010 << 5
+	_                     byte = 0b011 << 5 // invalid
 	mCompressedSmallest   byte = 0b100 << 5
 	mCompressedLargest    byte = 0b101 << 5
 	mCompressedInfinity   byte = 0b110 << 5
+	_                     byte = 0b111 << 5 // invalid
 )
 
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bls12-377 object values to an output stream
 type Encoder struct {
@@ -103,6 +105,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -135,6 +155,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -155,6 +182,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -186,6 +220,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -245,6 +286,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -315,6 +363,12 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return
 }
 
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
 	return !((mData == mUncompressed) || (mData == mUncompressedInfinity))
@@ -398,6 +452,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -501,6 +557,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -586,6 +644,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 48
 
@@ -598,7 +675,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -682,6 +759,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG1AffineUncompressed {
@@ -854,7 +936,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -944,6 +1026,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG2AffineUncompressed {
diff --git a/ecc/bls12-377/marshal_test.go b/ecc/bls12-377/marshal_test.go
index c1b60a0d2..87dd70bf0 100644
--- a/ecc/bls12-377/marshal_test.go
+++ b/ecc/bls12-377/marshal_test.go
@@ -216,6 +216,26 @@ func TestIsCompressed(t *testing.T) {
 
 }
 
+func TestG1AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG1AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G1Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG1AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -309,6 +329,26 @@ func TestG1AffineSerialization(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestG2AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG2AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G2Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG2AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
diff --git a/ecc/bls12-377/pairing.go b/ecc/bls12-377/pairing.go
index ede3a0380..f670902e4 100644
--- a/ecc/bls12-377/pairing.go
+++ b/ecc/bls12-377/pairing.go
@@ -78,6 +78,12 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	result.FrobeniusSquare(&t[0]).
 		Mul(&result, &t[0])
 
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
 	// Hard part (up to permutation)
 	// Daiki Hayashida, Kenichiro Hayasaka and Tadanori Teruya
 	// https://eprint.iacr.org/2020/875.pdf
diff --git a/ecc/bls12-378/fr/kzg/kzg.go b/ecc/bls12-378/fr/kzg/kzg.go
index d0cde383b..cd51d243a 100644
--- a/ecc/bls12-378/fr/kzg/kzg.go
+++ b/ecc/bls12-378/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bls12378.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bls12378.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bls12378.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bls12378.G2Affine // [G₂, [α]G₂ ]
+	G1 bls12378.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bls12378.G1Affine, size)
+	srs.Pk.G1 = make([]bls12378.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bls12378.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bls12378.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bls12378.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bls12378.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bls12378.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bls12378.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bls12378.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bls12378.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bls12378.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bls12378.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bls12378.PairingCheck(
-		[]bls12378.G1Affine{fminusfaG1Aff, negH},
-		[]bls12378.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bls12378.G1Affine{totalG1Aff, negH},
+		[]bls12378.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bls12378.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bls12378.PairingCheck(
 		[]bls12378.G1Affine{foldedDigests, foldedQuotients},
-		[]bls12378.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bls12378.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bls12-378/fr/kzg/kzg_test.go b/ecc/bls12-378/fr/kzg/kzg_test.go
index 475f39b33..ac3431326 100644
--- a/ecc/bls12-378/fr/kzg/kzg_test.go
+++ b/ecc/bls12-378/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bls12378.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bls12-378/fr/kzg/marshal.go b/ecc/bls12-378/fr/kzg/marshal.go
index f7cc449fe..ff56c7b9e 100644
--- a/ecc/bls12-378/fr/kzg/marshal.go
+++ b/ecc/bls12-378/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bls12378.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bls12378.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bls12378.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bls12378.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bls12378.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bls12378.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bls12378.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bls12378.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bls12-378/fr/pedersen/pedersen.go b/ecc/bls12-378/fr/pedersen/pedersen.go
index 3508d51d0..a526dd71c 100644
--- a/ecc/bls12-378/fr/pedersen/pedersen.go
+++ b/ecc/bls12-378/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bls12-378"
+	curve "github.com/consensys/gnark-crypto/ecc/bls12-378"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bls12378.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bls12378.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bls12378.G1Affine
-	basisExpSigma []bls12378.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bls12378.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls12378.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bls12378.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bls12378.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bls12378.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bls12378.G1Affine, knowledgeProof bls12378.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bls12378.G1Affine, knowled
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bls12378.G1Affine, knowledgeProof bls12378.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bls12378.Pair([]bls12378.G1Affine{commitment, knowledgeProof}, []bls12378.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bls12378.G1Affine, knowledgeProof
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bls12-378/fr/pedersen/pedersen_test.go b/ecc/bls12-378/fr/pedersen/pedersen_test.go
index 745d06334..b2119020d 100644
--- a/ecc/bls12-378/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-378/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bls12-378"
+	curve "github.com/consensys/gnark-crypto/ecc/bls12-378"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bls12378.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls12378.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bls12378.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bls12378.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bls12378.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bls12-378/fr/permutation/permutation.go b/ecc/bls12-378/fr/permutation/permutation.go
index 59eab17b3..e10836ec0 100644
--- a/ecc/bls12-378/fr/permutation/permutation.go
+++ b/ecc/bls12-378/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bls12-378/fr/permutation/permutation_test.go b/ecc/bls12-378/fr/permutation/permutation_test.go
index 9519e05b8..8e67b6850 100644
--- a/ecc/bls12-378/fr/permutation/permutation_test.go
+++ b/ecc/bls12-378/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-378/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bls12-378/fr/plookup/plookup_test.go b/ecc/bls12-378/fr/plookup/plookup_test.go
index 5695819ea..e9cb4eee4 100644
--- a/ecc/bls12-378/fr/plookup/plookup_test.go
+++ b/ecc/bls12-378/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bls12-378/fr/plookup/table.go b/ecc/bls12-378/fr/plookup/table.go
index 11881a885..7e1d67413 100644
--- a/ecc/bls12-378/fr/plookup/table.go
+++ b/ecc/bls12-378/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bls12-378/fr/plookup/vector.go b/ecc/bls12-378/fr/plookup/vector.go
index c8759cba4..67384cf7b 100644
--- a/ecc/bls12-378/fr/plookup/vector.go
+++ b/ecc/bls12-378/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bls12-378/g1.go b/ecc/bls12-378/g1.go
index 85e515305..1c246ca4b 100644
--- a/ecc/bls12-378/g1.go
+++ b/ecc/bls12-378/g1.go
@@ -92,6 +92,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bls12-378/g2.go b/ecc/bls12-378/g2.go
index b67b46779..61b0f209e 100644
--- a/ecc/bls12-378/g2.go
+++ b/ecc/bls12-378/g2.go
@@ -81,6 +81,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bls12-378/hash_to_g1.go b/ecc/bls12-378/hash_to_g1.go
index 46986092d..7a2b8bf9a 100644
--- a/ecc/bls12-378/hash_to_g1.go
+++ b/ecc/bls12-378/hash_to_g1.go
@@ -168,9 +168,9 @@ func g1MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve1 implements the SSWU map
+// MapToCurve1 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{15314533651602404840, 3999629397495592995, 17991228730268553058, 13253234862282888158, 4784493033884022421, 276795783356562829}
 	var sswuIsoCurveCoeffB = fp.Element{10499526804702755432, 6768914877862902950, 8287496811509120276, 9263962031121981469, 5075273437274786541, 60255618913255595}
@@ -270,7 +270,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SSWU map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	//this is in an isogenous curve
 	g1Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -289,7 +289,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	//this is in an isogenous curve
 	g1Isogeny(&res)
@@ -307,8 +307,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g1Isogeny(&Q0)
diff --git a/ecc/bls12-378/hash_to_g1_test.go b/ecc/bls12-378/hash_to_g1_test.go
index 2964a0869..74040eb56 100644
--- a/ecc/bls12-378/hash_to_g1_test.go
+++ b/ecc/bls12-378/hash_to_g1_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !isOnE1Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bls12-378/hash_to_g2.go b/ecc/bls12-378/hash_to_g2.go
index d20ff1a77..4c72d0f6f 100644
--- a/ecc/bls12-378/hash_to_g2.go
+++ b/ecc/bls12-378/hash_to_g2.go
@@ -21,7 +21,7 @@ import (
 
 // https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-4.1
 // Shallue and van de Woestijne method, works for any elliptic curve in Weierstrass curve
-func svdwMapG2(u fptower.E2) G2Affine {
+func MapToCurve2(u fptower.E2) G2Affine {
 
 	var res G2Affine
 
@@ -91,7 +91,7 @@ func svdwMapG2(u fptower.E2) G2Affine {
 // MapToG2 maps an fp.Element to a point on the curve using the Shallue and van de Woestijne map
 // https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-2.2.1
 func MapToG2(t fptower.E2) G2Affine {
-	res := svdwMapG2(t)
+	res := MapToCurve2(t)
 	res.ClearCofactor(&res)
 	return res
 }
diff --git a/ecc/bls12-378/internal/fptower/e12.go b/ecc/bls12-378/internal/fptower/e12.go
index 39adbff08..431228a08 100644
--- a/ecc/bls12-378/internal/fptower/e12.go
+++ b/ecc/bls12-378/internal/fptower/e12.go
@@ -230,15 +230,17 @@ func (z *E12) DecompressKarabina(x *E12) *E12 {
 	var one E2
 	one.SetOne()
 
-	// g3 == 0
-	if x.C1.B2.IsZero() {
+	if x.C1.B2.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.C0.B1, &x.C1.B2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.C0.B2)
 
-		// g3 != 0
-	} else {
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
+
 		// t0 = g1^2
 		t[0].Square(&x.C0.B1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -302,20 +304,24 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t0 := make([]E2, n)
 	t1 := make([]E2, n)
 	t2 := make([]E2, n)
+	zeroes := make([]bool, n)
 
 	var one E2
 	one.SetOne()
 
 	for i := 0; i < n; i++ {
-		// g3 == 0
-		if x[i].C1.B2.IsZero() {
+		if x[i].C1.B2.IsZero() /* g3 == 0 */ {
 			t0[i].Mul(&x[i].C0.B1, &x[i].C1.B2).
 				Double(&t0[i])
 			// t1 = g2
 			t1[i].Set(&x[i].C0.B2)
 
-			// g3 != 0
-		} else {
+			if t1[i].IsZero() /* g3 == g2 == 0 */ {
+				x[i].SetOne()
+				zeroes[i] = true
+				continue
+			}
+		} else /* g3 != 0 */ {
 			// t0 = g1^2
 			t0[i].Square(&x[i].C0.B1)
 			// t1 = 3 * g1^2 - 2 * g2
@@ -335,6 +341,10 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t1 = BatchInvertE2(t1) // costs 1 inverse
 
 	for i := 0; i < n; i++ {
+		if zeroes[i] {
+			continue
+		}
+
 		// z4 = g4
 		x[i].C1.B1.Mul(&t0[i], &t1[i])
 
@@ -717,7 +727,7 @@ func (z *E12) SetBytes(e []byte) error {
 func (z *E12) IsInSubGroup() bool {
 	var a, b E12
 
-	// check z^(Phi_k(p)) == 1
+	// check z^(phi_k(p)) == 1
 	a.FrobeniusSquare(z)
 	b.FrobeniusSquare(&a).Mul(&b, z)
 
diff --git a/ecc/bls12-378/marshal.go b/ecc/bls12-378/marshal.go
index 33bd800dd..bc006c35f 100644
--- a/ecc/bls12-378/marshal.go
+++ b/ecc/bls12-378/marshal.go
@@ -32,25 +32,27 @@ import (
 // To encode G1Affine and G2Affine points, we mask the most significant bits with these bits to specify without ambiguity
 // metadata needed for point (de)compression
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
 	mUncompressed         byte = 0b000 << 5
+	_                     byte = 0b001 << 5 // invalid
 	mUncompressedInfinity byte = 0b010 << 5
+	_                     byte = 0b011 << 5 // invalid
 	mCompressedSmallest   byte = 0b100 << 5
 	mCompressedLargest    byte = 0b101 << 5
 	mCompressedInfinity   byte = 0b110 << 5
+	_                     byte = 0b111 << 5 // invalid
 )
 
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bls12-378 object values to an output stream
 type Encoder struct {
@@ -103,6 +105,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -135,6 +155,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -155,6 +182,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -186,6 +220,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -245,6 +286,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -315,6 +363,12 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return
 }
 
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
 	return !((mData == mUncompressed) || (mData == mUncompressedInfinity))
@@ -398,6 +452,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -501,6 +557,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -586,6 +644,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 48
 
@@ -598,7 +675,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -682,6 +759,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG1AffineUncompressed {
@@ -854,7 +936,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -944,6 +1026,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG2AffineUncompressed {
diff --git a/ecc/bls12-378/marshal_test.go b/ecc/bls12-378/marshal_test.go
index ac3963924..89693623b 100644
--- a/ecc/bls12-378/marshal_test.go
+++ b/ecc/bls12-378/marshal_test.go
@@ -216,6 +216,26 @@ func TestIsCompressed(t *testing.T) {
 
 }
 
+func TestG1AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG1AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G1Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG1AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -309,6 +329,26 @@ func TestG1AffineSerialization(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestG2AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG2AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G2Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG2AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
diff --git a/ecc/bls12-378/pairing.go b/ecc/bls12-378/pairing.go
index 179694408..af736e67b 100644
--- a/ecc/bls12-378/pairing.go
+++ b/ecc/bls12-378/pairing.go
@@ -77,6 +77,12 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	result.FrobeniusSquare(&t[0]).
 		Mul(&result, &t[0])
 
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
 	// Hard part (up to permutation)
 	// Daiki Hayashida, Kenichiro Hayasaka and Tadanori Teruya
 	// https://eprint.iacr.org/2020/875.pdf
diff --git a/ecc/bls12-381/fr/kzg/kzg.go b/ecc/bls12-381/fr/kzg/kzg.go
index 3f5c98b03..ab879ec51 100644
--- a/ecc/bls12-381/fr/kzg/kzg.go
+++ b/ecc/bls12-381/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bls12381.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bls12381.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bls12381.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bls12381.G2Affine // [G₂, [α]G₂ ]
+	G1 bls12381.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bls12381.G1Affine, size)
+	srs.Pk.G1 = make([]bls12381.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bls12381.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bls12381.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bls12381.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bls12381.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bls12381.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bls12381.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bls12381.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bls12381.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bls12381.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bls12381.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bls12381.PairingCheck(
-		[]bls12381.G1Affine{fminusfaG1Aff, negH},
-		[]bls12381.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bls12381.G1Affine{totalG1Aff, negH},
+		[]bls12381.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bls12381.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bls12381.PairingCheck(
 		[]bls12381.G1Affine{foldedDigests, foldedQuotients},
-		[]bls12381.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bls12381.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bls12-381/fr/kzg/kzg_test.go b/ecc/bls12-381/fr/kzg/kzg_test.go
index 94b32ee58..eb72cadb3 100644
--- a/ecc/bls12-381/fr/kzg/kzg_test.go
+++ b/ecc/bls12-381/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bls12381.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bls12-381/fr/kzg/marshal.go b/ecc/bls12-381/fr/kzg/marshal.go
index 527d3ddf3..52a2e7102 100644
--- a/ecc/bls12-381/fr/kzg/marshal.go
+++ b/ecc/bls12-381/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bls12381.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bls12381.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bls12381.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bls12381.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bls12381.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bls12381.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bls12381.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bls12381.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bls12-381/fr/pedersen/pedersen.go b/ecc/bls12-381/fr/pedersen/pedersen.go
index 38cc4d32c..e9efb6008 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bls12-381"
+	curve "github.com/consensys/gnark-crypto/ecc/bls12-381"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bls12381.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bls12381.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bls12381.G1Affine
-	basisExpSigma []bls12381.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bls12381.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls12381.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bls12381.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bls12381.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bls12381.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bls12381.G1Affine, knowledgeProof bls12381.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bls12381.G1Affine, knowled
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bls12381.G1Affine, knowledgeProof bls12381.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bls12381.Pair([]bls12381.G1Affine{commitment, knowledgeProof}, []bls12381.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bls12381.G1Affine, knowledgeProof
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bls12-381/fr/pedersen/pedersen_test.go b/ecc/bls12-381/fr/pedersen/pedersen_test.go
index 111f63590..78e04273e 100644
--- a/ecc/bls12-381/fr/pedersen/pedersen_test.go
+++ b/ecc/bls12-381/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bls12-381"
+	curve "github.com/consensys/gnark-crypto/ecc/bls12-381"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bls12381.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls12381.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bls12381.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bls12381.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bls12381.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bls12-381/fr/permutation/permutation.go b/ecc/bls12-381/fr/permutation/permutation.go
index 996b48d04..79ac12e44 100644
--- a/ecc/bls12-381/fr/permutation/permutation.go
+++ b/ecc/bls12-381/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bls12-381/fr/permutation/permutation_test.go b/ecc/bls12-381/fr/permutation/permutation_test.go
index e706653d4..968772c83 100644
--- a/ecc/bls12-381/fr/permutation/permutation_test.go
+++ b/ecc/bls12-381/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bls12-381/fr/plookup/plookup_test.go b/ecc/bls12-381/fr/plookup/plookup_test.go
index 8ad930532..27627c623 100644
--- a/ecc/bls12-381/fr/plookup/plookup_test.go
+++ b/ecc/bls12-381/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bls12-381/fr/plookup/table.go b/ecc/bls12-381/fr/plookup/table.go
index 209a65d2b..3b1190776 100644
--- a/ecc/bls12-381/fr/plookup/table.go
+++ b/ecc/bls12-381/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bls12-381/fr/plookup/vector.go b/ecc/bls12-381/fr/plookup/vector.go
index 9f23921ae..0bcc48769 100644
--- a/ecc/bls12-381/fr/plookup/vector.go
+++ b/ecc/bls12-381/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bls12-381/g1.go b/ecc/bls12-381/g1.go
index 6f93fe409..fdedb8aa8 100644
--- a/ecc/bls12-381/g1.go
+++ b/ecc/bls12-381/g1.go
@@ -92,6 +92,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bls12-381/g2.go b/ecc/bls12-381/g2.go
index d30c7b34b..f54168f46 100644
--- a/ecc/bls12-381/g2.go
+++ b/ecc/bls12-381/g2.go
@@ -81,6 +81,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bls12-381/hash_to_g1.go b/ecc/bls12-381/hash_to_g1.go
index 3f57d725a..d47d1f7ec 100644
--- a/ecc/bls12-381/hash_to_g1.go
+++ b/ecc/bls12-381/hash_to_g1.go
@@ -177,9 +177,9 @@ func g1MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve1 implements the SSWU map
+// MapToCurve1 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{3415322872136444497, 9675504606121301699, 13284745414851768802, 2873609449387478652, 2897906769629812789, 1536947672689614213}
 	var sswuIsoCurveCoeffB = fp.Element{18129637713272545760, 11144507692959411567, 10108153527111632324, 9745270364868568433, 14587922135379007624, 469008097655535723}
@@ -279,7 +279,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SSWU map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	//this is in an isogenous curve
 	g1Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -298,7 +298,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	//this is in an isogenous curve
 	g1Isogeny(&res)
@@ -316,8 +316,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g1Isogeny(&Q0)
diff --git a/ecc/bls12-381/hash_to_g1_test.go b/ecc/bls12-381/hash_to_g1_test.go
index bcadce17a..9ace94ccc 100644
--- a/ecc/bls12-381/hash_to_g1_test.go
+++ b/ecc/bls12-381/hash_to_g1_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !isOnE1Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bls12-381/hash_to_g2.go b/ecc/bls12-381/hash_to_g2.go
index ace9c207a..0deb5eb7e 100644
--- a/ecc/bls12-381/hash_to_g2.go
+++ b/ecc/bls12-381/hash_to_g2.go
@@ -213,9 +213,9 @@ func g2MulByZ(z *fptower.E2, x *fptower.E2) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve2 implements the SSWU map
+// MapToCurve2 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve2(u *fptower.E2) G2Affine {
+func MapToCurve2(u *fptower.E2) G2Affine {
 
 	var sswuIsoCurveCoeffA = fptower.E2{
 		A0: fp.Element{0},
@@ -339,7 +339,7 @@ func g2Sgn0(z *fptower.E2) uint64 {
 
 // MapToG2 invokes the SSWU map, and guarantees that the result is in g2
 func MapToG2(u fptower.E2) G2Affine {
-	res := mapToCurve2(&u)
+	res := MapToCurve2(&u)
 	//this is in an isogenous curve
 	g2Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -358,7 +358,7 @@ func EncodeToG2(msg, dst []byte) (G2Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve2(&fptower.E2{
+	res = MapToCurve2(&fptower.E2{
 		A0: u[0],
 		A1: u[1],
 	})
@@ -379,11 +379,11 @@ func HashToG2(msg, dst []byte) (G2Affine, error) {
 		return G2Affine{}, err
 	}
 
-	Q0 := mapToCurve2(&fptower.E2{
+	Q0 := MapToCurve2(&fptower.E2{
 		A0: u[0],
 		A1: u[1],
 	})
-	Q1 := mapToCurve2(&fptower.E2{
+	Q1 := MapToCurve2(&fptower.E2{
 		A0: u[2+0],
 		A1: u[2+1],
 	})
diff --git a/ecc/bls12-381/hash_to_g2_test.go b/ecc/bls12-381/hash_to_g2_test.go
index b48b87ff2..1a29cd5e6 100644
--- a/ecc/bls12-381/hash_to_g2_test.go
+++ b/ecc/bls12-381/hash_to_g2_test.go
@@ -95,7 +95,7 @@ func TestMapToCurve2(t *testing.T) {
 	properties.Property("[G2] mapping output must be on curve", prop.ForAll(
 		func(a fptower.E2) bool {
 
-			g := mapToCurve2(&a)
+			g := MapToCurve2(&a)
 
 			if !isOnE2Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -118,7 +118,7 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range encodeToG2Vector.cases {
 		var u fptower.E2
 		g2CoordSetString(&u, c.u)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -126,12 +126,12 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range hashToG2Vector.cases {
 		var u fptower.E2
 		g2CoordSetString(&u, c.u0)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g2CoordSetString(&u, c.u1)
-		q = mapToCurve2(&u)
+		q = MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bls12-381/internal/fptower/e12.go b/ecc/bls12-381/internal/fptower/e12.go
index 35a43eb6d..bc6391723 100644
--- a/ecc/bls12-381/internal/fptower/e12.go
+++ b/ecc/bls12-381/internal/fptower/e12.go
@@ -230,15 +230,17 @@ func (z *E12) DecompressKarabina(x *E12) *E12 {
 	var one E2
 	one.SetOne()
 
-	// g3 == 0
-	if x.C1.B2.IsZero() {
+	if x.C1.B2.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.C0.B1, &x.C1.B2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.C0.B2)
 
-		// g3 != 0
-	} else {
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
+
 		// t0 = g1^2
 		t[0].Square(&x.C0.B1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -302,20 +304,24 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t0 := make([]E2, n)
 	t1 := make([]E2, n)
 	t2 := make([]E2, n)
+	zeroes := make([]bool, n)
 
 	var one E2
 	one.SetOne()
 
 	for i := 0; i < n; i++ {
-		// g3 == 0
-		if x[i].C1.B2.IsZero() {
+		if x[i].C1.B2.IsZero() /* g3 == 0 */ {
 			t0[i].Mul(&x[i].C0.B1, &x[i].C1.B2).
 				Double(&t0[i])
 			// t1 = g2
 			t1[i].Set(&x[i].C0.B2)
 
-			// g3 != 0
-		} else {
+			if t1[i].IsZero() /* g3 == g2 == 0 */ {
+				x[i].SetOne()
+				zeroes[i] = true
+				continue
+			}
+		} else /* g3 != 0 */ {
 			// t0 = g1^2
 			t0[i].Square(&x[i].C0.B1)
 			// t1 = 3 * g1^2 - 2 * g2
@@ -335,6 +341,10 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t1 = BatchInvertE2(t1) // costs 1 inverse
 
 	for i := 0; i < n; i++ {
+		if zeroes[i] {
+			continue
+		}
+
 		// z4 = g4
 		x[i].C1.B1.Mul(&t0[i], &t1[i])
 
@@ -717,7 +727,7 @@ func (z *E12) SetBytes(e []byte) error {
 func (z *E12) IsInSubGroup() bool {
 	var a, b E12
 
-	// check z^(Phi_k(p)) == 1
+	// check z^(phi_k(p)) == 1
 	a.FrobeniusSquare(z)
 	b.FrobeniusSquare(&a).Mul(&b, z)
 
diff --git a/ecc/bls12-381/marshal.go b/ecc/bls12-381/marshal.go
index f1efa51ff..244a1c17b 100644
--- a/ecc/bls12-381/marshal.go
+++ b/ecc/bls12-381/marshal.go
@@ -32,25 +32,27 @@ import (
 // To encode G1Affine and G2Affine points, we mask the most significant bits with these bits to specify without ambiguity
 // metadata needed for point (de)compression
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
 	mUncompressed         byte = 0b000 << 5
+	_                     byte = 0b001 << 5 // invalid
 	mUncompressedInfinity byte = 0b010 << 5
+	_                     byte = 0b011 << 5 // invalid
 	mCompressedSmallest   byte = 0b100 << 5
 	mCompressedLargest    byte = 0b101 << 5
 	mCompressedInfinity   byte = 0b110 << 5
+	_                     byte = 0b111 << 5 // invalid
 )
 
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bls12-381 object values to an output stream
 type Encoder struct {
@@ -103,6 +105,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -135,6 +155,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -155,6 +182,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -186,6 +220,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -245,6 +286,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -315,6 +363,12 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return
 }
 
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
 	return !((mData == mUncompressed) || (mData == mUncompressedInfinity))
@@ -398,6 +452,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -501,6 +557,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -586,6 +644,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 48
 
@@ -598,7 +675,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -682,6 +759,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG1AffineUncompressed {
@@ -854,7 +936,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -944,6 +1026,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG2AffineUncompressed {
diff --git a/ecc/bls12-381/marshal_test.go b/ecc/bls12-381/marshal_test.go
index d21e2910f..7080b13d7 100644
--- a/ecc/bls12-381/marshal_test.go
+++ b/ecc/bls12-381/marshal_test.go
@@ -216,6 +216,26 @@ func TestIsCompressed(t *testing.T) {
 
 }
 
+func TestG1AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG1AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G1Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG1AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -309,6 +329,26 @@ func TestG1AffineSerialization(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestG2AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG2AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G2Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG2AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
diff --git a/ecc/bls12-381/pairing.go b/ecc/bls12-381/pairing.go
index 4c2c867f8..e2c362f9b 100644
--- a/ecc/bls12-381/pairing.go
+++ b/ecc/bls12-381/pairing.go
@@ -77,6 +77,12 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	result.FrobeniusSquare(&t[0]).
 		Mul(&result, &t[0])
 
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
 	// Hard part (up to permutation)
 	// Daiki Hayashida, Kenichiro Hayasaka and Tadanori Teruya
 	// https://eprint.iacr.org/2020/875.pdf
diff --git a/ecc/bls24-315/fr/kzg/kzg.go b/ecc/bls24-315/fr/kzg/kzg.go
index 9dfbc6431..dcca454ff 100644
--- a/ecc/bls24-315/fr/kzg/kzg.go
+++ b/ecc/bls24-315/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bls24315.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bls24315.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bls24315.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bls24315.G2Affine // [G₂, [α]G₂ ]
+	G1 bls24315.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bls24315.G1Affine, size)
+	srs.Pk.G1 = make([]bls24315.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bls24315.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bls24315.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bls24315.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bls24315.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bls24315.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bls24315.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bls24315.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bls24315.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bls24315.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bls24315.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bls24315.PairingCheck(
-		[]bls24315.G1Affine{fminusfaG1Aff, negH},
-		[]bls24315.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bls24315.G1Affine{totalG1Aff, negH},
+		[]bls24315.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bls24315.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bls24315.PairingCheck(
 		[]bls24315.G1Affine{foldedDigests, foldedQuotients},
-		[]bls24315.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bls24315.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bls24-315/fr/kzg/kzg_test.go b/ecc/bls24-315/fr/kzg/kzg_test.go
index 37fd8c023..31183a618 100644
--- a/ecc/bls24-315/fr/kzg/kzg_test.go
+++ b/ecc/bls24-315/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bls24315.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bls24-315/fr/kzg/marshal.go b/ecc/bls24-315/fr/kzg/marshal.go
index 157c265a6..d6785b1d7 100644
--- a/ecc/bls24-315/fr/kzg/marshal.go
+++ b/ecc/bls24-315/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bls24315.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bls24315.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bls24315.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bls24315.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bls24315.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bls24315.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bls24315.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bls24315.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bls24-315/fr/pedersen/pedersen.go b/ecc/bls24-315/fr/pedersen/pedersen.go
index 09e19bea1..0580e8449 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bls24-315"
+	curve "github.com/consensys/gnark-crypto/ecc/bls24-315"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bls24315.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bls24315.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bls24315.G1Affine
-	basisExpSigma []bls24315.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bls24315.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls24315.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bls24315.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bls24315.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bls24315.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bls24315.G1Affine, knowledgeProof bls24315.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bls24315.G1Affine, knowled
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bls24315.G1Affine, knowledgeProof bls24315.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bls24315.Pair([]bls24315.G1Affine{commitment, knowledgeProof}, []bls24315.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bls24315.G1Affine, knowledgeProof
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bls24-315/fr/pedersen/pedersen_test.go b/ecc/bls24-315/fr/pedersen/pedersen_test.go
index 841896894..475026061 100644
--- a/ecc/bls24-315/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-315/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bls24-315"
+	curve "github.com/consensys/gnark-crypto/ecc/bls24-315"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bls24315.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls24315.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bls24315.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bls24315.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bls24315.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bls24-315/fr/permutation/permutation.go b/ecc/bls24-315/fr/permutation/permutation.go
index e7612e717..15ba2ecc3 100644
--- a/ecc/bls24-315/fr/permutation/permutation.go
+++ b/ecc/bls24-315/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bls24-315/fr/permutation/permutation_test.go b/ecc/bls24-315/fr/permutation/permutation_test.go
index 5997348fa..73de6a0c5 100644
--- a/ecc/bls24-315/fr/permutation/permutation_test.go
+++ b/ecc/bls24-315/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bls24-315/fr/plookup/plookup_test.go b/ecc/bls24-315/fr/plookup/plookup_test.go
index 321354b72..d7b70587c 100644
--- a/ecc/bls24-315/fr/plookup/plookup_test.go
+++ b/ecc/bls24-315/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bls24-315/fr/plookup/table.go b/ecc/bls24-315/fr/plookup/table.go
index d9d9f8f31..cf2cced57 100644
--- a/ecc/bls24-315/fr/plookup/table.go
+++ b/ecc/bls24-315/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bls24-315/fr/plookup/vector.go b/ecc/bls24-315/fr/plookup/vector.go
index c24632ae0..b88c6d5a6 100644
--- a/ecc/bls24-315/fr/plookup/vector.go
+++ b/ecc/bls24-315/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bls24-315/g1.go b/ecc/bls24-315/g1.go
index 762e42196..59e1e91ed 100644
--- a/ecc/bls24-315/g1.go
+++ b/ecc/bls24-315/g1.go
@@ -92,6 +92,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bls24-315/g2.go b/ecc/bls24-315/g2.go
index 266eaab42..89d1555ab 100644
--- a/ecc/bls24-315/g2.go
+++ b/ecc/bls24-315/g2.go
@@ -81,6 +81,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bls24-315/hash_to_g1.go b/ecc/bls24-315/hash_to_g1.go
index ecaa0185c..5b507ea88 100644
--- a/ecc/bls24-315/hash_to_g1.go
+++ b/ecc/bls24-315/hash_to_g1.go
@@ -168,9 +168,9 @@ func g1MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve1 implements the SSWU map
+// MapToCurve1 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{5402807948305211529, 9163880483319140034, 7646126700453841420, 11071466103913358468, 124200740526673728}
 	var sswuIsoCurveCoeffB = fp.Element{16058189711238232929, 8302337653269510588, 11411933349841587630, 8954038365926617417, 177308873523699836}
@@ -270,7 +270,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SSWU map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	//this is in an isogenous curve
 	g1Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -289,7 +289,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	//this is in an isogenous curve
 	g1Isogeny(&res)
@@ -307,8 +307,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g1Isogeny(&Q0)
diff --git a/ecc/bls24-315/hash_to_g1_test.go b/ecc/bls24-315/hash_to_g1_test.go
index d536b1a23..bdbbcf42f 100644
--- a/ecc/bls24-315/hash_to_g1_test.go
+++ b/ecc/bls24-315/hash_to_g1_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !isOnE1Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bls24-315/hash_to_g2.go b/ecc/bls24-315/hash_to_g2.go
index 2a4b37a32..df1af0d75 100644
--- a/ecc/bls24-315/hash_to_g2.go
+++ b/ecc/bls24-315/hash_to_g2.go
@@ -21,7 +21,7 @@ import (
 
 // https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-4.1
 // Shallue and van de Woestijne method, works for any elliptic curve in Weierstrass curve
-func svdwMapG2(u fptower.E4) G2Affine {
+func MapToCurve2(u fptower.E4) G2Affine {
 
 	var res G2Affine
 
@@ -98,7 +98,7 @@ func svdwMapG2(u fptower.E4) G2Affine {
 // MapToG2 maps an fp.Element to a point on the curve using the Shallue and van de Woestijne map
 // https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-2.2.1
 func MapToG2(t fptower.E4) G2Affine {
-	res := svdwMapG2(t)
+	res := MapToCurve2(t)
 	res.ClearCofactor(&res)
 	return res
 }
diff --git a/ecc/bls24-315/internal/fptower/e24.go b/ecc/bls24-315/internal/fptower/e24.go
index 888123993..053e329da 100644
--- a/ecc/bls24-315/internal/fptower/e24.go
+++ b/ecc/bls24-315/internal/fptower/e24.go
@@ -12,16 +12,15 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
 	"errors"
-	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 	"math/big"
 	"sync"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 )
 
 var bigIntPool = sync.Pool{
@@ -229,15 +228,16 @@ func (z *E24) DecompressKarabina(x *E24) *E24 {
 	var one E4
 	one.SetOne()
 
-	// g3 == 0
-	if x.D1.C0.IsZero() {
+	if x.D1.C0.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.D0.C1, &x.D1.C2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.D0.C2)
 
-		// g3 != 0
-	} else {
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
 		// t0 = g1^2
 		t[0].Square(&x.D0.C1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -744,7 +744,6 @@ func (z *E24) Bytes() (r [SizeOfGT]byte) {
 
 	buf = z.D1.C2.B1.A1.Bytes()
 	copy(r[offset:offset+sizeOfFp], buf[:])
-	offset += sizeOfFp
 
 	return
 }
@@ -803,7 +802,6 @@ func (z *E24) SetBytes(e []byte) error {
 	z.D1.C2.B1.A0.SetBytes(e[offset : offset+sizeOfFp])
 	offset += sizeOfFp
 	z.D1.C2.B1.A1.SetBytes(e[offset : offset+sizeOfFp])
-	offset += sizeOfFp
 
 	return nil
 }
@@ -812,7 +810,7 @@ func (z *E24) SetBytes(e []byte) error {
 func (z *E24) IsInSubGroup() bool {
 	var a, b E24
 
-	// check z^(Phi_k(p)) == 1
+	// check z^(phi_k(p)) == 1
 	a.FrobeniusQuad(z)
 	b.FrobeniusQuad(&a).Mul(&b, z)
 
diff --git a/ecc/bls24-315/internal/fptower/e24_test.go b/ecc/bls24-315/internal/fptower/e24_test.go
index 3d7b64712..d57ee2806 100644
--- a/ecc/bls24-315/internal/fptower/e24_test.go
+++ b/ecc/bls24-315/internal/fptower/e24_test.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
diff --git a/ecc/bls24-315/marshal.go b/ecc/bls24-315/marshal.go
index 10e20cefe..7a4ad467c 100644
--- a/ecc/bls24-315/marshal.go
+++ b/ecc/bls24-315/marshal.go
@@ -32,25 +32,27 @@ import (
 // To encode G1Affine and G2Affine points, we mask the most significant bits with these bits to specify without ambiguity
 // metadata needed for point (de)compression
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
 	mUncompressed         byte = 0b000 << 5
+	_                     byte = 0b001 << 5 // invalid
 	mUncompressedInfinity byte = 0b010 << 5
+	_                     byte = 0b011 << 5 // invalid
 	mCompressedSmallest   byte = 0b100 << 5
 	mCompressedLargest    byte = 0b101 << 5
 	mCompressedInfinity   byte = 0b110 << 5
+	_                     byte = 0b111 << 5 // invalid
 )
 
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bls24-315 object values to an output stream
 type Encoder struct {
@@ -103,6 +105,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -135,6 +155,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -155,6 +182,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -186,6 +220,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -245,6 +286,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -315,6 +363,12 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return
 }
 
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
 	return !((mData == mUncompressed) || (mData == mUncompressedInfinity))
@@ -398,6 +452,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -501,6 +557,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -586,6 +644,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 40
 
@@ -598,7 +675,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -682,6 +759,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG1AffineUncompressed {
@@ -854,7 +936,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -950,6 +1032,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG2AffineUncompressed {
diff --git a/ecc/bls24-315/marshal_test.go b/ecc/bls24-315/marshal_test.go
index a18756f96..553c5e1b3 100644
--- a/ecc/bls24-315/marshal_test.go
+++ b/ecc/bls24-315/marshal_test.go
@@ -216,6 +216,26 @@ func TestIsCompressed(t *testing.T) {
 
 }
 
+func TestG1AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG1AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G1Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG1AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -309,6 +329,26 @@ func TestG1AffineSerialization(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestG2AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG2AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G2Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG2AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
diff --git a/ecc/bls24-315/pairing.go b/ecc/bls24-315/pairing.go
index 1ef5569e1..66ae0715e 100644
--- a/ecc/bls24-315/pairing.go
+++ b/ecc/bls24-315/pairing.go
@@ -78,6 +78,12 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	result.FrobeniusQuad(&t[0]).
 		Mul(&result, &t[0])
 
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
 	// Hard part (up to permutation)
 	// Daiki Hayashida and Kenichiro Hayasaka
 	// and Tadanori Teruya
diff --git a/ecc/bls24-317/fr/kzg/kzg.go b/ecc/bls24-317/fr/kzg/kzg.go
index 39d229288..f136128ba 100644
--- a/ecc/bls24-317/fr/kzg/kzg.go
+++ b/ecc/bls24-317/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bls24317.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bls24317.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bls24317.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bls24317.G2Affine // [G₂, [α]G₂ ]
+	G1 bls24317.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bls24317.G1Affine, size)
+	srs.Pk.G1 = make([]bls24317.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bls24317.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bls24317.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bls24317.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bls24317.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bls24317.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bls24317.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bls24317.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bls24317.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bls24317.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bls24317.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bls24317.PairingCheck(
-		[]bls24317.G1Affine{fminusfaG1Aff, negH},
-		[]bls24317.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bls24317.G1Affine{totalG1Aff, negH},
+		[]bls24317.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bls24317.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bls24317.PairingCheck(
 		[]bls24317.G1Affine{foldedDigests, foldedQuotients},
-		[]bls24317.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bls24317.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bls24-317/fr/kzg/kzg_test.go b/ecc/bls24-317/fr/kzg/kzg_test.go
index 1a68e5901..079aa49ee 100644
--- a/ecc/bls24-317/fr/kzg/kzg_test.go
+++ b/ecc/bls24-317/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bls24317.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bls24-317/fr/kzg/marshal.go b/ecc/bls24-317/fr/kzg/marshal.go
index 6d508202e..54b6954de 100644
--- a/ecc/bls24-317/fr/kzg/marshal.go
+++ b/ecc/bls24-317/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bls24317.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bls24317.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bls24317.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bls24317.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bls24317.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bls24317.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bls24317.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bls24317.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bls24-317/fr/pedersen/pedersen.go b/ecc/bls24-317/fr/pedersen/pedersen.go
index 9b6777fa8..3b8fc2509 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bls24-317"
+	curve "github.com/consensys/gnark-crypto/ecc/bls24-317"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bls24317.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bls24317.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bls24317.G1Affine
-	basisExpSigma []bls24317.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bls24317.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls24317.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bls24317.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bls24317.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bls24317.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bls24317.G1Affine, knowledgeProof bls24317.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bls24317.G1Affine, knowled
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bls24317.G1Affine, knowledgeProof bls24317.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bls24317.Pair([]bls24317.G1Affine{commitment, knowledgeProof}, []bls24317.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bls24317.G1Affine, knowledgeProof
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bls24-317/fr/pedersen/pedersen_test.go b/ecc/bls24-317/fr/pedersen/pedersen_test.go
index fe0f0b48f..ee64c9aa3 100644
--- a/ecc/bls24-317/fr/pedersen/pedersen_test.go
+++ b/ecc/bls24-317/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bls24-317"
+	curve "github.com/consensys/gnark-crypto/ecc/bls24-317"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bls24317.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bls24317.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bls24317.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bls24317.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bls24317.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bls24-317/fr/permutation/permutation.go b/ecc/bls24-317/fr/permutation/permutation.go
index 7dab3039f..bf5254c91 100644
--- a/ecc/bls24-317/fr/permutation/permutation.go
+++ b/ecc/bls24-317/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bls24-317/fr/permutation/permutation_test.go b/ecc/bls24-317/fr/permutation/permutation_test.go
index 31311c3f9..575d5215a 100644
--- a/ecc/bls24-317/fr/permutation/permutation_test.go
+++ b/ecc/bls24-317/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bls24-317/fr/plookup/plookup_test.go b/ecc/bls24-317/fr/plookup/plookup_test.go
index 3bf93489b..9a98faf8b 100644
--- a/ecc/bls24-317/fr/plookup/plookup_test.go
+++ b/ecc/bls24-317/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bls24-317/fr/plookup/table.go b/ecc/bls24-317/fr/plookup/table.go
index 63a00ed47..4db32c5ef 100644
--- a/ecc/bls24-317/fr/plookup/table.go
+++ b/ecc/bls24-317/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bls24-317/fr/plookup/vector.go b/ecc/bls24-317/fr/plookup/vector.go
index 38ae00599..b3ef82389 100644
--- a/ecc/bls24-317/fr/plookup/vector.go
+++ b/ecc/bls24-317/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bls24-317/g1.go b/ecc/bls24-317/g1.go
index ce5b72561..9827f258f 100644
--- a/ecc/bls24-317/g1.go
+++ b/ecc/bls24-317/g1.go
@@ -92,6 +92,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bls24-317/g2.go b/ecc/bls24-317/g2.go
index 8a0b6c0b6..52d088f19 100644
--- a/ecc/bls24-317/g2.go
+++ b/ecc/bls24-317/g2.go
@@ -81,6 +81,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bls24-317/hash_to_g1.go b/ecc/bls24-317/hash_to_g1.go
index 5e5055043..4040b00be 100644
--- a/ecc/bls24-317/hash_to_g1.go
+++ b/ecc/bls24-317/hash_to_g1.go
@@ -145,9 +145,9 @@ func g1MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve1 implements the SSWU map
+// MapToCurve1 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{2751493217506761890, 10508083672876982400, 9568653941102734201, 1934905759174260726, 590687129635764257}
 	var sswuIsoCurveCoeffB = fp.Element{14477170886729819615, 1154054877908840441, 13400991584556574205, 3277375072715511934, 979998381373634863}
@@ -247,7 +247,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SSWU map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	//this is in an isogenous curve
 	g1Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -266,7 +266,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	//this is in an isogenous curve
 	g1Isogeny(&res)
@@ -284,8 +284,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g1Isogeny(&Q0)
diff --git a/ecc/bls24-317/hash_to_g1_test.go b/ecc/bls24-317/hash_to_g1_test.go
index 4abccacc1..e287586e0 100644
--- a/ecc/bls24-317/hash_to_g1_test.go
+++ b/ecc/bls24-317/hash_to_g1_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !isOnE1Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bls24-317/hash_to_g2.go b/ecc/bls24-317/hash_to_g2.go
index 6e2411b78..597de9ed6 100644
--- a/ecc/bls24-317/hash_to_g2.go
+++ b/ecc/bls24-317/hash_to_g2.go
@@ -21,7 +21,7 @@ import (
 
 // https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-4.1
 // Shallue and van de Woestijne method, works for any elliptic curve in Weierstrass curve
-func svdwMapG2(u fptower.E4) G2Affine {
+func MapToCurve2(u fptower.E4) G2Affine {
 
 	var res G2Affine
 
@@ -97,7 +97,7 @@ func svdwMapG2(u fptower.E4) G2Affine {
 // MapToG2 maps an fp.Element to a point on the curve using the Shallue and van de Woestijne map
 // https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-2.2.1
 func MapToG2(t fptower.E4) G2Affine {
-	res := svdwMapG2(t)
+	res := MapToCurve2(t)
 	res.ClearCofactor(&res)
 	return res
 }
diff --git a/ecc/bls24-317/internal/fptower/asm.go b/ecc/bls24-317/internal/fptower/asm.go
index 0ec192019..ba19dae3e 100644
--- a/ecc/bls24-317/internal/fptower/asm.go
+++ b/ecc/bls24-317/internal/fptower/asm.go
@@ -15,8 +15,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import "golang.org/x/sys/cpu"
diff --git a/ecc/bls24-317/internal/fptower/asm_noadx.go b/ecc/bls24-317/internal/fptower/asm_noadx.go
index 6a09c11c4..5cfde1587 100644
--- a/ecc/bls24-317/internal/fptower/asm_noadx.go
+++ b/ecc/bls24-317/internal/fptower/asm_noadx.go
@@ -15,8 +15,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 // note: this is needed for test purposes, as dynamically changing supportAdx doesn't flag
diff --git a/ecc/bls24-317/internal/fptower/e24.go b/ecc/bls24-317/internal/fptower/e24.go
index a8d403b6b..dc9dc25b6 100644
--- a/ecc/bls24-317/internal/fptower/e24.go
+++ b/ecc/bls24-317/internal/fptower/e24.go
@@ -12,16 +12,15 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
 	"errors"
-	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 	"math/big"
 	"sync"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 )
 
 var bigIntPool = sync.Pool{
@@ -229,15 +228,16 @@ func (z *E24) DecompressKarabina(x *E24) *E24 {
 	var one E4
 	one.SetOne()
 
-	// g3 == 0
-	if x.D1.C0.IsZero() {
+	if x.D1.C0.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.D0.C1, &x.D1.C2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.D0.C2)
 
-		// g3 != 0
-	} else {
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
 		// t0 = g1^2
 		t[0].Square(&x.D0.C1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -278,84 +278,6 @@ func (z *E24) DecompressKarabina(x *E24) *E24 {
 	return z
 }
 
-// BatchDecompressKarabina multiple Karabina's cyclotomic square results
-// if g3 != 0
-//
-//	g4 = (E * g5^2 + 3 * g1^2 - 2 * g2)/4g3
-//
-// if g3 == 0
-//
-//	g4 = 2g1g5/g2
-//
-// if g3=g2=0 then g4=g5=g1=0 and g0=1 (x=1)
-// Theorem 3.1 is well-defined for all x in Gϕₙ\{1}
-//
-// Divisions by 4g3 or g2 is batched using Montgomery batch inverse
-func BatchDecompressKarabina(x []E24) []E24 {
-
-	n := len(x)
-	if n == 0 {
-		return x
-	}
-
-	t0 := make([]E4, n)
-	t1 := make([]E4, n)
-	t2 := make([]E4, n)
-
-	var one E4
-	one.SetOne()
-
-	for i := 0; i < n; i++ {
-		// g3 == 0
-		if x[i].D1.C0.IsZero() {
-			t0[i].Mul(&x[i].D0.C1, &x[i].D1.C2).
-				Double(&t0[i])
-			// t1 = g2
-			t1[i].Set(&x[i].D0.C2)
-
-			// g3 != 0
-		} else {
-			// t0 = g1^2
-			t0[i].Square(&x[i].D0.C1)
-			// t1 = 3 * g1^2 - 2 * g2
-			t1[i].Sub(&t0[i], &x[i].D0.C2).
-				Double(&t1[i]).
-				Add(&t1[i], &t0[i])
-			// t0 = E * g5^2 + t1
-			t2[i].Square(&x[i].D1.C2)
-			t0[i].MulByNonResidue(&t2[i]).
-				Add(&t0[i], &t1[i])
-			// t1 = 4 * g3
-			t1[i].Double(&x[i].D1.C0).
-				Double(&t1[i])
-		}
-	}
-
-	t1 = BatchInvertE4(t1) // costs 1 inverse
-
-	for i := 0; i < n; i++ {
-		// z4 = g4
-		x[i].D1.C1.Mul(&t0[i], &t1[i])
-
-		// t1 = g2 * g1
-		t1[i].Mul(&x[i].D0.C2, &x[i].D0.C1)
-		// t2 = 2 * g4² - 3 * g2 * g1
-		t2[i].Square(&x[i].D1.C1)
-		t2[i].Sub(&t2[i], &t1[i])
-		t2[i].Double(&t2[i])
-		t2[i].Sub(&t2[i], &t1[i])
-
-		// t1 = g3 * g5 (g3s can be 0s)
-		t1[i].Mul(&x[i].D1.C0, &x[i].D1.C2)
-		// z0 = E * (2 * g4² + g3 * g5 - 3 * g2 * g1) + 1
-		t2[i].Add(&t2[i], &t1[i])
-		x[i].D0.C0.MulByNonResidue(&t2[i]).
-			Add(&x[i].D0.C0, &one)
-	}
-
-	return x
-}
-
 // Granger-Scott's cyclotomic square
 // https://eprint.iacr.org/2009/565.pdf, 3.2
 func (z *E24) CyclotomicSquare(x *E24) *E24 {
@@ -744,7 +666,6 @@ func (z *E24) Bytes() (r [SizeOfGT]byte) {
 
 	buf = z.D1.C2.B1.A1.Bytes()
 	copy(r[offset:offset+sizeOfFp], buf[:])
-	offset += sizeOfFp
 
 	return
 }
@@ -803,7 +724,6 @@ func (z *E24) SetBytes(e []byte) error {
 	z.D1.C2.B1.A0.SetBytes(e[offset : offset+sizeOfFp])
 	offset += sizeOfFp
 	z.D1.C2.B1.A1.SetBytes(e[offset : offset+sizeOfFp])
-	offset += sizeOfFp
 
 	return nil
 }
@@ -812,7 +732,7 @@ func (z *E24) SetBytes(e []byte) error {
 func (z *E24) IsInSubGroup() bool {
 	var a, b E24
 
-	// check z^(Phi_k(p)) == 1
+	// check z^(phi_k(p)) == 1
 	a.FrobeniusQuad(z)
 	b.FrobeniusQuad(&a).Mul(&b, z)
 
diff --git a/ecc/bls24-317/internal/fptower/e24_test.go b/ecc/bls24-317/internal/fptower/e24_test.go
index 770201b5d..3d36a2142 100644
--- a/ecc/bls24-317/internal/fptower/e24_test.go
+++ b/ecc/bls24-317/internal/fptower/e24_test.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
@@ -398,40 +396,6 @@ func TestE24Ops(t *testing.T) {
 		genA,
 	))
 
-	properties.Property("[BLS24-317] batch decompress and individual decompress (Karabina) should be the same", prop.ForAll(
-		func(a *E24) bool {
-			var _a, b E24
-			_a.SetOne().Double(&_a)
-
-			// put a and _a in the cyclotomic subgroup
-			// a (g3 !=0 probably)
-			b.Conjugate(a)
-			a.Inverse(a)
-			b.Mul(&b, a)
-			a.FrobeniusQuad(&b).Mul(a, &b)
-			// _a (g3 == 0)
-			b.Conjugate(&_a)
-			_a.Inverse(&_a)
-			b.Mul(&b, &_a)
-			_a.FrobeniusQuad(&b).Mul(&_a, &b)
-
-			var a2, a4, a17 E24
-			a2.Set(&_a)
-			a4.Set(a)
-			a17.Set(a)
-			a2.nSquareCompressed(2) // case g3 == 0
-			a4.nSquareCompressed(4)
-			a17.nSquareCompressed(17)
-			batch := BatchDecompressKarabina([]E24{a2, a4, a17})
-			a2.DecompressKarabina(&a2)
-			a4.DecompressKarabina(&a4)
-			a17.DecompressKarabina(&a17)
-
-			return a2.Equal(&batch[0]) && a4.Equal(&batch[1]) && a17.Equal(&batch[2])
-		},
-		genA,
-	))
-
 	properties.Property("[BLS24-315] Exp and CyclotomicExp results must be the same in the cyclotomic subgroup", prop.ForAll(
 		func(a *E24, e fp.Element) bool {
 			var b, c, d E24
diff --git a/ecc/bls24-317/internal/fptower/e2_amd64.go b/ecc/bls24-317/internal/fptower/e2_amd64.go
index 7145007fa..15488b613 100644
--- a/ecc/bls24-317/internal/fptower/e2_amd64.go
+++ b/ecc/bls24-317/internal/fptower/e2_amd64.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 //go:noescape
diff --git a/ecc/bls24-317/internal/fptower/e2_fallback.go b/ecc/bls24-317/internal/fptower/e2_fallback.go
index 0ce4d8333..3e9886c87 100644
--- a/ecc/bls24-317/internal/fptower/e2_fallback.go
+++ b/ecc/bls24-317/internal/fptower/e2_fallback.go
@@ -15,8 +15,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 func addE2(z, x, y *E2) {
diff --git a/ecc/bls24-317/internal/fptower/e2_test.go b/ecc/bls24-317/internal/fptower/e2_test.go
index 69a1ec9e6..c68d3f184 100644
--- a/ecc/bls24-317/internal/fptower/e2_test.go
+++ b/ecc/bls24-317/internal/fptower/e2_test.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
diff --git a/ecc/bls24-317/marshal.go b/ecc/bls24-317/marshal.go
index d353ba8e3..9c9b662c9 100644
--- a/ecc/bls24-317/marshal.go
+++ b/ecc/bls24-317/marshal.go
@@ -32,25 +32,27 @@ import (
 // To encode G1Affine and G2Affine points, we mask the most significant bits with these bits to specify without ambiguity
 // metadata needed for point (de)compression
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
 	mUncompressed         byte = 0b000 << 5
+	_                     byte = 0b001 << 5 // invalid
 	mUncompressedInfinity byte = 0b010 << 5
+	_                     byte = 0b011 << 5 // invalid
 	mCompressedSmallest   byte = 0b100 << 5
 	mCompressedLargest    byte = 0b101 << 5
 	mCompressedInfinity   byte = 0b110 << 5
+	_                     byte = 0b111 << 5 // invalid
 )
 
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bls24-317 object values to an output stream
 type Encoder struct {
@@ -103,6 +105,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -135,6 +155,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -155,6 +182,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -186,6 +220,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -245,6 +286,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -315,6 +363,12 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return
 }
 
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
 	return !((mData == mUncompressed) || (mData == mUncompressedInfinity))
@@ -398,6 +452,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -501,6 +557,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -586,6 +644,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 40
 
@@ -598,7 +675,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -682,6 +759,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG1AffineUncompressed {
@@ -854,7 +936,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -950,6 +1032,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG2AffineUncompressed {
diff --git a/ecc/bls24-317/marshal_test.go b/ecc/bls24-317/marshal_test.go
index 97874cb5b..98eb09e68 100644
--- a/ecc/bls24-317/marshal_test.go
+++ b/ecc/bls24-317/marshal_test.go
@@ -216,6 +216,26 @@ func TestIsCompressed(t *testing.T) {
 
 }
 
+func TestG1AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG1AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G1Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG1AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -309,6 +329,26 @@ func TestG1AffineSerialization(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestG2AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG2AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G2Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG2AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
diff --git a/ecc/bls24-317/pairing.go b/ecc/bls24-317/pairing.go
index c82e7e63f..fe28317a7 100644
--- a/ecc/bls24-317/pairing.go
+++ b/ecc/bls24-317/pairing.go
@@ -78,7 +78,13 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	result.FrobeniusQuad(&t[0]).
 		Mul(&result, &t[0])
 
-	// hard part (up to permutation)
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
+	// Hard part (up to permutation)
 	// Daiki Hayashida and Kenichiro Hayasaka
 	// and Tadanori Teruya
 	// https://eprint.iacr.org/2020/875.pdf
diff --git a/ecc/bn254/ecdsa/ecdsa.go b/ecc/bn254/ecdsa/ecdsa.go
index 9bd86a847..9ea97fe71 100644
--- a/ecc/bn254/ecdsa/ecdsa.go
+++ b/ecc/bn254/ecdsa/ecdsa.go
@@ -140,20 +140,14 @@ func RecoverP(v uint, r *big.Int) (*bn254.G1Affine, error) {
 	if y.ModSqrt(y, fp.Modulus()) == nil {
 		return nil, errors.New("no square root")
 	}
-	// y2 is -y
-	y2 := new(big.Int).Sub(fp.Modulus(), y)
-	// if yChoice == 0, return min(y, y2), else max(y, y2)
-	if (y.Cmp(y2) < 0) == (yChoice == 0) {
-		return &bn254.G1Affine{
-			X: *new(fp.Element).SetBigInt(x),
-			Y: *new(fp.Element).SetBigInt(y),
-		}, nil
-	} else {
-		return &bn254.G1Affine{
-			X: *new(fp.Element).SetBigInt(x),
-			Y: *new(fp.Element).SetBigInt(y2),
-		}, nil
+	// check that y has same oddity as defined by v
+	if y.Bit(0) != yChoice {
+		y = y.Sub(fp.Modulus(), y)
 	}
+	return &bn254.G1Affine{
+		X: *new(fp.Element).SetBigInt(x),
+		Y: *new(fp.Element).SetBigInt(y),
+	}, nil
 }
 
 type zr struct{}
@@ -241,8 +235,6 @@ func (privKey *PrivateKey) Public() signature.PublicKey {
 //
 // SEC 1, Version 2.0, Section 4.1.3
 func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v uint, r, s *big.Int, err error) {
-	halfp := new(big.Int).Sub(fp.Modulus(), big.NewInt(1))
-	halfp.Div(halfp, big.NewInt(2))
 	r, s = new(big.Int), new(big.Int)
 
 	scalar, kInv := new(big.Int), new(big.Int)
@@ -265,10 +257,8 @@ func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v ui
 			P.X.BigInt(r)
 			// set how many times we overflow the scalar field
 			v |= (uint(new(big.Int).Div(r, order).Uint64())) << 1
-			// set if y is small or big
-			if P.Y.BigInt(new(big.Int)).Cmp(halfp) >= 0 {
-				v |= 1
-			}
+			// set if y is even or odd
+			v |= P.Y.BigInt(new(big.Int)).Bit(0)
 
 			r.Mod(r, order)
 			if r.Sign() != 0 {
diff --git a/ecc/bn254/ecdsa/marshal.go b/ecc/bn254/ecdsa/marshal.go
index 5561e6e0b..1aecbaaa9 100644
--- a/ecc/bn254/ecdsa/marshal.go
+++ b/ecc/bn254/ecdsa/marshal.go
@@ -18,6 +18,7 @@ package ecdsa
 
 import (
 	"crypto/subtle"
+	"errors"
 	"io"
 	"math/big"
 
@@ -61,6 +62,12 @@ func (pk *PublicKey) SetBytes(buf []byte) (int, error) {
 // methods sets the current public key to the recovered value. Otherwise returns
 // error and leaves current public key unchanged.
 func (pk *PublicKey) RecoverFrom(msg []byte, v uint, r, s *big.Int) error {
+	if s.Cmp(fr.Modulus()) >= 0 {
+		return errors.New("s is larger than modulus")
+	}
+	if s.Cmp(big.NewInt(0)) <= 0 {
+		return errors.New("s is negative")
+	}
 	P, err := RecoverP(v, r)
 	if err != nil {
 		return err
diff --git a/ecc/bn254/fr/kzg/kzg.go b/ecc/bn254/fr/kzg/kzg.go
index 3a90e10fd..b53097d64 100644
--- a/ecc/bn254/fr/kzg/kzg.go
+++ b/ecc/bn254/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bn254.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bn254.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bn254.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bn254.G2Affine // [G₂, [α]G₂ ]
+	G1 bn254.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bn254.G1Affine, size)
+	srs.Pk.G1 = make([]bn254.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bn254.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bn254.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bn254.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bn254.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bn254.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bn254.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bn254.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bn254.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bn254.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bn254.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bn254.PairingCheck(
-		[]bn254.G1Affine{fminusfaG1Aff, negH},
-		[]bn254.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bn254.G1Affine{totalG1Aff, negH},
+		[]bn254.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bn254.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bn254.PairingCheck(
 		[]bn254.G1Affine{foldedDigests, foldedQuotients},
-		[]bn254.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bn254.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bn254/fr/kzg/kzg_test.go b/ecc/bn254/fr/kzg/kzg_test.go
index bf78f0d71..e571341ae 100644
--- a/ecc/bn254/fr/kzg/kzg_test.go
+++ b/ecc/bn254/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bn254.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bn254/fr/kzg/marshal.go b/ecc/bn254/fr/kzg/marshal.go
index 9b0bb9bf3..5dc2f317b 100644
--- a/ecc/bn254/fr/kzg/marshal.go
+++ b/ecc/bn254/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bn254.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bn254.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bn254.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bn254.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bn254.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bn254.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bn254.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bn254.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bn254/fr/pedersen/pedersen.go b/ecc/bn254/fr/pedersen/pedersen.go
index 475644705..b7f60bf2e 100644
--- a/ecc/bn254/fr/pedersen/pedersen.go
+++ b/ecc/bn254/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bn254"
+	curve "github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bn254.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bn254.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bn254.G1Affine
-	basisExpSigma []bn254.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bn254.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bn254.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bn254.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bn254.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bn254.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bn254.G1Affine, knowledgeProof bn254.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bn254.G1Affine, knowledgeP
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bn254.G1Affine, knowledgeProof bn254.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bn254.Pair([]bn254.G1Affine{commitment, knowledgeProof}, []bn254.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bn254.G1Affine, knowledgeProof bn2
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bn254/fr/pedersen/pedersen_test.go b/ecc/bn254/fr/pedersen/pedersen_test.go
index eac9cebe6..14fa00d83 100644
--- a/ecc/bn254/fr/pedersen/pedersen_test.go
+++ b/ecc/bn254/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bn254"
+	curve "github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bn254.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bn254.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bn254.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bn254.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bn254.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bn254/fr/permutation/permutation.go b/ecc/bn254/fr/permutation/permutation.go
index c5f96ea8e..37a42f524 100644
--- a/ecc/bn254/fr/permutation/permutation.go
+++ b/ecc/bn254/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bn254/fr/permutation/permutation_test.go b/ecc/bn254/fr/permutation/permutation_test.go
index 00699fa6c..d8615cd51 100644
--- a/ecc/bn254/fr/permutation/permutation_test.go
+++ b/ecc/bn254/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bn254/fr/plookup/plookup_test.go b/ecc/bn254/fr/plookup/plookup_test.go
index cea61ec3b..918a0d8b2 100644
--- a/ecc/bn254/fr/plookup/plookup_test.go
+++ b/ecc/bn254/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bn254/fr/plookup/table.go b/ecc/bn254/fr/plookup/table.go
index 2e2bc5b2c..4f110699a 100644
--- a/ecc/bn254/fr/plookup/table.go
+++ b/ecc/bn254/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bn254/fr/plookup/vector.go b/ecc/bn254/fr/plookup/vector.go
index 0971c0470..30179a31d 100644
--- a/ecc/bn254/fr/plookup/vector.go
+++ b/ecc/bn254/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bn254/fr/sis/sis.go b/ecc/bn254/fr/sis/sis.go
index 79114f23c..411db7887 100644
--- a/ecc/bn254/fr/sis/sis.go
+++ b/ecc/bn254/fr/sis/sis.go
@@ -91,7 +91,16 @@ func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*R
 	// capacity == [degree * n * logTwoBound] / 8
 	// n == (capacity*8)/(degree*logTwoBound)
 
-	n := capacity * 8 / logTwoBound // number of coefficients
+	// First n <- #limbs to represent a single field element
+	n := (fr.Bytes * 8) / logTwoBound
+	if n*logTwoBound < fr.Bytes*8 {
+		n++
+	}
+
+	// Then multiply by the number of field elements
+	n *= maxNbElementsToHash
+
+	// And divide (+ ceil) to get the number of polynomials
 	if n%degree == 0 {
 		n /= degree
 	} else {
@@ -160,53 +169,11 @@ func (r *RSis) Sum(b []byte) []byte {
 	}
 
 	// clear the buffers of the instance.
-	defer func() {
-		r.bufMValues.ClearAll()
-		for i := 0; i < len(r.bufM); i++ {
-			r.bufM[i].SetZero()
-		}
-		for i := 0; i < len(r.bufRes); i++ {
-			r.bufRes[i].SetZero()
-		}
-	}()
-
-	// bitwise decomposition of the buffer, in order to build m (the vector to hash)
-	// as a list of polynomials, whose coefficients are less than r.B bits long.
-	// Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this:
-	// 10111110 00001111. BitAt(0)=1 (=leftmost bit), bitAt(1)=0 (=second leftmost bit), etc.
-	nbBits := len(buf) * 8
-	bitAt := func(i int) uint8 {
-		k := i / 8
-		if k >= len(buf) {
-			return 0
-		}
-		b := buf[k]
-		j := i % 8
-		return b >> (7 - j) & 1
-	}
+	defer r.cleanupBuffers()
 
-	// now we can construct m. The input to hash consists of the polynomials
-	// m[k*r.Degree:(k+1)*r.Degree]
 	m := r.bufM
-
-	// mark blocks m[i*r.Degree : (i+1)*r.Degree] != [0...0]
 	mValues := r.bufMValues
-
-	// we process the input buffer by blocks of r.LogTwoBound bits
-	// each of these block (<< 64bits) are interpreted as a coefficient
-	mPos := 0
-	for i := 0; i < nbBits; mPos++ {
-		for j := 0; j < r.LogTwoBound; j++ {
-			// r.LogTwoBound < 64; we just use the first word of our element here,
-			// and set the bits from LSB to MSB.
-			m[mPos][0] |= uint64(bitAt(i) << j)
-			i++
-		}
-		if m[mPos][0] == 0 {
-			continue
-		}
-		mValues.Set(uint(mPos / r.Degree))
-	}
+	limbDecomposeBytes(buf, m, r.LogTwoBound, r.Degree, mValues)
 
 	// we can hash now.
 	res := r.bufRes
@@ -312,3 +279,93 @@ func mulModAcc(res []fr.Element, pLagrangeCosetBitReversed, qLagrangeCosetBitRev
 		res[i].Add(&res[i], &t)
 	}
 }
+
+// Returns a clone of the RSis parameters with a fresh and empty buffer. Does not
+// mutate the current instance. The keys and the public parameters of the SIS
+// instance are not deep-copied. It is useful when we want to hash in parallel.
+// Otherwise, we would have to generate an entire RSis for each thread.
+func (r *RSis) CopyWithFreshBuffer() RSis {
+	res := *r
+	res.buffer = bytes.Buffer{}
+	return res
+}
+
+// Cleanup the buffers of the RSis instance
+func (r *RSis) cleanupBuffers() {
+	r.bufMValues.ClearAll()
+	for i := 0; i < len(r.bufM); i++ {
+		r.bufM[i].SetZero()
+	}
+	for i := 0; i < len(r.bufRes); i++ {
+		r.bufRes[i].SetZero()
+	}
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is reprented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func LimbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound int) {
+	limbDecomposeBytes(buf, m, logTwoBound, 0, nil)
+}
+
+// Split an slice of bytes representing an array of serialized field element in
+// big-endian form into an array of limbs representing the same field elements
+// in little-endian form. Namely, if our field is reprented with 64 bits and we
+// have the following field element 0x0123456789abcdef (0 being the most significant
+// character and and f being the least significant one) and our log norm bound is
+// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e,
+// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. mValues is
+// an optional bitSet. If provided, it must be empty. The function will set bit "i"
+// to indicate the that i-th SIS input polynomial should be non-zero. Recall, that a
+// SIS polynomial corresponds to a chunk of limbs of size `degree`. Additionally,
+// we have the guarantee that 2 bits contributing to different field elements cannot
+// be part of the same limb.
+func limbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound, degree int, mValues *bitset.BitSet) {
+
+	// bitwise decomposition of the buffer, in order to build m (the vector to hash)
+	// as a list of polynomials, whose coefficients are less than r.B bits long.
+	// Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this:
+	// 10111110 00001111. BitAt(0)=1 (=leftmost bit), bitAt(1)=0 (=second leftmost bit), etc.
+	nbBits := len(buf) * 8
+	bitAt := func(i int) uint8 {
+		k := i / 8
+		if k >= len(buf) {
+			return 0
+		}
+		b := buf[k]
+		j := i % 8
+		return b >> (7 - j) & 1
+	}
+
+	// we process the input buffer by blocks of r.LogTwoBound bits
+	// each of these block (<< 64bits) are interpreted as a coefficient
+	mPos := 0
+	for fieldStart := 0; fieldStart < nbBits; {
+		for bitInField := 0; bitInField < fr.Bytes*8; {
+
+			j := bitInField % logTwoBound
+
+			// r.LogTwoBound < 64; we just use the first word of our element here,
+			// and set the bits from LSB to MSB.
+			at := fieldStart + fr.Bytes*8 - bitInField - 1
+			m[mPos][0] |= uint64(bitAt(at) << j)
+			bitInField++
+
+			// Check if mPos is zero and mark as non-zero in the bitset if not
+			if m[mPos][0] > 0 && mValues != nil {
+				mValues.Set(uint(mPos / degree))
+			}
+
+			if j == logTwoBound-1 || bitInField == fr.Bytes*8 {
+				mPos++
+			}
+		}
+		fieldStart += fr.Bytes * 8
+	}
+}
diff --git a/ecc/bn254/fr/sis/sis.sage b/ecc/bn254/fr/sis/sis.sage
index 48e438ba4..29fe873ca 100644
--- a/ecc/bn254/fr/sis/sis.sage
+++ b/ecc/bn254/fr/sis/sis.sage
@@ -6,6 +6,7 @@ import json
 # BN254 Fr
 r = 21888242871839275222246405745257275088548364400416034343698204186575808495617
 frByteSize = 32
+countToDeath = int(5)
 gfr = GF(r)
 Fr = GF(r)
 Fr.<x> = Fr[]
@@ -78,16 +79,37 @@ def splitCoeffs(b, logTwoBound):
 
     Returns:
         an array of coeffs, each coeff being the i-th chunk of logTwoBounds bits of b.
+        The coeffs are formed as follow. The input byte string is implicitly parsed as
+        a slice of field elements of 32 bytes each in bigendian-natural form. the outputs
+        are in a little-endian form. That is, each chunk of size 256 / logTwoBounds of the
+        output can be seen as a polynomial, such that, when evaluated at 2 we get the original
+        field element.
     """
     nbBits = len(b)*8
     res = [] 
     i = 0
-    while i < nbBits:
+
+    if len(b) % frByteSize != 0:
+        exit("the length of b should divide the field size")
+
+    # The number of fields that we are parsing. In case we have that
+    # logTwoBound does not divide the number of bits to represent a
+    # field element, we do not merge them.
+    nbField = len(b) / 32
+    nbBitsInField = int(frByteSize * 8)
+    
+    for fieldID in range(nbField):
+        fieldStart = fieldID * 256
         e = 0
-        for j in range(logTwoBound):
-            e += bitAt(i, b) << j
-            i += 1
-        res.append(e)
+        for bitInField in range(nbBitsInField):
+            j = bitInField % logTwoBound
+            at = fieldStart + nbBitsInField - 1 - bitInField
+            e |= bitAt(at, b) << j 
+            # Switch to a new limb
+            if j == logTwoBound - 1 or bitInField == frByteSize * 8 - 1:
+                res.append(e)
+                e = 0
+
     # careful Montgomery constant...
     return [Fr(e)*rr**-1 for e in res]
 
diff --git a/ecc/bn254/fr/sis/sis_test.go b/ecc/bn254/fr/sis/sis_test.go
index ed08ad407..6a9432d4e 100644
--- a/ecc/bn254/fr/sis/sis_test.go
+++ b/ecc/bn254/fr/sis/sis_test.go
@@ -69,7 +69,7 @@ func TestReference(t *testing.T) {
 	err = json.Unmarshal(data, &testCases)
 	assert.NoError(err, "reading test cases failed")
 
-	for _, testCase := range testCases.Entries {
+	for testCaseID, testCase := range testCases.Entries {
 		// create the SIS instance
 		sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash)
 		assert.NoError(err)
@@ -88,7 +88,11 @@ func TestReference(t *testing.T) {
 					assert.True(e.IsZero(), "mismatch between reference test and computed value")
 				}
 			} else {
-				assert.EqualValues(testCase.Expected[i], got, "mismatch between reference test and computed value")
+				assert.EqualValues(
+					testCase.Expected[i], got,
+					"mismatch between reference test and computed value (testcase %v - input n° %v)",
+					testCaseID, i,
+				)
 			}
 
 			// ensure max nb elements to hash has no incidence on result.
@@ -155,6 +159,73 @@ func TestMulMod(t *testing.T) {
 
 }
 
+// Test the fact that the limb decomposition allows obtaining the original
+// field element by evaluating the polynomial whose the coeffiients are the
+// limbs.
+func TestLimbDecomposition(t *testing.T) {
+
+	// Skipping the test for 32 bits
+	if bits.UintSize == 32 {
+		t.Skip("skipping this test in 32bit.")
+	}
+
+	sis, _ := NewRSis(0, 4, 4, 3)
+
+	testcases := []fr.Vector{
+		{fr.One()},
+		{fr.NewElement(2)},
+		{fr.NewElement(1 << 32), fr.NewElement(2), fr.NewElement(1)},
+	}
+
+	for _, testcase := range testcases {
+
+		// clean the sis hasher
+		sis.bufMValues.ClearAll()
+		for i := 0; i < len(sis.bufM); i++ {
+			sis.bufM[i].SetZero()
+		}
+		for i := 0; i < len(sis.bufRes); i++ {
+			sis.bufRes[i].SetZero()
+		}
+
+		buf := bytes.Buffer{}
+		for _, x := range testcase {
+			xBytes := x.Bytes()
+			buf.Write(xBytes[:])
+		}
+		limbDecomposeBytes(buf.Bytes(), sis.bufM, sis.LogTwoBound, sis.Degree, sis.bufMValues)
+
+		// Just to test, this does not return panic
+		dummyBuffer := make(fr.Vector, 192)
+		LimbDecomposeBytes(buf.Bytes(), dummyBuffer, sis.LogTwoBound)
+
+		// b is a field element representing the max norm bound
+		// used for limb splitting the input field elements.
+		b := fr.NewElement(1 << sis.LogTwoBound)
+		numLimbsPerField := fr.Bytes * 8 / sis.LogTwoBound
+
+		// Compute r (corresponds to the Montgommery constant)
+		var r fr.Element
+		r.SetString("6350874878119819312338956282401532410528162663560392320966563075034087161851")
+
+		// Attempt to recompose the entry #i in the test-case
+		for i := range testcase {
+			// allegedly corresponds to the limbs of the entry i
+			subRes := sis.bufM[i*numLimbsPerField : (i+1)*numLimbsPerField]
+
+			// performs a Horner evaluation of subres by b
+			var y fr.Element
+			for j := numLimbsPerField - 1; j >= 0; j-- {
+				y.Mul(&y, &b)
+				y.Add(&y, &subRes[j])
+			}
+
+			y.Mul(&y, &r)
+			require.Equal(t, testcase[i].String(), y.String(), "the subRes was %v", subRes)
+		}
+	}
+}
+
 func makeKeyDeterminitic(t *testing.T, sis *RSis, _seed int64) {
 	t.Helper()
 	// generate the key deterministically, the same way
diff --git a/ecc/bn254/fr/sis/test_cases.json b/ecc/bn254/fr/sis/test_cases.json
index d9670587a..0c510be29 100644
--- a/ecc/bn254/fr/sis/test_cases.json
+++ b/ecc/bn254/fr/sis/test_cases.json
@@ -41,67 +41,67 @@
         ],
         [],
         [
-            "0x1953dbbb634990faadd67e97e5e6c8e3cbabdfd3f7ed8ca5040715fe43bbe68"
+            "0x209380554d9bfcc80d188d662c2a4770308a5f2e27aa6e8ceeb2a53c6c0173d1"
         ],
         [
-            "0x1190505c2f7a21b542aa8f126dc496c4e1298a82523e3ff138b55b48410112de",
-            "0x1128a3e193e09b54c3cde5782ff1a25e23282d25081b934c87a8795df7d4da9a"
+            "0x13dbb9f2161c4aa4a98018373a516327fbeaec0895ae261e28638d70b542d2d4",
+            "0x21e56ded404a8204175893db3b661b30df2be2d1df2973cda367303354d09541"
         ],
         [
-            "0x1f9bc9c4c9def284975f15edc5f92c676a9b1b69028dfd28c04e6d8befd2db97",
-            "0xadf5554096830c3ea0a19bf456cceb527efeacdf084ecb6d67ec83b28896af0",
-            "0x2e9148ed36601088250070eb97bca6fe4e28636f48afebf4f091384b3263a529"
+            "0x251f07678b99d4e88deeb42002e54cc927294021dff580ed0d3480d1e8f2e471",
+            "0x24aa770fdcac7e2fd7dbd66ec107ab99bbf9cf61effaf03b7cc12e9fe8d348f",
+            "0x2941968b1a6bac3effc83e6b07a95bed3355ce4d004821fe58859f8e711ce05e"
         ],
         [
-            "0x2ba8b06b43e2760ba1632e6a9c49478e8340198ba39ee704ad342a2d6d7017fb",
-            "0x29b5e27571aa73fcb82be64540cf064c27849f1f9d7b44b8d42288a48938d3b2",
-            "0x20fbaaf9b529196b0ed6611aada418edfa43e4f3d183ccb61838e6e967ed993b",
-            "0x8b691cc078b5fa8ff09a016b9d6640f18defabc164d6871283460a4c6b2408e"
+            "0x262b4378376d2335d5642f991fb4b3bf394ab142fbf077a1a3d60fce27cf75e9",
+            "0x2cab7ad173900cdc2c6b6733cff2ce5a3ff52085c182146cdb65ac04fb83d819",
+            "0x168e14f1b9131dc97d4a40824e9f5c2d59a24d754ebc84945dddf186cf79c7d5",
+            "0x2693046c52d1a8f7fa801d98fda8c7307364747108cae5a345426040bd6a2dc2"
         ],
         [
-            "0xd3599652f6bc068fd8603592e23868fef5a016bf69d73338154fd9fe76ff731",
-            "0x22971883de8edb4e4fb4f466c487c1788f66cac767c9d21a6d40886cc5c87c33",
-            "0x19aec750c3a061724e982edf92e606465ac6cc93faa2e427b9b9acb58831d5fe",
-            "0x25fcb8106463fe82451bf05fef2e50e3af9cbec0d8f84b319ee77da37f776f48",
-            "0x305d195021ed6c7c48fdff5d8c11cf511321fd149dc72d2b50de4f61da24d30d"
+            "0x23a60754846b22f334c68aa83921bb94fb1b01372ed82f98570ed8aa438c072f",
+            "0x23fe9f7295768e774018a70099c27b1de95e5730427aae4ec1c74528e5ffc7ff",
+            "0xf2c04cee909519905072e754124b194e41ca8571c23ba883b3464d0564955c4",
+            "0x197c9c57bff24feebfd35e8e71295ca5e2d9606d81a7f3ad9e2736220ab11e84",
+            "0x276984217f63e53f95cfb61b03ab2f73136cd67900c40a67cf9da37309c59a03"
         ],
         [
-            "0x1024023fb13eba11f47d31a83ca3f4124cd26f37262f79f58a2612c66efcb87e",
-            "0x513fc19aa7edfa049871cb5e49496807d80e60a5448bdd9ca2bf261b2df746b",
-            "0xf30b03b1d521d16995e6ad9846209a28d195a6ba7f65f79b52ed4904f43a86f",
-            "0xc420d16d3e3b9c58f73750e0666910428ee8d203e915823479dac4046b64b79",
-            "0x22caea91c23e6f88e511e8437929d0ca19222b4bb68c7359ddf562e3435141ce",
-            "0x24dae7ec932013fe51532866b9152bb5799f806be55d531769ed21340ada87b3"
+            "0x2369c0c562fc02c62b5dae010279898da72ce370d9b42bfaeaf2e3b36381fb72",
+            "0x2a934924d57f906aba85cecf5b58f87cc5cc612dc14c6fad7341036d461f6d7f",
+            "0xaf676ed976beaa8fb9c1d53eeba67bbb4bcbd907e1e4fab348464dc8919443e",
+            "0x1aa7631d7be70060a8fe5d30d630477112702d044f04f5654685451a5ccdfdd",
+            "0x148267a8db6901034000fafcda7e8be796c8b37bd05978cef864dcae2bdc35f2",
+            "0x26c1c5d3386e7f5be1c77edec2c4d6a3378a2b76ead35c48575e0c0788a0f786"
         ],
         [
-            "0x2b9f8f8f4d5d268c0c5b437236182ff955f32e33a2f66e61eb9440c944dd2d96",
-            "0x15fb5330f3b8ccbe471ed6a92646a23cbb2be21c7b88362e6f5c9f9bc53de542",
-            "0xa0fca9f166a18f1bf1fd2dd4b192a8ff62acf53927b30d43a621dc9aa1e305a",
-            "0x10260608c495ad76b116e80b8dd1a9dbeed8d70ed304f43aad933c3f3e018eb4",
-            "0x120c7ad092da390c6f96dce89227e878a125436cc7823e419030e291833ada62",
-            "0x272391116afe4e7d39a5e933547ae768f87074c85b0bd7fc75f723838b829cb",
-            "0x1b96330177d660ba230171ff3bac2f6afaf8b6a9d9eb56832d197149fcb4d658"
+            "0x1a1e9976b72fedfe43458c69a9118c6321699c3017cb99598280f1795d4ac807",
+            "0x9e2c0662a2be98563afad98e74870edd4b40609788707e4ca45fc9a6b9fb7cb",
+            "0x5e7afb960d75ed43f797b3130e349689db89aeed81f5cb3b321362b26815203",
+            "0x2fc91f4ea8df4c9b3eb20443988c7554777f498c8b46da4e1b00d9b68a171d07",
+            "0x659ecd05f43f42dc8b70f551ac70014e7ce0c5cd2585f7c9231087d5f893afc",
+            "0x258d023ec602c60416ea565d3c41de84644c8ff68eedd500560216d3d17cd9b1",
+            "0xa1560afac066832282ff8af8f3a8db9a619e49a08dea6e58770a69a8037f866"
         ],
         [
-            "0xb0e053b2e3708e1189877d544f4f743c65daf1d6a36a4bb9b4beb9cbcf3bfd7",
-            "0x2ac6c19f91433bb89b3da17817acda7603e936015584dc22b0454cbc5aaaed84",
-            "0x24eb8b65910ae56bdef523e0ad39c5bed0dbf4ab1f7257c1537edf3b133f28f6",
-            "0x1856044636dde257959ab1efd8890d9518290403461630f763a51440ec7d47eb",
-            "0x941fbca04f207972ac703a707ee6fc2710d7ecf33ee30fddff7fa558bf33631",
-            "0x2cd676e77c8d851b93eeb676bc80c7a9a6173a0641f6a739a98665fc49b0a506",
-            "0x245eca36b95cc89e118df96e9da80ca4f19a2549b5b894b1a43f1d845bede58c",
-            "0xa85bcf9c516aa10e28fc407e1db96e88fc2ecf3909ceb4f970140a3da576742"
+            "0x2cde3150fd3ed4aabceea2c87a9d2ea9b6eecb8ce0b87d8b84ae213f98cdd9d6",
+            "0xc1ba7330d37931e3eceb0998cf1c341de483a69ace3bf6f6a1f43e6e5f8fddf",
+            "0xb3850d522d259f8b293f5e924ce87f5fda10e63732d9cc4da325aa6d77a5319",
+            "0x11878a2db086f5a10b4a104391d1792627a2d454725d7c62334aa50d4804efee",
+            "0x189c62eee85d0ffbcbc8cd08ea9dc931276bcbf1913b9a4d8a60e2ecfbd5dba8",
+            "0x127f72e9d8f4917243b21966533309ddfc212826a0807db5d88c16fe219e28d2",
+            "0x23050fcc8fea42124ad9b87b24514f318dd85d78bd1f407c7c3ba38293a9ea61",
+            "0x126f201eadccb6d7532a26c69664059c87624582ee665aa21d8f438bb2df135d"
         ],
         [
-            "0x2a8819a1ff4fd2049b7524632d81c33252f193e7fdc6b86f522b1fac72fe917e",
-            "0x20135547eeb12ce5cccbac7ead533b7374499282a5d1fcfff3f8f9c0c0a607c",
-            "0x1f499c65bf95a2623e6fc3cf8eb33c4a00c2809a1dd9fc9d487a07740caf4778",
-            "0x27a6ee22a28368bfbbcb05adceee8d6b8b6196aac567053fe4486d9902af1a40",
-            "0xa83c1e3cd25c83fabe443871a255576bd1edbf2d13f460a7ce8745282e532d7",
-            "0x2c5c371490189a9737fd773f58bf1ba214df623e120e162b5994a4980da344",
-            "0x1b69784e8efa60cbdb84334addc2407feeb953e02a668f43df3efd88d72606b9",
-            "0x297c52e9d5a14cd4b7400495e5aad685038def2f69bd9185acd468716d108d44",
-            "0x2ddd89d24634349420a192c7b4e7145aa69570759862e3d6b937c91d768f5a2a"
+            "0xed90d5f67f91a87c4c08b40e549bda84e5e6c86ec944297899c989bd60c051c",
+            "0x21b30377ea42638b724d217be13bb8b39959c83c3b1fd25c888de2f1b0a92d95",
+            "0x1770a9c557dd7b7634797016bb40dcf4cca850b3eca7e556d69231988b464018",
+            "0x1b12e4c03a00f438f66316605fc9b721b70eac2160ef8ddd06519df795f2a581",
+            "0xafbcf781856f21612ba2ddc7ce78c58ed277567417d29634e3a61121380cba4",
+            "0xdd910556b2038cf081734b01bc68c34491b03906cf80331534092ac63c12276",
+            "0xe8a1ca2da75330560eb3f602762abb22c08408f96430e1898856a7064c5ba90",
+            "0x14b295d7be68ade138df30ff97b77719df2557e3507b4abc52aa7ff6537e26c",
+            "0x20e5f7aa379697e874ba707463bc50fe0710790c32c12893d48c6384c52551d6"
         ]
     ],
     "entries": [
@@ -114,103 +114,103 @@
             },
             "expected": [
                 [
-                    "0xd72358d583ad89491891e29b239ace6b26e6684e974c6e84b70fee280c67d08",
-                    "0x1f34a96f9614be31af7a43eeda9a9deedf4fe84986843ed5cb69757b4cc4f6b0",
-                    "0xe37bf3583a0887c2feb13b09dbedc5c37d72200de67fa53cae9741746614c31",
-                    "0x58facca03217b1f179868d96aabf46cbe333097c87188d35b188d95618b656d"
+                    "0x2266680c9e3e9a28773cba7ec9866f4ef64791ab9e17952669648bd202e43581",
+                    "0x278665ff30eefd90d5493f5c5a2ea98865fea676edf40cafebd56dfd64f2f1",
+                    "0x128a83ffd273771a4e9564ea4d255f166ec8c040c7ca197ef689fd4a30d42df5",
+                    "0x1d4f2b390d887293d8449b41ebd3a779fe127a347823a5049f8654e2e9871562"
                 ],
                 [
-                    "0x12a21a823cea450c225996591ed876dca10665475891cdd6fec3fae5801868cf",
-                    "0xb3895ec23c34e2234895bb6923aea51dd750df4d3ac091ebddb0380c7a6d0c6",
-                    "0x244c158d357cb8e669cbb2e338c0e76849774e54c5477ca7f8a399e8f47f4a3c",
-                    "0x18ee8253e56212743101a585b0019d2244f0f220d5156d07f86f4c2d848bc4d5"
+                    "0xfbbfa0618236e04a0445c7d7f725215283b0279bfc843069a3d132c664b7893",
+                    "0x638f70151e8bd25e42ada8d661f4127ac23fb9fecc3071af0e732b67d5ec653",
+                    "0x11ba865299b3bc787389ca2dd9e274beb3a0bacafe312b60edd6114d14623053",
+                    "0x1ea05720c862342cec537f518d052bc7882d6dfef6a6040f0b5175600428b8f0"
                 ],
                 [
-                    "0x8071e3af0be3ad03a6dc0092ed371c845c735a88bf91e04c93cd14e7d59a270",
-                    "0x950b1b5b3f5394752c9a62eab66ac59cc0221bc1d7ff6afc97a551c0d87ef76",
-                    "0x19610398189b77ac06eb0647aa773a6543ffc2d5d6484a9de1a867362ead75bd",
-                    "0xe7fcf0d97bbe6a4f23dac5eaac4ad63c31fb3c30a5bc13f673c08d26c56d44b"
+                    "0x2dd4713360b194181af9605699e44442f8020d59f969f4accff022de1607a263",
+                    "0x300208d4fd79f59b7a86a61e187f54099a3cb543eb42d89e8a5a363b3a1532de",
+                    "0x2c772c5199b09806cbd047ebb28590ab9f65904ca22807714fc181181abf311a",
+                    "0x23b43702924632aa74d1d9409236b367c9fbaf4a4583e1ff7b4c799ca6195328"
                 ],
                 [
-                    "0x197eb97ddc0dd52b32aee7cd072ed3f72d191c8b65fdd2e8929a417da8b32fa0",
-                    "0xed43f3aa2d85390222e130555523661a21e05739e27ae4cfb28ef07e839c112",
-                    "0x1938567c34ca4995e3f077e13812170fcce19c70f20d65c420d98c7b943814e3",
-                    "0x19d408e87c3366bd1c4ca3f7ed259aa4e455bbe9e32a674f93434b90b12459a4"
+                    "0x1f040e764712e847ce1617b259ffaf3edff798774addb1e6282a79ca99dbf928",
+                    "0x276f59df9af7b4890377199471fdde403187a928fa1a8a670db7c321f5ffbece",
+                    "0x123485bd7f1800b417bab2d410652fb7bf9cae068d40815cd5ca9284ea51560a",
+                    "0x213622fcede98a94f3078e08795b7dfaf5ddf37f69b9dc216006211421ca5597"
                 ],
                 [
-                    "0x12a21a823cea450c225996591ed876dca10665475891cdd6fec3fae5801868cf",
-                    "0xb3895ec23c34e2234895bb6923aea51dd750df4d3ac091ebddb0380c7a6d0c6",
-                    "0x244c158d357cb8e669cbb2e338c0e76849774e54c5477ca7f8a399e8f47f4a3c",
-                    "0x18ee8253e56212743101a585b0019d2244f0f220d5156d07f86f4c2d848bc4d5"
+                    "0xfbbfa0618236e04a0445c7d7f725215283b0279bfc843069a3d132c664b7893",
+                    "0x638f70151e8bd25e42ada8d661f4127ac23fb9fecc3071af0e732b67d5ec653",
+                    "0x11ba865299b3bc787389ca2dd9e274beb3a0bacafe312b60edd6114d14623053",
+                    "0x1ea05720c862342cec537f518d052bc7882d6dfef6a6040f0b5175600428b8f0"
                 ],
                 [
-                    "0x173c2e8b00e2ceb8f4c3bc3e507d461c62486b68420d131ac48bc80c4587bf7",
-                    "0x1891158f405b8dd9797ad267c0045a4d1f70a18baa7db97bace263c0436261cd",
-                    "0x125b80c09ca1f49c754add0505b78f6f1670ff3ec4db21354c0f14581a56ac4b",
-                    "0x2f9d806d4a3f11a87c893aa0e906c4fc335407aaab8c81f25c569f8b95e4afe6"
+                    "0x1775cc1efbcf8db5874ea030d17fbb3ae342f627a4a403894b72a9666b743b2c",
+                    "0x12a21a823cea450c225996591ed876dca10665475891cdd6fec3fae5801868cf",
+                    "0xb3895ec23c34e2234895bb6923aea51dd750df4d3ac091ebddb0380c7a6d0c6",
+                    "0x244c158d357cb8e669cbb2e338c0e76849774e54c5477ca7f8a399e8f47f4a3c"
                 ],
                 [],
                 [],
                 [
-                    "0x9a7beacf8f3873ab42765da7d805b2f1733f146ab32e4eb0fd1d8b63d1e8416",
-                    "0x2f97cfbe8974bb4184191d7e7141e195d290e830b6f97649fd26981cbafdebf4",
-                    "0x2b5786391600eaf2d543ee984316ddc6763386019bbf9d48c53fad05933362",
-                    "0x2b42a304fd5ec26eb1dba21f6ee7d14db6b5517387e8a88ab8f1d7386f47a90"
+                    "0x23a32eb79d071592a95701193f4a585dd44494bbc1e5d0b11a30d7a339aa80f4",
+                    "0x2dc8a24b61a68c5e9c5e9102b6026130dfaeb5ca82df233a9b4531ae4843a6c",
+                    "0x1b3a080d11c1f4af701b28d569c9b263a97ba8c6a1da3445ea593c46e56135d9",
+                    "0x1a67fa02a2319d4395fca524c0083d9738e3bcc819a407a1b9cad0eff7a7baf2"
                 ],
                 [],
                 [
-                    "0x2baf070682dc2e09fb298267a97cfc1744adee5d54ad3082d408e6e5c73053a0",
-                    "0x163339c74fa5ce42a540af79a6d07e0c61a92a29451fd6e8613dbde05d6d46e",
-                    "0x386dd4945d65aa4dabdc22fe9a8184da2eb3409ceaa0a2d6112ef7178f03ddf",
-                    "0x9fd4d98aede2de90d43b3152affe2c047fffeb80fd85104385720011c8d71f2"
+                    "0x53a0a2ac4c399053d3d98958b6439138cff68ca255dc4199c148d7f60f72adb",
+                    "0x12a122233c1b23c680482565607a126c459d3fd37ed311754342b25167b2f422",
+                    "0x8139be023e76db0716ee6241121119b91a267963350816c1bab818dc0b88a2d",
+                    "0x23db257427ff0ac09ad40e5c2afca1e18dc8e671b879334e3048b9cf1609594"
                 ],
                 [
-                    "0xfb8519a5cce778a6b7228a3bc2908759278f8cbd6c8fa5519a58dad0c441d83",
-                    "0xdb176f7ca9ebbdce9a009717f37984abdc7b1fbc9ccac198e8c4a4912c28d40",
-                    "0x259d5968c7fd912ea24ab829d203ac9bfd6892970941ff67e71943bb68958e53",
-                    "0x260482927bb556086263f08bd816539885c88d2c0b84b4f7e4bc609099a928a1"
+                    "0x2abe5d4d44efc2ade68fec59d7f3e6f9376a628f571d8a883ca3c437f70e8f82",
+                    "0x7f56e333ca801c88a99043a1376a9da9eefdb8b6fe9f2aacf333144505565a5",
+                    "0x67fd092226fcce11a1e07c776f38639b3689a417f5b4c3a130ac5fc22008b40",
+                    "0xb54a5132c6fc222c8f8cbb6f08e84d74865490db753b131e384e8984fcfc73a"
                 ],
                 [
-                    "0x1ccc93de4cbbf922789d32d6486cb00ce5b8566b5c4294caf30aafbdc16b7789",
-                    "0x40e0c2d0cc8a4022a8fc5579a9eee3c1b51403b7706fa3c09a81618599170dc",
-                    "0x2147c572c47695e7db68b4231148817980511d9aa36a98e229b6ca8713911326",
-                    "0x1e8846c9bfc325419e0e36786a11148e70cd0ae07eea02eba62baecee92d490c"
+                    "0x223779b4b6244034fd992be5b5dec2686bd4c1cccbb98047d31987ad857049ed",
+                    "0x1a3d4ebd00b04e6a36c0817ba3414d0ae6929b5098cbc511140c4301d9288e21",
+                    "0x21e5d0f0f5865d4cd3aa80fc548350dc19a98beca06b8ed686450cc30884604a",
+                    "0x1a36f520181e5b65ea3206d349dc0fa77567fb3ffbb5e23ff8b44138f9062546"
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                 [
-                    "0x1faf9c48cf2e4f868d6ce0cf56ac6105a6bd20cc5d9ce972024fe134a755ef3e",
-                    "0x88cdfdf4267ad2ac07723d61a25da9a59b7ab235f57f93d9f53eabe15994851",
-                    "0x179a242acfda101c01d0a9037222164651a647533cd078f4e18ba516e6a99e2c",
-                    "0x142be6a9d4efbbbdd325748935c01a3563addb8fac3b74ebcde8d0bb01a436df"
+                    "0x2ba3b59daa08fa46341d8bc30305f945c79ec003570738e63134d0ae18aed01e",
+                    "0x241d1e8aba9af4314d1f9514f9d375a91a8efceacb0469b915e98678f208b8db",
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                 [
-                    "0x1a7d72bac1ae3217fc9203db691251a58f743adba3af68716d8c5cde4e7c7e26",
-                    "0x1d91f314ae9f5960ae40a041e7b1c9e9bfe9adb9a1ceed361193a23f399b7aab",
-                    "0x7a8b60515c3f3f2bee16becd1bbfc0128eff3b784a901db319a710745ea507d",
-                    "0x4ef2a6047ba9518c5d3de00bff3247f425311e18a28b1dd0c8a30110a74ad91"
+                    "0x3be679ae63563fb52dde79608d95aad286f862e05078b73b99cf71bac3e3a4d",
+                    "0x95c3639e4eaea77e47f74f73746ee32ba3cb071db96b9893624fa22f3ecebce",
+                    "0xb5aef105b978a694516b9145106666bcf0310c86452e1d82b94ca23f813f78e",
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                 [
-                    "0xdffc58823e22e9606623575557cb163d44ac29bb6341b02d7f2422dcd4e24f1",
-                    "0x20280bad9469bec09611463788f6ef42e4d932c14a62fe1f5c02958754f4320e",
-                    "0x268c03c09a57274fc148645b2f94e517549bea2900f25ce7c1438cc36b9b595b",
-                    "0x9e1e38490d40f6587415763f1258fcc1c11820e161da52a8a7e22d89e04afb7"
+                    "0x2cdbee8a97e4711e17640f7610c999ee00389cbc0c5c7bd788f0f01c5f551c8e",
+                    "0xa0e06429764dbca887bdf2b762bcf9db56e6e9170f8b9e55a68c7cf6393a58b",
+                    "0x20c6e42b9d82b74881446a79db552b9c85a2d0b64a40089687c86b825e8b8e9d",
+                    "0x79780c4e3493fd28c2fc5bdb68531b9947a0c2856f3306bb373ddcc7d5879fb"
                 ],
                 [
-                    "0x1d0284801eb6829517d39236844ac3f749eee579d71c913246c263812a16053c",
-                    "0x1e5213fa34409cddcfed9024cff441041b8bd0eb22ddf972a796a821d9223686",
-                    "0x1948c0db4002f0083d00db238d00ee25b11384f108371f8ae5bdb10d7ca70b33",
-                    "0x2200961707a11266454e48edcddf0ef4d973dcc3b9a6a09a9f7f3e48bf56b343"
+                    "0x13f439a9235414539e2d95d0dd86cfd426730f24ef1cd31d042bfa67be2780c0",
+                    "0x2d60bf69bfaa0570ab161e2b134bb600968ab0a1e9f5b03e46f453a234aa939f",
+                    "0x26f2ef7e8df55aeccdc1046e78a355e302f55d23f37fae08aa98964f6bfc9061",
+                    "0x267b80a16394db8af4f6ae10845581ec12000adf2bbfef2b1db9aeb716d7b77c"
                 ],
                 [
-                    "0x478200982a58cb8ba01e3b94fc61a3ab3a907b08a6e51f177514ca33e98ae5e",
-                    "0x24e3e276142fbb9c2d42ee82a6fe4767f74d532794aa66a045e28f4f2ab91c6d",
-                    "0x1cdf1cc83e443b757b636191b64e3569c959c4b2f13c9bd241c2c08e1297f216",
-                    "0x2e0c9e95cb5970884a4665a31454997ea964ad847b2a292ec108c3f86adeb3fd"
+                    "0x2f2750ee725d389f249f122d7d58be060e87a775d977172ff472cbd442b3996c",
+                    "0x2fe8ff89c933eeb3a95ee698aab658b99edec3e6e12f5811dc8781192fe114e",
+                    "0x1dbe2e11d7ebc4c5ced0682d680b4566459a2e767a36549341ac7e1fae8e9ec8",
+                    "0x1598d0048bbb586f4153990f942b61a34084c2c6be069ba7d092d17ffc36b25f"
                 ],
                 [
-                    "0x546421370dcb7ae599dbd6eed49252279f2646e4e6486620fb2fc1ef775598b",
-                    "0x1ddf73f5eaff0dc51f3c8087788e86317775b29338e26f4ad974cae9c7cca16a",
-                    "0x220b3c172defe3b93d06a4ba6f6378e76116cdb96c1d0215adb968d58afbe53",
-                    "0x11fd0c9ae41bb5a496ed45ffc4284f8f0970afcab089403d373de805df30d07b"
+                    "0x1a1b88743c182e52589382c6558ac1016e213f070ae5b7aa1ded888a9b39f1fc",
+                    "0x2ebe552dfae4525f46a92c0fca5f45bbfcb6f63bde608b8b281b39c89e434404",
+                    "0x2ffacb8776526565ac9107dc9e834d9a8e7e54be7b66dbe12da97a9fa88e378f",
+                    "0x186e4938e7638c327623ec1a0308f41ed0dd85e953f8f6ca3e90ecf8051b174c"
                 ]
             ]
         },
@@ -223,78 +223,97 @@
             },
             "expected": [
                 [
-                    "0x2e4dc469b7ecfbb89ca4f401cc98a151c485ec4b927b33740417ea0f2993c3e1",
-                    "0x13f14bf81889e11e3d0ec26d518884adb61421bfc8f201470db57976b12e740e",
-                    "0x1b9cec0daff5ddc272434cb9a8336795d597123ed6f791df3e933f12164748cb",
-                    "0x1644adc1eb1fd002624f448092a6f0c07fac5103f51981adc085b55a3625472c",
-                    "0x1a6b96a99118d4dd0a54337087133fec82dd69ef4de7b44ce87a74b97e96e5ce",
-                    "0x1a172ba7464117eed0f3b329247545b20bba546c682eac422e77e682c790a802",
-                    "0x16115ee33e14e629eb5fa66b6f8412121688a49d92b29ced0de7604a64fabad2",
-                    "0x1549e3cbf3a9ea8ab44c81a5d32851b1254a198fbb5adc60d1739cf903039307",
-                    "0xe42542c35cde35bd24bf71513b1746ed1542ba9d1ea951ed6ddb634cd245797",
-                    "0x146d95f61c63bad2b6c4d030ec9ac8ee969fa52ed3d05f75af3aa7da933a1c66",
-                    "0x1468f6c6de67b09ca6b46e36e3eeae71cc19548612d498ae259a36e69d4e36f",
-                    "0x13c3e8b599ec0c41cb381c27eff18c99b00993dbe9058afb41b6d9d4cfade5ee",
-                    "0x1fef36b76c670f33080f7546e17a86448e1d0e1fcee4216b31a45822b9fa977e",
-                    "0x149586c1a66b9cb1318d5e80563ab3b6760485954b02f5775b24379423174411",
-                    "0x2374e560aa1fc966420c1742d28a648b40c080dde3f278f033534d4d2b20ff01",
-                    "0x166f5b8e88b0c2491122ee8f7d0c13cd8a0f1a08864ceed8f5e2a62debf5acf4"
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+                    "0x128573d948aa1e5d7c8f04379bd043d114b09ab4a1d51b807a3b4be49661cac6",
+                    "0x295e7874cc5929896f892882548b9a9fc0ac1bb1fe5fe0e22d357c32e645018a",
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+                    "0x1aee8bf9f2410de53580cce26720152663e95b7b96daca6fd0741ca33ac89759",
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-                    "0x2f1ffc6577bcb510b83b2af328e756614043254aeaa552accf16a841f516b202"
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@@ -309,209 +328,190 @@
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-                    "0x15f5503cecadbf2f0d077c724ded2d020b68b1b626905024681d05fad41d1ae6",
-                    "0x26bd14b019cd84f9e4c6099e570b38a669076f7628f8ceb289d53d621d172ca",
-                    "0x18b45c0c86a928487621021374b4f855d95556fcaacf94f92caec6e38b42f6fb"
+                    "0x27b2b889743022264d640bc12362197a58351540ae492f58ea2ba5889961ad0d",
+                    "0x2288f7a625a81f5ca4f775a29846f9766a4a83225eb026b89368808d63e6302d",
+                    "0x1aece1b31eb13c6205facf0e274a68bc2cdaee95ec89569ff6bc4fd7d39e2764",
+                    "0x25ea4367ab4ae364171684b40bc82f4aa51e6e35a122c52c0c910a872ea559af",
+                    "0x23d6832621fd19460674fd9d72fb37bf24fd3937e0339bab71e4a15e5d6f77af",
+                    "0x14999d905878abae9efdeffc9c3db439f1afddf8b642a4bf92206c74c7e8ca9c",
+                    "0x10638812513242890421b90b9608460167c4845a638c8a9b5a3e8fc4070745ed",
+                    "0x2da779b59dac70cd4951d908821c9dedaf2d6feb66eedb39dec323d5290d7124",
+                    "0xd8a72e9d9c3a37d1ec8a2b54d52721d22e9af5bc6557173af789a627992c39b",
+                    "0xf12cadcc0b9509c7fc47adc70a464d04d937563230414fe75a7c4ef50bd3ac2",
+                    "0x13e2668ce7147be54f488d67d2687a13194b3f3a7d59fd2180020cd2ea6d3707",
+                    "0x20a2ea5cb9f4671470316bbbe5e2a398323a1a6c4fd6bba03faa3d27ec5ccb27",
+                    "0x18b036c6fdf6847ebe9c925064c7fbd3b08f0d80d0d4ce2a7fa7b7d65bb19652",
+                    "0x288afcda74a2086f27f1f11bf0b3ade317c08e010f26222f8f0ba2e24cb148c8",
+                    "0x19b4e04b1ed95e3b43693006b8397f67a6a10a0484ad025ee6dac6506ca25241",
+                    "0xffa3f556fcd906315c3633b11b03359acb51c8aaffddd5e3a39231dd7972f83"
                 ]
             ]
         },
@@ -524,295 +524,295 @@
             },
             "expected": [
                 [
-                    "0x7e5ace972938a231c1472ccbb2d3bce10253581559f45078e92baefe753342",
-                    "0x249307cf39f7863b2a9a7e9633c0cbd8ef4bb807f169de6288507a12cf8d473c",
-                    "0x9aff6b7a3beba01427296d7149a9910319492524a08982d64ca1830bb80504d",
-                    "0x18ee6dd98759f7f10878f383059f9fa06cacc2a40f1b3ae7d5c61ad3494577eb",
-                    "0x1921b1c4bb745dae27cd599b351eb825c312d27745453eda5d3ad8cb195265d8",
-                    "0x205159c59e67da9283b217654f5a02079ddc43a64a94b18448a8eebcd0ceec78",
-                    "0x230407139ae483b15acc3670be77198b9f8f277de0002d35cf0364a40db0c17d",
-                    "0x1ecfde4b7ad57ce77dd63ea6636a34ef067591ebad2982f06e87272f253c500b",
-                    "0x18038c20943404ced129bfe400a51311d5b41891c4bd03189b71a918aa98e85f",
-                    "0x22c913854c092cb6286d26f55174d85b0f323fa2712a0a85e346c9368af7808",
-                    "0x1613d0080f29e5819fa35f510e72c6c6575b1429e2e7f86959c92a8dde94346",
-                    "0x16a6c4e970fed48f266b7a6b39fa936db04d6fc929f990bc9d934fb0332a14a9",
-                    "0x1239629fa41b411c73e2a40dc26c4d16f2e39f450dad7fae4f2ddfbfe2ced022",
-                    "0x3517e5b5344b03a130d61d221c2232339b50b51cbecb68a4264ba1e18756299",
-                    "0x20eed2a430b2e12f87388d9b4fcca914711194c7b1346705ec3da39125a1015f",
-                    "0xc9070945d44edfaf722b180fb719444b3de890803d30a920645fd1a2953d010"
+                    "0xce7ba98b1eb73ab55fbc0186eefc1cdab5f2f22fc4b7b2c46730742b7e3c982",
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+                    "0x272ec5437c2b03826008f3d81ef9fb01afe9270f7b4e9d4aa831e2f2ae8235b0",
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+                    "0x1588f3726b2cbdfa0af2f7cc9e5e2d881ffb1add3891a86b879afd91a385b87b",
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+                    "0x11ac39e11d082be41a4e7618ac845a4ae0ef20a31cca64c369ec42121ee45a1d",
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+                    "0x1be8af1b149da79718941328339a6c39f89326aec868e304b9d8389cf462d90b",
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+                    "0x2cab401b171cf896b86bd8a92ab1dcc68128ab19a0e4d6d362d739f8bab82d0e",
+                    "0x19a921ebcac157cbc3f8379c80cf082bdd73c625390f60b6ada18593b78c74b3",
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                 ],
                 [
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-                    "0x474f81ceb0561e9ece8bb59cacd1b9ff20fa520b5a5ab0e87362212039fc179",
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-                    "0x30339a7b4a4172ec6bc46c9d531568be053cacf71c5caae99819883e8ca141d5",
-                    "0x145fed9358b90f206d54cc81e9bb08e615f6664070c25fb3ab38f8e84ff91f2a",
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-                    "0x2aa21f15ac19de8ee717142972177a2e3d40437b8d66accd9726c282d4f94ae0",
-                    "0x139b0efda8ea0d0847b7de6576f33ce4e9abf80787d5f7ff9defb66f4d9de122",
-                    "0x538ee9a07a632e4383bda8159b0c6ba8aedef154ca46a71fdd565bb537e841b",
-                    "0x2d6fd95c56e2b3eafbace1ae9503fe02d714ba5c4d847ca4765b725dd2329b19"
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+                    "0x235b1af447ff50b4e77da328cbd0f6e4e27909194182393e0791e598fdba410e",
+                    "0xdf5243284a48369042452c05644fd901b59e25d57a5b02c5c307428f5d184a0",
+                    "0x10e59d9021715c9282d94c556be4f11bc78025d614e49e88a802165b9928bc7d",
+                    "0xa6e58f66006b2a864e6d6358f1dcbda2db2b3e9ef8aafe9d51ca39acb5a4ed2",
+                    "0x43182d8f1f6b33391fc3c271c5e7b41b7922020c893a89ab96d87e5ef1d7925",
+                    "0x21ccca5a12e0c9c1a35e00dd88fab22c0154af6be66b0a66d50b2b39b2eb5efd"
                 ]
             ]
         },
@@ -825,551 +825,551 @@
             },
             "expected": [
                 [
-                    "0xe8e0e4723111154ec26770600a560ae4d15ce373e0509ec88e02445f7c9dd34",
-                    "0x2f347de607d265056c16e89323b82e72fa5afb604e0fb6e37db255c5dee7b967",
-                    "0x280007f13d0d1f36974e1f53a08f6551e5d46340600eccddcf2b47215991422",
-                    "0x274d3b2a0a2a8c7de3034494e68a43fe551167d6bfb9d772a84d26ac13bbbd36",
-                    "0x19149644f08f9a87dd6bb5a0dd3c40e5b817ef23bd7b07b6b4ad133499d5e9aa",
-                    "0x274a6dab03bcbc839ce5dfcd728820828f6f7ba6e094b9ae7ee0f389dcefbe23",
-                    "0x1f1ac479d3ffed65294245875155beb8b7673096469b5bce66afec8e69608ccc",
-                    "0x9bbd4713140b585d4cb48e532f1591e3838c7f4874e6e01c84165fe2f6b382f",
-                    "0x482951bf22c7d58c2f5bded2d8cee8ee89c59aecd7bf347e8c005399aa08a36",
-                    "0x27811629f186e2d759c7fccae4470fde01edc3dc78104a1ea78972c486838c3c",
-                    "0xf17682ca2b7c00eb9001d2b9733aea290f12a609be1a93545d71725f28e689",
-                    "0x7fc1479ef8c919524763a1a60d6917d3e39c9937409d538f0f41faf20cf2e3f",
-                    "0x706ada2692bba4966a7e254b417dec4f3f50d40eee52c6c6f6d7db1a514ccac",
-                    "0x2c8e4d6f5a4060c1cbf8cca4221123b482648993e82ef40c3fe7b5f2f519b8ad",
-                    "0x1d3de79d52fcab893c7a40ab80cf4e26af8ce8211d5b27461dafa94c197e6ca5",
-                    "0x112780ae5a5f221a7a6e112d50d979fafaa2d0a2a7ff0a200bebe317c04d2ef8",
-                    "0xf8d5aab87d838008a19c2728c850a1895086c4dae488951244baa3b2e6e90a8",
-                    "0x2f132f74ddef5c38a91f19bbd9a9b061318f7baa0b90976091ecc8eacfa192a5",
-                    "0x1260b9ef666df0cb162cd6bee6d490f055a0bc5ec786dac0cd68ef9a2027d5e6",
-                    "0xacba59811e7eaf23ec797445814765aafb4bc31e19201fdb390def05554efc1",
-                    "0x262235d7c14314397f4af46630f61a2cb356884d758ad93b6094e6ea6fd18000",
-                    "0x254cb8c4cc330af3709468705605354334cf50a08ecf65c0f4dd38e8a52fcf2e",
-                    "0x22e3bb76d05e95cc0a630eb0e405a35b39ec7f1589373807259003305058a08c",
-                    "0x1f2d95addeb9da0e585b534dc688a4876bc175b17ef1374f7a581d681ae49f05",
-                    "0x81c4b44d9fd39d2066df0596f06e02d960d6ef9b6b49fc43ce685803006c594",
-                    "0x172241de8b6a6c1972edd78984d721d5cdba31480ad7e8d125830b9593f83108",
-                    "0x2285e9b1224a90d2b8de5688b0d822293822ea68ae22aa6816cef59b8f3b716b",
-                    "0x27b2dd2a3af00c42371e42f7b34b75eefa83a8efd36b8f6901f7e17225eaefcc",
-                    "0x8b7c976e5975ebc32ea895dda34dc4fc2a75e98222dc07e960ee3e80cd8bf51",
-                    "0x123d38bd24ab962a4d005e7dc58cfd8d6687405778842ebc73d61154e9939a0f",
-                    "0x1b3de97848e2606f89aa3df5ca45fbc5a3f5b0859b8a2c3afced014114099da4",
-                    "0x1a929893eb4c7024276ed5521a58eda7b3ed96c3593aa3f8da5c7dd3a3233532"
+                    "0xab048ca1f78a0f47f1ce9dfd599d29b6f802463ccc2bc790e567922fe883bc3",
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+                    "0x45d361c358e3612dac386694b7853e22ff045aa10b75cdaaf046e9ed1f32e7e",
+                    "0x3c7e10643a8607d232928b9e692d5f4a42f93a197365089abcbc697bbf4b635",
+                    "0x2d85547048260c3f73ef8dd791e5c17313cb87d6684b0a6c6b8cfed6e7fe3cc5",
+                    "0x2bdff532534a2012091d072e79b3179686b2909d97c2020c5fb64b2b45a6a0f0",
+                    "0x226ba81edb399a357d11ba041fc640d3497d417de6d5b0a52f8cd7237c60d6b7",
+                    "0xdcdc8d363040d29e7c31e19fede76f7a1730181eb3a02b48b6beeef72f7953f",
+                    "0x100d639d1f6d63c5ebeb5dba8649c1622c54b6fc71e47fbe43196b7eff57d967",
+                    "0x28e43db7697feadf9e2fd05df4f1301afbb47875390697e5cfedbcb148f1ea74",
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+                    "0x779998639f37fadd74b4bc7774904cbd2c05326171aaf30031e9b1a3ec0fcc0",
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+                    "0x24a9fb0a8b1800661fab46256256cc7054110b80e51d69022af5ca176aa7981f",
+                    "0x179d2b4ce1deef0503fa1044441611ff3027cc75d230bc28d7ad9052247d8e38",
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+                    "0x2662e649f81b5c6e590a12337eae6f355ec700176f14211160fad605ecb49da0",
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+                    "0x295911930c2f3cf9ff381766a97a5d11fc1058e167f81be551c86e649019a262",
+                    "0x1af08d24b0cf18aa5082942dcc5653dd8bd66cafaa11a294aff58b01a7ab5da",
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+                    "0x4d8f36522ccf0bc97c9528babfa80d3b9aa986d4b40925614fcf1e1b3acc096",
+                    "0x1745addd4ffcbb2f9c74e7ede87e9540264bdea5e1b7c6916cdc6d6b00a4ce64",
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+                    "0x2f1109111ba95af5ae8fb96543da982cb70cdc1b868e6e0e0ae4e3ddc0c1720e",
+                    "0x1cb13e45647ca14ccd8e09dc1562fc5471c16133851fda69892bd819f0e3ca56",
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+                    "0x2ee588b7daf5e8985e89afd026d16652dfac53ec5fdaf29c126ded6e3a909a19",
+                    "0x1cc220dcbb0307f0c5173483a9b7a301e588f9575e776feb69d090464c7f62b3",
+                    "0x24d8c81af4c3b515d2ceb215629b9e98b75ad89e416a3bb1228cab590d25efe0"
                 ],
                 [
-                    "0xb71f4958f8c8fccb39c63e9f3690d47c28379a60576dae9fe01eb73eb7f3b59",
-                    "0x19006fd58a468a6ef7c67c3977379beeab8c31da2a0bb2f2c5a07003541c715e",
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-                    "0x282cd7ca8f8679d8bebadf83b87600fb7acb349c94ff2f8eed489242cd4931ce",
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-                    "0x21db1351c8cd33b8714f2986d5a775f65b5997a83dd6c68b6a2848f438f7c65b",
-                    "0x9d5d874202935ff891c95ce5e4adca77d6efb520256270f630af296ea661ad7",
-                    "0x26228a296ee4993c0aa1640e2c5d929a8d9bc7422f9e5c824278fda12c5a16",
-                    "0xbe4b742785969488986362e618bb38d96d2681c26cfc0f04ac87c3d53c0d5a2",
-                    "0xd5a4f146195de65d684fb328b0768d02dc98988ed5d8d531f763b1430b96513",
-                    "0x2ea0439122c53b590c35da987f03af7f45cdb5bbbd951c0e306a3989472f5538",
-                    "0x11292655e90ba96647370930d76909dfb487f61019706dd917a91481c9974d91",
-                    "0xc80e8e22b9484c344d0212c9182f0a14c5e0d3ff498cd3534a76af3ad7e5ece",
-                    "0x71bbd24f747adbd705dbeed04b84779e96a9912eb7f176c7a295e0681b92b2f",
-                    "0x69a1e1452fea54d277a5f0bacde83bb87fb2173a42e26892004c97ffd2ac63c",
-                    "0xbf864e908443b396e832e52bc045aac573abde5decca1207e60331814390ce5",
-                    "0x24fc81dd9f550bb9f8c14ffe6c911e39d0228289bc0bdd3d4fcbf26f8983cda",
-                    "0x197857a04c6969e92bcc994cfc9abcf6a02cf9edc00f9ad562c40e7a40486ec3",
-                    "0x2ba3c0db50f1a7fb6187866833ba8fdced08944bb5224dcd6f3abe662b2f5893",
-                    "0x2d3e24d96aae2b20cd7d1d0c9aa9a6def3c7d7db7f0eda06c97efb42a0266851",
-                    "0x30a8edd7575f3daa8c4c5a81d60280ddc4ae888825a875be90fdcd667eaaa9b",
-                    "0x28cf9c4721945402ad0da94427e5aa802bdc35810bae4396972a1afeafd673d5",
-                    "0x1c6d4dc9346e2bc1abc1c9a65128fcf587a31db26645ac734418b4e62dc9375e",
-                    "0x70fb03f595e0118164dd4e83e957ed7adc5d507b5c61f8895ab9051d29f426c",
-                    "0xb39aa1469beb753232b9cd346b691b4c0f0aa10dd2e64ddad5a709f36f9deb9",
-                    "0x270adb28072c5b6fdab5b7e6e1a88acbcaa4cc4fdeeee441810d1d8c3a700121",
-                    "0x1688a55cc2cc6b31920c3a96cbba295bc6786a4f63feef136e5550fb873c773e"
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-                    "0x26000f9f5600bcd496c14480a52bbeab35db264bc5b591fb6323da552d9ca00",
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-                    "0x14ff7816eaaae95d7e857e2e31aa608f9830d4b686008808ef59990a3e560797",
-                    "0x9e7616e2d59bb629d421d1407016655f006b90a7e6f78f9a879fb18fee481c",
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-                    "0x26c0ee9d9babcb116d3fc00c57a8794720e781d48ea60bba0776276179da59b1",
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-                    "0x4cc4698b09f0be5674898228f0d130f1c5a1467835eba36d73f6c4fda3c0575",
-                    "0x228228c2f54a7bc49e39c46b994741f30358117ebdbfcb331a6db0bb5dc7ab00",
-                    "0x24914a1ac6dfd2ac1ac44dfc3fda71303889edfdd416cea8ee1218452edfd110",
-                    "0x12b709d8ae725c206125948dbb9895634170244d86ebd0a813e773ed3fa35a7f",
-                    "0x163203a63d7fec642c0ea123c9a3d6708c0c9ada2ebab96f0f3ade79a6841487",
-                    "0x13ed31553ca35499dd053a15c6b5ba2d5e4b8c130640d6ad44673c69297060fa",
-                    "0x2bc5a2bba2b07ffafac9bee0db31f5ab02d6921d722d9e53da6774739daeb6cb",
-                    "0x1ac84f7c8fed839ec2d4a465962c2abcc54d5fecad6d3c438b26538465b591da",
-                    "0x14f5f85e182359d897a6ba449096a723adbac491023f0064928eeb88de82a1c4",
-                    "0x2bdfc3962ddee0d12818bb10818b16b7fc78235522a091b1f22a9d125d54eb35",
-                    "0x28db7daaa8fba069f32ed0c553db439792c41fec58777a863f46ab29471e8feb",
-                    "0x1b302da99b2712a91d435a8b509856468724e04c13fa3beaaf4b8c31fd9892dc",
-                    "0x16ef8d726480fb8ae7b19f389d32ee61b102b1192610d65d27d2c171c3e407ae",
-                    "0x20c5e64340181190585f3a4b0d518a8fbd6d0e9fa5872557ead009daeec9d4e8",
-                    "0x21ee72844db1c4a6a0528803a45b38288f1f43b5306fcf03d9a35ea8283be77f"
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+                    "0x26d8309ce05c02c9e3226441efe899f407881edd85123ef2b1675f83f3c05598",
+                    "0x272fc4baaa1de94a500648ffa5d2ea876fe66d990df9f32cced326014c1dc7ba",
+                    "0x2f93fc571f6d771271f721b09e3bfbb4695166426f7355cb194ef4ce7fe4e127",
+                    "0x2f50b49a718715143e85d6922eb5b4dbed07f303eaeac5faebf268b02bc2255",
+                    "0x2eb39d140b061a9bf0e1ea79f542c2150e24ba919ffc560128e3c2a389cf2ef0",
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                 ],
                 [
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-                    "0x1ee41982da15f44166015f10c10bdabd77aba54827b62f8eb6971ab194a87178",
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-                    "0x3712fc54522c9db71526e050f6778a582fb6b4ee6c6924a7b3db18515eb143",
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-                    "0x9ee2aab8720425240ed7f95bbd6110e76247f5de712e2aa3a94599064eca464"
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+                    "0x2885100636cf2884915819c82d2bb246fd3284d725a929f6601a101cb0575790"
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                 [
-                    "0x21c72ef19cc99cbb7bca161ce06b97e5c1ea0a0f687955cae3c2ad14aefd3e98",
-                    "0x291ea068bcc34bf4b0ea34cd870e07eaccb02c6699cd61ff5d0801cbca00b79c",
-                    "0x203ca2474bf5beae1e6d705193c8cad1885909fee1f2633b5a2b8397e3c0259d",
-                    "0x1a3da23de325e824b3a46dde9ac9863fa72038d4e72ad3d09c5aef7e48059b4",
-                    "0x3054b942f32aa83ae3627754a1727da30cf787791b1c66a572ca70bdfd2bc380",
-                    "0x4ece20fd51844342c4c52adc29b11978b0134912b84431880cede14a663aa0d",
-                    "0x129b556737c4909df1f12364095ce25befabbea90d8eac372c8002b70836bc57",
-                    "0x86e8a27a76f86b555a0ea14b48124b2ff319c533180895a2327c4d4b321f4fd",
-                    "0x89dfd2f2bdbe85c5671602bcf1c7797b25a26f9967c4ebe3b53b7344ebad85e",
-                    "0x1a1072828ffafa2e03c768ae178c8e11bb93fcc19379e6686731dd1fd588e425",
-                    "0x1be077a0e53b826dbdd119e5e8502f4c000477c81be12745d2c89736ca13e57",
-                    "0xdecf54eeba6cb5e103d9202c2c6b346471b1849861823eeec9aa374d86cfc24",
-                    "0x1e4da55dc7f1010f6986ede53381ef2be828bd8aa2712272e1f2e92b1ed10d1f",
-                    "0x1f86c7cc05acc593c56fba2b39123d2c229d7c87aa623451199721dc3254c8aa",
-                    "0xc1c0dd50b0711759f40b2ce4e38cff9e5c1ddbff5e958e3da86402c694f3e43",
-                    "0x12a5c3c73dd6944db4b707336316e64fd96c43dba014cb2266679381cae834b6",
-                    "0x10df7ec266839d9962d406497c8cbbeebb7b8b4f3488667b5b815e58c829b112",
-                    "0x40788f8b157f3a0758311734fda93c3a38e21861b310839f1c3c709cefe08c1",
-                    "0xbf2c278b3b36315f6fb3e5182396b0067bcbb35a4301d0474ec58cbdae538b1",
-                    "0x1de9a90ffadc8767cf4869b4dc6f10d14dd88d92164d0ab0ec4938fc819deb8f",
-                    "0x10d67a00a3e3191ed69db1aadbe472391f32fc3374722098e49be162c9f9dda8",
-                    "0xedb19cd0020e618a8e5091a32bd05b23992b932f8d90e9f68114b92e8af8f72",
-                    "0x2a135682d85b5b5cccae0656573b72535b81325a64182f7feb08877b2a249ae",
-                    "0x143c7d066d152c1f6387220113dc509747c30d2d8cf27dc91237cb32543a22e1",
-                    "0x22061fb5dd4703aab34c0a657cc267221c6c579439cec2370a84ba81bdcf8427",
-                    "0x60f188fdc42db397704e3c5ebf04180f1befd400f44bce33d3458b33665fa28",
-                    "0x154b8698c721685ba953dc195a296b02f0f1e2a28bba2fcf8fe6d735fe4c91b7",
-                    "0x1d19e42a64f13f63169a0ad7a4e706591b397813a830a2ce668812c430cf05ca",
-                    "0xfe5160397751f34ace2ce3697b9f16be68d6436550fd1e4f97ce672cc315279",
-                    "0x4c1deed1a1d10a08c4c7b568531857ac4ead9f5aae04838a593ecc987da60b5",
-                    "0x18223c4d6f24a96005990a9778fcf05da97c365d237c07695359ced15a087ac",
-                    "0x28478882ee4c406b73a32ef72b25bd45e495cff781c67359e381b8b357302601"
+                    "0x28a605e5aab56efb7c33f7509e7980ee7244f2363c6b69e852874951271a680c",
+                    "0x272564c0444586014c0474d8f5798b9b7f9dc0248e755c426f1a7cdb93d10914",
+                    "0x90c09140b1d743ba1a725c9ebb27cd328a1447543028152ae4bbb278be58c8c",
+                    "0x1ae06f9a38c37e2638d6a8044d10b303ced8db12e6a8f4c5a8a98fb53fae08e6",
+                    "0x2432311f1baddb26856daf78c86ca60cc6b4d984ba6ccf294cb28fc269059b27",
+                    "0x24575acb3c89ac683ceac50c4bd0b0d9bcbbe215022026f308947b409d463a8f",
+                    "0xd80e27af8f9ed50e637017b43858bce3d671dea5d78ed39f03c3c53c4f3dfad",
+                    "0x998c36c91fddf2fac9a7a253091451cfea8de25c0cae2504442eb5bcc092655",
+                    "0x7287d2f11b840199c6c4489ce1d5366cfaeae39c9f6cef6f561ee6a1626a577",
+                    "0x6dd0e0042e3f85fd8e83e901b29f350fb534d5405bab5eed38e475912569596",
+                    "0x51b68ce31030c9bf4f5b248b83874428daba4c7b96d36bcef11b77941095d18",
+                    "0x1becaae21ea1cf9b170fcab22388952d6f2037e621874bcced0438e95c65f3b4",
+                    "0x14d436bc8e09aec69b4849289f274e0aa419dbb8dc27003db28bf8ec387cdb49",
+                    "0xe0ab51fc2981bbb554719a3d82ffd6fa03cec3c79917bdcf89d5e1bf8ed006d",
+                    "0x3ba2dc4f29418fb0b4ad5b6f2c911ada0ef0eb372cac594247b5e36e8d1d9af",
+                    "0x1a4504b5e36e39fb0ce083a8d0bc5aecd0d0b7e3f6dbda9e9d3dee3520d6743c",
+                    "0x267de26e0adff6d7f72cc8a77600a4e61cf5d82525ff7153abe053e27ea54d94",
+                    "0x251cec8ec68a889007ee8be167fb8d9e200b344f8c2e9648825cb5bfa56b4ace",
+                    "0x76bfa27e38a83d65ab710b6d64c57900b834a124acd2c8d22a738757a9ddfc3",
+                    "0x62ae5f97fa6c176d37395c78581836eeca30ed1f31567cd4726555b27d60ae4",
+                    "0x14e96d537e70969cccfed132cee32d6c6036dacdc1dbf4fd9211069519c3e43e",
+                    "0x8473460916d545431810a56ad5d86d3d0b24eacd9d7a0cf58907fadcfa7131d",
+                    "0x2700914cebe62eebd2e29900eb7fcbd0211872301494781e21ea6f3c02da760b",
+                    "0x1b6be4fe3da2ce6e69d272640fea2aa6924f1b5f3f0b491fad357172b4449d42",
+                    "0x24fd88ab4e43fc64cd97f1caba871a407504ab4a34a32dc9519ae7ca13bd1a40",
+                    "0x12df4aa829a8e6e3330b10ab5b6c477db431f20ec05286317f6a1485a4a0dfca",
+                    "0x19de347f1c69bf697eff1c4e898574f83c0b62c112c2a531d74ec1f36252a564",
+                    "0xb1f5ec243584d0f478efd11050aaec38b7f53957368d0404826c6a6e6fee4bf",
+                    "0x187364278909c0c63da0641f2fbd88dbd6eb8d696e1d49595d997d0da1357a88",
+                    "0x800a9f3b7b6a291cd8ad52e3c5a88462a8f486e8fea9ea03fefc95ec6ea8639",
+                    "0xf1cf4b85d6d8b8613984ae33b853e8ebdd50c5419943388ba7d54d0a246075e",
+                    "0x1d056c6d165c15da8434a5f79413ff28d1b25787e528a0b42d5db1d8097dfb27"
                 ]
             ]
         },
@@ -1382,123 +1382,72 @@
             },
             "expected": [
                 [
-                    "0x60c30f666d696f7d55b3bc0528380b0812de457d5d8a4b727208493555473f5",
-                    "0xa5f4ca8bae5b5c6c816905b5d97f3e16afd7efdeb9f4e02318325508266ef76",
-                    "0xa45d93b4e45ef347b3e469968192e24a6232660906908bc36483eb2812746bd",
-                    "0x5f5e1616b25a31775e6424ae3ad157ce9cbef7d0340fe4daf77339eb2bbc7ee",
-                    "0x3d0a98479c9bf5744e39be265ef67661254282ccb7bf8008dffac5c2bbede75",
-                    "0x27395bdc734fc33f3304d3da558b1313a084d88997851c29086c720160620b75",
-                    "0x212334b5397abc37445e0d3a16a70f021932bdb8a0a336937c920eeadbf58ce",
-                    "0x17534106b82e19c046a8f722ddf16457dc50c23a01f646a8b8458e0f434ede85",
-                    "0x2f1cdd89abb64d791580d5dfc44c47105a197631e027a70b2c4826caf09f06c4",
-                    "0x2f4d1db67d86d814e8feec5742c5560a67c16803acf109422debdda308aed18f",
-                    "0xd89e1d1ced9dd02bac0865c0dfb9f157d713c5817e68ffd79bc4b5f0fb89cee",
-                    "0x2a4e68b285c0bc2ab161895048465da1a3cdc90247f44bd0dd7714706790bccb",
-                    "0x2e5844b9c26abb15f591fe5e4dfacf1e31ba044601eebdfdc685236b8c6d80a7",
-                    "0x2fadf71e280ee90aeb83d6d26670f3148c04fd46b8dabc0754d2fda636da57dd",
-                    "0x1ffa8aa9556cf00a67bc439697658e7a9efdeecefea7f94a48192de55a995b74",
-                    "0xf030ae8ba815e751e5ab5bf835b21670e231ddcec32217a133b6b57f89720ef",
-                    "0x7300d2cac8e4d89e2e7589a79d333d543c64d64b198b4348f3c58bb1909dd6e",
-                    "0x10d4fa3bfac20f733ba21591ff089c8bc01b8b86bf68bd6f380e392d11820f29",
-                    "0x22de7fef86aef7bd632961368dc9e50ea81690e4a0eac80a981797a187abbb4b",
-                    "0x2f8f7cea0923beaa5aa4ed938a65915694bccc687a2df3031f67f455c30e13b1",
-                    "0x2b3180f6dae94db6147ace7713a2f3e9674f7f0e1c7a29279737443cdda072de",
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+                    "0x1107304a4a20deb37dc8d4abe5f3be4c78c505398b714e29ef80554089732ba",
+                    "0x19a24dbf936731605e78712d64010c781f48337ec8d7687982ad782dcb85d003",
+                    "0x2a050a08ec14aa51a8477b7311dc42fafb3580162165e6c1c2215c1f24cebc2",
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+                    "0x121eecba93fa035b4f4e70a1ff08a5f5c9077f7841236d868e8f25e394af9bcd",
+                    "0x184cfa5c6673ed7ddfd1f0e432d62674f15a82d2842d19b0835782a13ecac40e",
+                    "0x1ba4709076e512b726be5cc2e52e2bde2fca614164641f2d3592bce9bf3f1322",
+                    "0x213514d2a31d65fe6fba3a8d8176ff12e48c4b575fdd021fbd190ac38b048094",
+                    "0x16009ec047eb9f1e1bb92eee8fdf667ee02b0216f5e6d6ac6a1d65de1f69eae5",
+                    "0x19104836cd7a75a29e0d6a0790592a5d17e2e6c1c48c09f7a7b9653178a473bf",
+                    "0x1a9371252345dc7a54f8b1bada133aadc536a1f01160100036509544c514f7b7",
+                    "0x1b9c7d75b60f5c0129e966ee6ef228a5f724888c6f12fdd764ab3f5659cbc602",
+                    "0x28168007ab1e488f5ebeb75e847da321246f97ffae3d78ae2a01093f30ec55dc",
+                    "0x1dd7b283836b0a773d22cb2ce03dd8cb43fb1219fa7f52c5255e17d828d2b9dd",
+                    "0x106acbc509badd4f2cbe70a093cd92a43fa9e6886e0c8fe362ae3432f4f8b01",
+                    "0x4c933d555d32097c71a0eff88f46dcf6cbbf361ca2e4c3a442c6124c6c754de",
+                    "0x5dec12012b071f4705055326da676124646788e01b8f09e436254d78ce4a5f3",
+                    "0x2d7dae244b208b00f0cc46a3a847e1f3c8dddb110aa946cc043fe78bec3e847e",
+                    "0x1c964420335051f3c5739463b499b13f6e5a3f2222108aa8b5c8db3dcf19221d",
+                    "0xe40cc024af127ad4e339ea36fc80fe0525e6ce066d28923e58d87bc12f2bc24",
+                    "0x1cd18ec6be9b311b2557d20ef705772f505e80bc3ace661c03a15e47566a6996",
+                    "0x1665893e90455d0051192be58752deb39796f53bc3c83d95ad89656b3e3306fc",
+                    "0x2992bcd4e0206c45c1951430db07c8bd9603ae870ec542ca40eb5ef6292b70ae",
+                    "0x20216b38fef0bae1ac40ab6cecb40d1e810118356023844c2373bc7a6d805316",
+                    "0x2774a9084a9ac02cb62151b86301238388c83af8d1cd127e58feef92116738dc",
+                    "0xe3c2f4066f7e62e7ae163340876255c7eb33b6f454383802412600871387f7",
+                    "0x2a8e12c4437298d81d8940131c507c86247e2207d46d8fe9ef6937239d98434a",
+                    "0x5750e2fe3f37561cf708cd4238f9c813fc617eb85623fc7a03fa7c6984a8f6a",
+                    "0x223332f8a90bb9fdcf738672471747ff13b9c659afe07a25377834db3c7dbecc"
                 ]
             ]
         },
@@ -2451,26758 +2451,1032 @@
             },
             "expected": [
                 [
-                    "0x3022ce699d1633b4e8b3b4a93999caf475d3541bb74c5f9aa8dcfa765358e9d5",
-                    "0x2f142ff5bf47c3df074a4a3b943e4ff1cc5cc6941c634c8bdef5266606666b82",
-                    "0x8f0baa64dfb9fb415df2a40e651e4117310745034e944706415e92ac0fdf669",
-                    "0xc35735824fb4f1c9600e3138d02efae3a0a973b9b2f3207bff84c7577edb48e",
-                    "0x2ba200f5596637d09768755751c5955416486899e05f37b50a6654edd17400cf",
-                    "0x1c56321288be982a337a097b8a3f2f9a0530506b4f7abfa0ac46a83e0a4d1df3",
-                    "0xac9cdfdac25b1cfc22485947e28202f716b07dbf7a200a4c882666f864375b4",
-                    "0x2ae82ca893d2b7c3fa32a0a6edea68979672050421a1525df9866a7cacdf4e4d",
-                    "0x1b191a4ac4111e3b31fdd54fd61b04abab9be1ee75a9f31b612ee2d9376ce267",
-                    "0x24ff84f487eee5ce0917c1320f67eeab11aba99a4a02917081951a9027a9f1e7",
-                    "0x1638162347d3a02d166eccd3c60aef56199e283895b77ca24615642f88e60294",
-                    "0x231a777bb85d78a9e37184a1aac5da1a8ad9b7fcc02530c09d859473dba55813",
-                    "0x236ecd8c890a31440b83beea81a17b36c87d1b21c6ea04d68989eb6b0085bce2",
-                    "0x1eb8cfb8898f3f25440d509ec0cc1b1d2b97b1debf765a263616e23d17f198fa",
-                    "0x24e238cd271f8fb6a07cce93ce79b100e8c9665e50da49d1cd0c1c79613c6cd4",
-                    "0x288397734c1658df918b950a7a72511abbbadc9d9740f94b30452a16c9ec85ac",
-                    "0x2eb343c750ae4151e5ae3ecfca19a91a8b61eb92ddee8679a800e7711caaeb",
-                    "0x10f6a57a1379c9254ab5856398750784bb4e76592074f8c8879866f81c0d8505",
-                    "0x27afe8470b5c19943428c18cfc087bf90c3934308c4d26943085478f471c680",
-                    "0x10b25ee02eeba8c0a9873d654526faea39a2d944613bece6502a3d57ff3432d6",
-                    "0x4198eaf9ac9914701c19ca8f339417db02c5768f050cbf59da1d5e6e59fa2fb",
-                    "0x251732b9e4bc375cdb1d7368369aeac13d99f7f10246b75946ee05f952bdecde",
-                    "0xb108e3f37cc87365f09c4c590a71fc01870d62a537cfbb09ecb6f8895d3e797",
-                    "0x2d295891645a3c8750b25957b35145c82915eb9d923127ac26cc0e945f6e2360",
-                    "0x2584b504cf616e3cc8952147c076a32858e7a16970e3e39994c77cc0895f9976",
-                    "0x301688419e02bc37f82d247cbaff346425f772daa3fa769645353c9eada77b4b",
-                    "0x246e08d27d8386f04cd79d37c025513801a108e2d954164e7bb671029aa94333",
-                    "0x15c7c740d7560a7b17c636eaf74c608bb2d3ec9957cf0935eb623eae162c7d0e",
-                    "0x13d7e30201c1f406b38f3365658093346608e0b6e96e3eb22595b0117e094864",
-                    "0x1e0f6361c748d44fcbe2a8566af3708fa826d995f43ad6bf41ca7b3c23140db0",
-                    "0x1f03c6824aaa204a9e10aef8eb632799e4bcd82d110ff06e0b51344d792cc75b",
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-                    "0x388920bfe351eb56825596319ed27838755ec0d90fee707212a333fc21b15f6",
-                    "0x21bbd2805b52243570fc69640f9c483850245b7c0b743c6403990e7028862a74",
-                    "0x53dfb66d6b0837bf7c8fc79b329248c48ed1cdada94776f91ea4839fc82001b",
-                    "0x1882456dd82d98125e9f74aa277e1ed108ae71f009f57b57a5eb3643679a04d5",
-                    "0x16c9637dd19521bb11a55501c287a09bb93f137e24e10e1855549a3087ce6c53",
-                    "0x1a76afd24a5a10723a6a5a214f7f7fff27f01d05954ec6ad3c5bede57b311070",
-                    "0x149fdbee05528e2c8981e719ffd2796b77721fb216a94dcc8922077bfb44eec7",
-                    "0x2672734db237e115c05898f7900c6255db47b74f97203ca3b5c97a3a6e743114"
-                ]
-            ]
-        },
-        {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 11,
-                "logTwoBound": 7,
-                "maxNbElementsToHash": 10
-            },
-            "expected": [
-                [
-                    "0x10bda97fee75361285d4b64e2152dd95260cc37585c3601f85875ae3ccefcaad",
-                    "0x2716fab389ecf4bdf7936855537bdc85e53973266a9a3c57989e11f12ee5034e",
-                    "0x2e189e19c8c57b308fb5d535fb53e8e593988e11dd84cb7a9a23fb09c7674f7c",
-                    "0x272e021dcae6b5195946839598fcf94643a26dae0a1d8e9757d4d33ed313d952",
-                    "0x624c2efa46d355b8ef21730aab085c065c505ecaf0d5e0fd8be374c454f5ba4",
-                    "0x14dd8185aa7998b5c071637c1a04489d09d41d7f5a730d1dd44a4e520ed95fb3",
-                    "0xf8bcb22d4007ebdb6f0e15ed608158874b4cb4c59463259e4177a9f79e71d8a",
-                    "0x147ded4a22b77a26b6b1c780ebb62ccdbfc559f526fbb95e9d4be6c98ddb70dd",
-                    "0xd5dc9a211aedb6f1730c41e66fb52fc374cee2e6040878e560dd5bf899b3ad7",
-                    "0x2a28717c6c8ddae9da1e3e21a300f0898a7f9d49700de3256e7e411b98bdbeab",
-                    "0x2b814367b65613a104375a67fab75ac977eefa150cd9e36735393c11389ba2b8",
-                    "0x179af8793935aff6ef74eda6d005dcf86d0c263c7661ba62133a7ce65c2b543c",
-                    "0xec0bbc4f03e3b1e216beacd2a4d06773ecbced5e49c377611dd31a7bfee635f",
-                    "0x14d5be40569ec2a85ad4d8a7970a791503fc1793b0b90139afbbb70bc3b39bcd",
-                    "0x77db4a8563e7abadf408c8c1fcc8e338e7adbc67654716cc730493530db617b",
-                    "0x1160d118da3c9db53ea9bafc629d51570195a648d6f5fcd15f0faa194d0b9ab5",
-                    "0x15ee42dae2c167ee87974bca033dac5ae6744956863158d3fec134e343dead75",
-                    "0x1b6e2ec6dc78b3da8803193b2eedc10ea386b3d3efa555c5e4af9ea0d2162b8",
-                    "0x2b352141e64b23f6b1fe74ea94109d5d786c75c51f82149333daa215baa28ed3",
-                    "0x1957ec1e01eadac0337c8e4efd165adc1ba2418f4c63a999144ab7faab8d492d",
-                    "0x10013af5f9e38afa053db02b96d3c9c19a003f26e0cf2d6fd4867edc5be551e3",
-                    "0x1d9411521c63a437ef834538fa5bf16c4ccb4b468f0b5bd55107eac99d201a89",
-                    "0x27774b441394de2741144e9723164c233d086eafbe0d4adcb8215ade2ee78a96",
-                    "0x6ee16aa0791ee035ccacb989a5f8221aa0f1b6600920d8e9d375e8f679572d0",
-                    "0x1fc5066e972c6e4bd77a51c5b6736d2f33afdbba58b2387ec2be7ce87774f9c4",
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-                    "0x93a38d6f0c00c3e9a463b8bb87c484872bc181bc399ad986dd556f9c2ed44fe",
-                    "0xa7a0b884e46500fcaf9b54e936b37ec31289386c6437d1a97809259a49b977c",
-                    "0x3c8b9329cf5535c7fc8ff98ec66e3fd9bca3af6f9859167a14f969c5f855eb2",
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+                    "0xbac040ba5df880b66e09a540ff431a91f46babadad94e8f72a99548ab7a46ef",
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+                    "0xf195045649506daf08d749b843bd08455a08aac4f24a298ce75e4ee429023a7",
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+                    "0x13cd127a0e82e4c25560ec16be52fc473a604a35929828241428e61292c2d27d",
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+                    "0x19999b37599c47295c323c913e5b569ac3e50e4376a4b7a3edf7873d9ab6d7ef",
+                    "0x150c4c99202340f22629174a6285b220cac46ae780705e6fe63b7312c63f0ac7",
+                    "0xa679f2ce01c9b9aac54b2063670f4ae3ffc576fc68d8e5ef3d188e364b084db",
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+                    "0x97d72063cbab4990ce711161df1f39adbd45e9a4cc03a2e780f066c7f3c890e",
+                    "0x1e7c6374656d9891f636591af2f6c2a50721b621deeb80292b705a585eb0dace",
+                    "0xda50eeb3bd1a57f204483ef597eb9e3991142a9f55b893bdcaa35d6ed0f6bc1",
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+                    "0x26c827269206daef3ae786aa6a29004d018ec7445f95f17b6f5ef7c8338846ee",
+                    "0x11e3c3f81d68302b7bda591a3778e7d726ceebb0990bb2f80a3b9a86a85ef3ed",
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+                    "0x21cf9b8885319fb8904b37225ef47a7a2ef4b5aa63691a29d710cc5beb70af49",
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+                    "0x21fc1abf5a0145a75897fa2632fe073d74e95a90c0cfb7f12c87d4211e995daf",
+                    "0x125d236d7a7a64179177c476a080df81652512e59d15b667c0d338696b9fff93",
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+                    "0xe8ecc2608479dad9ae2a3db35ea089a0b0dfd02ecf6efeb517184dc5c81d4b3",
+                    "0x7fbe0ac06340d6d5bff9cbbaf41b768f0d45298c99735ef7221909ef11e6959",
+                    "0x109835e60ea855d0d0271a7e5070c14888092c0fde6c666b6d85ebd9ae29e00",
+                    "0x2597f1c3648a766b068c47f2bf223f4fd6e1f06e8026b64f8ebc9a64cd9c151b",
+                    "0x205edf522bfccfcef0c4fa9999a7e7add207eee2e948cfb570fc9961ac798bad",
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+                    "0xe81173cac4209ec0ec24431da813da235f32e10f7d50caee5be1c494e2c691d",
+                    "0x6d4c8898633658907dd7a65f1d29ab1b6824951f99b18e8f1950cfd3ece12c3",
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+                    "0x12495f94c1937b81159c7da4e56b9ebdd6920424e5cf49b10ab9cf067740b90c",
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+                    "0x12b56dc287f969093ddd0ea1dd869238c0889b31bd304b1e302e8677018126db",
+                    "0x186c086833a4958b4a8cb6bb2bc0bafd411266a09ac2e79bb4ace8b7cbdc584",
+                    "0x1d19edcd4e1fcdd90d30fce6ad82bc55eff7a2ad16ad013e046f82eb6dec59a0",
+                    "0xecabc6f2686f673725d05fca2314f27f1b9014f05588d08db00b2e70b1928d4",
+                    "0x10520cf0d86092239bf0f6497c6e122eed559288d93abf400ede67b934e87d84",
+                    "0xc347276fc2a8adff5223997dcb092f94dad3142d9a935b592b57d1254615d55",
+                    "0x2936feca499a70848f561041ce21757fcfbe812da0b1eae40ef362d8c155b70a",
+                    "0x54a1c7967970a3082c6da64ce3f00ae052d5ffb96e6570f1f326752218fb121",
+                    "0x12e48f6e6471eecb2eb069e0de884cc4e1bc353d6c9e77e15001c7b3489d7e81",
+                    "0xe79308ca3a3c576d20bb719c45220e2635a4da3919d79ff7eb10e1724841847",
+                    "0x1984907b77018c1df38e5459eeed9e5974e5a6957b547a5382a3fab314201110",
+                    "0x2cbfaa24c96b650769d4490356c417f43f835bd40e118aa705aa66954ce5c521",
+                    "0xf3fa491b33a6fa1db33c2e300c75e975eb3d8b865e1fd73118efc16ae29495f",
+                    "0x2e7e601dcae2905eb271e96d6ffb2529527f7c4b1439015695fe77b37dea8d41",
+                    "0x1e9383eee41f76ed4d2d3bb20d62bec1d64155a2e66bae3232509c8bd6906115",
+                    "0x287dfb3e6a5fe0f4693808d7bd4930a5c62bab6ec53e67a7c9abec4345316e7f",
+                    "0x44df91cfc001ac3ea80c6ed8158e12d217262a9a63648a47c796d03e111962a",
+                    "0x2d36c09ec2f2a56c84d2f817840a998689f260f12e23d53e4e16b283b6b02264",
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+                    "0xe532ab096b9df07ac708542676d3865208409d1480a8c563635104551204e9e",
+                    "0x1f290d97dae263fda4fe5359bdfb37547dfa6a8ef491abfb24d1d7f66909f430",
+                    "0x204d5e288febd9cde2c999de9ef58f6b7467530e6f123089d909f18e03611323",
+                    "0x178acd10fa67b12af2dffb0dcdac8aadb82db0bb91eca2416fc41c1d32044b8b",
+                    "0xf3ba1bc7c4044972ba208a4f18bf963cf7a45db90e141d439febce7003b8059",
+                    "0x84586b62b6a772bab0c8ebe3d211fc5151a03b920959add20202621b99175",
+                    "0x6239e7973892f891249e33c20f20c9c9f9101f1e37fd8a288d6f4990bc0ba69",
+                    "0x2c8f0cc53645bc12c3e1f86de78e08d92120eebecafd3a07ca1bdd8e75f4e3c1",
+                    "0x1b97cda2bfa3e47a5513d0b3e72adbecc7304c8c952e215a12e8728dcfe58975",
+                    "0x7b56eeddc55e4a39b77750db4ec954d22038729623ac7fe6dbf0b2ec96d51f0",
+                    "0x2d784448ab6897d5151486318cac12bbfec40706731e88534b7e3b31752620c5",
+                    "0x1671dafe02ed06446cbc679bd1e194f5203636a0fcca0b178f269a77555b9211",
+                    "0x157d95505dfa9fdec8dd6742dd7915ac3e252b87a3987b615cc6fae51f987b98",
+                    "0x18bcd8b28985fc57de6ab243039b218f1e0d40d00b87a5e6f05d058802cf1479",
+                    "0x2d28fa2e61176ca9ee4adb072b2cbda113d58f9e1d5ab45955086d6667297a87",
+                    "0x210e8a99ffb0002110d32c137d3976e05a2c1daf2f8df4b2b1c0cf477389317d",
+                    "0x59a2661b6ea1253613feabb7654229af5834858cd24abb44a059820c04d98e2",
+                    "0x1c086b5c99f3148e9c67ab50cfdcd031d6c98b2106eae4f22d6c97d501ef8c10",
+                    "0x87aa736a2aa9e5f77b30fdc0ab5ad36ee48b17f41aa0eb3ec82c9acfaf43ffb",
+                    "0xe9b06aa7b82bf6e5930e39a2f3a5f8d01b2f49334f4e97468d891c0d9e144ed",
+                    "0xbaabea808c2152e261389f1628f75e7f81132e7ec1ca645d6e395d621e16756",
+                    "0x107bc1f248cde39fa57f59916afd2addb42eb5c3bcdba928d4f8a24e491a5bfc",
+                    "0x162d03a264ab6be23611ebd950e9ce707d88e2c29d24b22408cf886a923d6acc",
+                    "0xae1a34f8acb24aacd6128e1d27daf0b6ca66a28b16eb570676ab9ce76f4f02f",
+                    "0x1b2fb8009f1d5f6b5342ddfa46ddf5b77612b8227550b1c234fce95f5b1803f0",
+                    "0x53805de70f31a0d9eb051694e3a18dd8a4b337e06a2180ae243dace3b5785a7",
+                    "0x2821c1735c3613299f8ac4df6068b0cc6d6aef4ea76c6a38bb43a62f671f9382",
+                    "0x30370796895548adfc3505d4bca73aa1c621299b66a19f8d9cc6b9f30cea3938",
+                    "0x1c9cb64df8055234202c1a41459f53299dfc4f92a0065e745821fc074f574ebb",
+                    "0xe7cfa4c0c9ab97edbf3275113e5ea584d450fe91f3bd52454c1e1ab018c85f5",
+                    "0x35711e89f73ef10e1ace61b09e5c9f80b3876e37389d1e2143e02cb0ba65670",
+                    "0xc7a644778e2bd8dba9bda623ea1dda3f8ca012f4ace05d3231d46ea8391efa1",
+                    "0x2d32435720ff9625cee466bbc65f70f2f8726a0d209a59467c33c2af245cc24d",
+                    "0x1585962ce9806533b8a6c874c69194ce8f4b88cfef2b0dcb7fffccdd3331b049",
+                    "0x2b6fd5767a4a76134317b223c5db265f7578945fce493e92050b775cb476b0",
+                    "0x261c2222551c8e5ad169e37667dde79392dd646275fd2fd2f65b659144cd6457",
+                    "0x20080496cc06840ad58622eaa4880346a9d06f61081c18dbb8f43567c5b3e418",
+                    "0x12804ed63128180f6edfc3803b2293c6d4242033acc053a39d05459df5c0dbaf",
+                    "0x11ad8752842f48a914f21310f6e8496a89b19c9ec8b6764e4ad715c0a352ed06",
+                    "0x1dc9dc78d428ee1a64b0abb7bf035483b0e32e174697bed3cefb200dbee96aeb",
+                    "0x83ed70baa4c140c0d387243b493db10d82425a317c865cc2cfe8992971ec31",
+                    "0x16e3d91010a656574e45eba6b9d35938ea9b9f7c46fe59c115ddaeb958732d63",
+                    "0x95d672fa94d5be885b5e9f4ace191e5fc53a3c5d64d1c8f9973ac605f3cf9db",
+                    "0x23aefc9377d4dd737c65bae859e9c8ebae0ade358f24f6c3d8f5e0bf4e73bc1",
+                    "0xab79be4aa51240da8680f4ba15a7f9c62126528ba352458435b8010e0911d31",
+                    "0x2690ff66edab13690d2b4dbee0e3606d453bffbcb0833c8c7985425bc5c7a6e3"
+                ]
+            ]
+        },
+        {
+            "params": {
+                "seed": 5,
+                "logTwoDegree": 11,
+                "logTwoBound": 7,
+                "maxNbElementsToHash": 10
+            },
+            "expected": [
+                [
+                    "0x305890103a90a06f4bdf5d860c4eed863ff8cd0b65fed337281d2ddec80e0e4d",
+                    "0x1c6da82890c4cd3564c4f9844d6d46ccb91090122f7328491a60f79895119d33",
+                    "0x8d97c596607dfb45ed45d24fee686e43e74eee790031b69b51e92b7dc9d682b",
+                    "0x238db799e3110e08f75baaae69cc2758808c4cd18a153290b2f97c5ef1570c37",
+                    "0x2ae20d68b0f8cc9a2b1a23bd6d15841e02155871b0d24423671bcf3f7bbd7ca3",
+                    "0xc3c0b22a82a7b03d023151f67b27e33de54615e784bcc787e3323c363ea485d",
+                    "0x24616427e5c338a09271c49bf4406efd581ae3bdec490220ef995d3337712ab2",
+                    "0x11a35f1817af04135b5c64df486c0ab8c4c00ab11b2a48ad22fedab2a8df18a3",
+                    "0x3637eedbf71830e740d53a32d72c94052dd6986362d9be1055fba8ac4de52cd",
+                    "0x12285bdf02c084df13779da1804a1e661fd559a8a57d2d8655ee6b5215fc0eb3",
+                    "0x2e7cbabcc3ede62d261173a08693604b6de972d4c0bcb08363588d3d5990ddd2",
+                    "0x27c8ed86c1752df7fcb729c19d2d58c667e6ba414865cdc1b6460899404922e5",
+                    "0x294b1d128c6d18b15e0f66d14f9841a8a672c75c880a9c7f1bada23450d7a841",
+                    "0xd1c4c03e2f210effe747166ce8b75aad1334ca799014b6e06ec76a4a103d462",
+                    "0x8b0acc6eb9cb17b4a81943ed31a2b24c1dcbe99d09288ba3cbdf5602b7025af",
+                    "0x1824f827b15199ebad7890541a867b3ff21e4e85f8c896fc7995d0b9dd746ebc",
+                    "0x1afe5ea364f012c184966c237d704c10005e01d5ef74f5dd2a7b09307d9500ed",
+                    "0x1391480d6d461cdd3b02b5363d87c3e5606ae9b77acb1f1624ef0785175c3f70",
+                    "0x2ff8bbad8bc8801f89a064a292c6139efd2b9bc31dba4b797828b40e9293c84d",
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+                    "0x20bc8c2cfa5e14bb2f79a76b2a13bfa69d5df7bf7d204ff3fb04b44e4dd401dd",
+                    "0x30307a21086bfc8b0ee4309f684bd799d9ab05af894e497f09ee64ed416b1aae",
+                    "0x300b95230feac01e9246cd38ac1f763dae73b05b0569ffd1b8ef0a4cb5e08774",
+                    "0x2b03367f8573ce94566e2f489959c355358174b51c3c0b1ce4b50ff9b6582a5",
+                    "0x1714017bbb4075977dde5057e8c1f204cb090f39c17b2b461ce29427e7edb0fa",
+                    "0xb0bbae77b69954ff37d50278399feacae53914322a2a5244a2ecd0fa8e6856d",
+                    "0x2183c163c4301e912330dc7de7c9d1d1e13ba49c546419937b00699d2629b84a",
+                    "0x13bb09bce303ceaa60c498cc6f4ea9b1d1272d6cc4e2c04220d3618336d1f8e0",
+                    "0x2ef746353d52375cbb08a539999c8ccb6712dfdb6a8322f37d195f884ada38e7",
+                    "0x1d9a102f7a648ab3ea444915f2324aa8ae356834bbf1c445aa92e52ac87becb9",
+                    "0x21864799c96a69793c4dbca52d1420bae8694bb1615c689364dce6533c793a4c",
+                    "0x8f7e0639e280125e0b85ac2406233aaba1fddf6ec0286a7092f679ffaf87dcf",
+                    "0x2d097e1d61bec53c3d13bf1d01f29280a00b9b06210bdec3f12dedf040dbb3b7",
+                    "0x1d30adcfd1e5deeedc9f0787f1ebe0b5c6f5980a142ccc8c1cee5f79ff8a73ea",
+                    "0x22127ab3b6ca69250f044618e74d5534a9d9bcd10eaaea62c8abe5a5a3fc63bc",
+                    "0x1592250b7a60b96fba7cfc114a74928fc9cfff94c973047bf84337a5ec7d1120",
+                    "0x3fc334f665d7655ff8a637a526dd960c478b50248db6df6b6d42a45362a9fbe",
+                    "0x19206c80edd5e6629998daa397f643155425e4ffbf6c823bce7167229faa3b94",
+                    "0x29c2e48485fcddcf31f09deac065630fbba14f7dc0e0959fd453497f275711d4",
+                    "0x47d7e8230deef165d4cb8bc353ff861269af0862c7f3cb2c989923d3e8138f4",
+                    "0x8b71c8b5f9ba1f75549bcc1b8bbbda33294991f2a95143054f8ac33f6c24bd0",
+                    "0x1db2f168843c83bc40d96890ca15e1182b5d7538dfeaa54b4c7e6991b2f37429",
+                    "0x2cb88a8239eb440b14921ab2e9187dcb24c6488c6b5223b4e018d44802d2157d",
+                    "0x1f77147af0ae1d23c2abd4b8fa13bfdb2edbd10d782df6b30abb36391a583b95",
+                    "0x5468188dcecdd5a0e6b172b2e79ea384473b6279309e401817f87a1f96807bd",
+                    "0x1d02063f1b4008f6fc65910910508ec6d1623d257956f5c0ea3f50e000d586d0",
+                    "0x25e26c7e91616c31883bb0a819257fb70a1cfc7eba7792abc700c4391d17718b",
+                    "0x130f5c1e848eae0aa54fe0152fd4f1c21d3432bc9fe29229e8ce482f79b02401",
+                    "0x21f8a3f6180237d1d55792c9a8a8d9552fab75c964d6b2b61388d520fe47504",
+                    "0x179c9a1cfc5ba924afefdc2d1a79cee540e8c8a7ff369259518c7b4e7863de9",
+                    "0x179e87b247e2b0ce7bbcc39b48c0950c0849a02e6a3aac728b75729372a16d2d",
+                    "0x128d51ae2aaff5f1f0b31b8262eb224c73bdf128c87fa90b597c23bda686caae",
+                    "0x150c61e9a24a9b67efb6fafd212ee2c94a82a3da9e00eefd6b5b5be19ce284cd",
+                    "0x128c9e0adae6758d090dfe081d72ba6192e9ef9f6fa10a384f0feb53f79046ef",
+                    "0xae310216f4dc62e210670cde4074911a1b85a8156a6a42bd69d1dd9c57055d2",
+                    "0x1483030d95bfe8cd221d5d7e0d769402e3cbb67b3f01313557b84885da55247",
+                    "0x23d27c497c105035d2841e5d558e5f730faf9a355137341fad34a96a73dcf872",
+                    "0x4130e12df9868de67b0358f03578d556f2835eba523588adfe361421cec9858",
+                    "0x3000d899d7af607ba98cb7ec6e63b7d2c9e7e052fa19f301bebce497c8027b79",
+                    "0x21e1c7031c57c035b89b5c62f1f9afef456add2760f0e3d10310b3eaa6b69e96",
+                    "0x21f46f4fe2d9db0c7838720d24202f37af0cdb7775685d86025976e7f1a55170",
+                    "0x1dc731c201a9168ff1e7973e760ba586c7ddcb9a2509db02c126ac817f2ffa9f",
+                    "0x146dd3007bdff4843b5b597a28ee19ba3951d37877bae30e22f822421dfaddb3",
+                    "0x14e1bb08926f811999a058954fbc1fad0100e2dd53e22244f36f48c6245c6d17",
+                    "0x1040512ce7f387fd7cc5cf7e7c9814548630ab64e37875614a441d39d7fa754",
+                    "0x81daea3e5fa6b31f8464aa0471507ded290683384b746b367580640ca32e9bb",
+                    "0x215ff600a2e0fdecde0122b1b8399ebe388de13a4ee0713ea11085c8fda3fe5d",
+                    "0x3dcb1b8447f8885a26b59907267a43343975b8ed06186130112f5faea89d4b5",
+                    "0xa5a69133139811c14300c9c405793797d82cf469173c8efe2e021a1921abdc4",
+                    "0x2e63c23e6a455e1bd20461faff2157ff89c217b5f4414b9223a83d4ecc20f462",
+                    "0x65bc0ce74c88a8b1ff739262d7afc045821e93d9b748fe66f4facfb0aa4bd26",
+                    "0x16340f1d0335acb899cee857c950b543b293b8af65c1a709a5dfb6f997449942",
+                    "0x27075570976d1a1984d82cd9fba309897f5afa469a40ed250d152bbc58e5d10c",
+                    "0x63a7ddd0219cab9b107fbc2562b085b9c4400e2b50b085a98c71a32cdba6035",
+                    "0x6a519bdfccf373ca36aeb382afb6241381f3561eda3bbcdd4fd516d7c4fa2f3",
+                    "0xbc609716e6ef7d98b28bf2555ed1e8fa1268881aaa7782889705deeacd57651",
+                    "0x2306f1c8058f1cfa90ce7febf1966211f1ce994680b786add8e956fdee1bd674",
+                    "0x22db425a8f5cbd5172fc4e18d959e687ff5d004edd4f2e103f421188df0a843f",
+                    "0xc4779364c73487f310415c2c4ecc903b2fcd12bcd0409727ba43d037f13e83a",
+                    "0x1654580d9c622b2280aef09ab4f9bd4902dd490f24453b73f413f004c8dfa8c8",
+                    "0x737684abcb73a97b8743ef79b56b529f98ba04577e3ba2bf5a9e9bb4d3d978",
+                    "0x242e79fd9ae580e668e7894d075c0abe95921e4e0c8af8d6f7e47af81c9b3fb4"
+                ]
+            ]
+        },
+        {
+            "params": {
+                "seed": 5,
+                "logTwoDegree": 12,
+                "logTwoBound": 7,
+                "maxNbElementsToHash": 10
+            },
+            "expected": [
+                [
+                    "0x262979080b1e153f76f52e84d7c99902b5030ce1f80d0d8ce5b24e81f83ee272",
+                    "0x1d0189f77dd34751b2a73ceab6356ebfb73fbd22893db53078ff8ab125fecb2f",
+                    "0x233768149d9b6030921485a6149c2b197368fee71be66d8514cc1e6ceaa21b6d",
+                    "0xa0bc65b2f258cb07773a356ee008dc3fa9d6984542b8cfdc66aa67e4c5d9d52",
+                    "0x1c55a49aed48797e6f1e8f2ad8a4a371838749d5cc9d615f9f613a1c91c33813",
+                    "0x1b037a57cf4dbcdabf291bd6d7772029c26f69f73e86d7d652d256062b8d1b08",
+                    "0x190ec066e990609f2e20ffcb0eb17e53e3441251bd209b21b51d08ca5e93847c",
+                    "0x2493f4ec82707e67e3ffe3b9c1f869f38a24fd835b7a4b8665f51fc1a32b6b92",
+                    "0x2462a1a73dc6bb711d37bb666405b841ba28f10c57d551a791199dcac51df4e1",
+                    "0x24917a24e50a0f05b0d1f20174214381880801297a6df6ad871c9d0f5d91b64e",
+                    "0x172e7c042c891c7081356314d3ba47118ae1452528b3536207cd098b2ddf10f7",
+                    "0xf76fab95cc6deb14632a0c5930c9d762dc16abd1e3f92af444b49263eb5893b",
+                    "0x1ac1969e1f4ca2843b2198cc5a38ab761ed084e8cba30b25e57c8b7fc4098231",
+                    "0x24a24b6ca97233afd2b1ac33cb8c762d0100ccac98f28c31e710f05f35979fd2",
+                    "0x2d1a14ae8beb38c0a9ef85170f932e539efbb3a84f31fbea8c1624ea94fdec73",
+                    "0x1a90a2aa1ffd28c461cdbd963f0f5edb842ca689ed0edc0ced50eb82c4606148",
+                    "0x12b49e794f83d909b0c858c5625499b7758b56edf524b3c600b4a8ae80c98508",
+                    "0xb2fe7d9d8480100ccf3e19c0e366e89bb5f06cac2dca7b24e5440c6b6d79ab3",
+                    "0x1c7b63a374c01d7f7c0bb844d36e757632a6bc883d43ee263307ce4e5c237450",
+                    "0x179da018c9328327376d5b634f08c409aa4349a89fc676a15c8251befbd724c6",
+                    "0x2f9439f4dc175ad24b590f52064fc38ed38f50f015be28b06d46c9dd88d26baa",
+                    "0x92aff8a1501c03738d260af8601e38058374a97fd6885efb2ed500824de601b",
+                    "0x91fef18e7f57cc26c33b840362b9f74ae8ea156ddba168b3b6d36fd11add3ee",
+                    "0x39a47cb9b51a891c925b3074128c6854a279ee489a604fc9a223a18b1197adf",
+                    "0x5c60bc146929ce870cb7ecd9ef82ca454509883316557dc1198e0559dc0a63a",
+                    "0x2778cbdd22b584e8067d55281952659b8a4996bc5294d917bcc7d37825a65859",
+                    "0xd2de0bcefeb8c92eb51edec5bd3047f5490ade666e57cd558bb0ed97e32768e",
+                    "0x127a7cdf5b41b0094f98a92a5fd1de2ffcf2e8e85a5b5d5d6993e18836882e1f",
+                    "0x4d7a9e75a04feed1d3671b5505bd9def9c064909f03f387af28986a0932c911",
+                    "0x29ca851569378a9d167a8a13bd7c7e85855801fe0e98160c7f524b515b7d6371",
+                    "0x25eb644318c31ca474b1eabc12fc3066c222747e80fe7479f15ac3a3ab3d5d8",
+                    "0x2ff53e09b754edc9023cdfe4001bab836358b1b15357ce08d70b63ddfbb5fbd9",
+                    "0xe5bd99f5e8b68bd7522062773aaa8acad2603c13a414c0e4f0e4315e34d51ae",
+                    "0x1279d92fb374d2e11730c7acb7356434c8dc7334abcbc1f977baeb518f31f3a2",
+                    "0x43c7bc54b1aca471e6603f7ae8b21dad42cf8cc62c06ba66712e4e56b01256f",
+                    "0xbb106ce60eaf84462231298bb1da7a3a2ef48ed6a1aad8c995e99fd7c55479e",
+                    "0x1040dccb01658f67ff132f36822bf55b53cb77753fb7fe948f236f6c3e3662f7",
+                    "0x181fb45d91216b5b6fe088d70daea8700edb84d49d9a5f3a61c64803a6562a50",
+                    "0x4f49a7b994d507a66c5156b6df8e151527fbd2d37134896e932a26c81fa293c",
+                    "0x16de63ea60d1f815e0cd5e37a68c18e6f7abe9a26f9f6d18961595e8a8394a13",
+                    "0x1089dd4a71f4d47a235017434ff630f9aee5595b02415e82c90417ef414773e6",
+                    "0x25b631522b500a3915c5fe0c64b0b1414adbed9d08e3ef623d41103973333946",
+                    "0xd31f0c0653aff3d093e84e2dd9868fe7b2daf2fa984a004c886a0434952ecc4",
+                    "0x299fa56afbf786a74835edf66a93ee1445c3089f0f04efacd6ae8afcffea7882",
+                    "0x54f2ec8270fdd725deecd1d3dd8d7cd4c2ec962b55798ba1c264647470c613",
+                    "0xfc47aeb9adae8e27187d155de86b0a6fc3f7860b034f6d73151ca1d7d1332f0",
+                    "0x2529f0875f716b4994488eddb2158db4b62d9ec07b323b8d13aae3788368fb36",
+                    "0x26bce93221dc34ef8c1e34389aac75bae165d3b3d9450471f2388ed0710cf296",
+                    "0xbe660cc8e9882517c8265434a407252a19f5cc75a7a6006c9f2f580812bbfc9",
+                    "0x2bc053a65060811bf41a0adf2150747a0561018572b20e7ce584625654c53d11",
+                    "0x29c184685342a254abf3c19f0d4393f678dec5a83b457e84bdb88cd90beaef0",
+                    "0x1a969e149366be4b1504af2fd73f115c2e38514b40a6a74f0a2af45a3d2a31d2",
+                    "0x297ba68c666666c41cd0b35b24a0bfd51fbd7cf6cca1ce8c9441716007dc4573",
+                    "0x2335f75d2541e3e05693788e98b9430311dd8609656b9a33b92e41dfd3a74a5b",
+                    "0x2a585a69b819d4d2e854c897f06ad1c1aa963255020b2e1f86897aaa389452bd",
+                    "0x80e6b553a8cc54350ae7bf347659a46ad8b024a2e20cfe12ad1d0cb111e13f3",
+                    "0x96eaeaed8d10f0049330ff5666028aaf9e36423ce65a986ded131906c1f046f",
+                    "0x414503d958d2163b27747907a685f296c1718f28a5e97363d084a8ab2ed2d9f",
+                    "0x125333024deee23257e23dc4258a4e72b8d9878f2b3253c33adee2eeee61f707",
+                    "0x1544179699dd439a63f4e6b3674b698f4be4776797a663242d35a750256ca2ff",
+                    "0x78856988d6b7be993c76639a2bee030996e26dccfda4e3003397a4e56a0201a",
+                    "0x2b8804e56f84ff9920d7952ccf4a6e2247a608e99eef1f099818ef602cf102ba",
+                    "0xda285034380486d9a1f62b2c4c5b0ae378cccb90c41ec13639975caeb4f639d",
+                    "0xe37697379572a630b37f3260a384e7fcc200ae38c04d0c26c107569028e5f6e",
+                    "0xacd7847f98d6e64e0607583d9ecd887e09f4a151acb8d1e45b743550aac8b59",
+                    "0x2e2793d7df5827ead5b713679d1fadb54e646a6b01e9a57db4ca36034bfcaa03",
+                    "0x846891ff149bb589f035a2b9e0a72b3ceb391d11b7687e6bc5a1b825a431aae",
+                    "0x16a2e9e1d4eebfe94d24f20dd6efefa48b275647631049090f68c203529fa876",
+                    "0x25e2b266f534edcad3dc6e69befc06fe288471b856db794d89a2d9c59ca69f86",
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+                    "0xcd9b0ec49ca43c675b6c0b295423c72e6b007a7016ad25652b8561b4e6a01e2",
+                    "0x21ccfa93e229eee5de4c62d6a77380d9019e902c4beb5701773dd5ebfb05ee05",
+                    "0x22059cab80c3dc8f5af0bcd8c9ab5a64644f9977037878b2d9fb2268efe4954a",
+                    "0x44a21a139ce3ca7e73d0cf41ff15ad6000e98b4ad510413196e582021d71500",
+                    "0x5fb4fd78a2fa4000a01e2cad9d3b75a47c0a9cd37b7e5c9b2d0157ce95624b",
+                    "0xdae3817a063ff347a262eca90ada7b114efb54fe56894f493a0f8bfa4042ed9",
+                    "0x28673d1d16550fa189bcf4984e6100cbc86d92baa832fff457977c21c67f0b45",
+                    "0x1944e87ab84f5c4dfdc828082be954faa1e3512bb2180ed46482cbb1fa771739",
+                    "0x245a2ec16681648ed8921d7de5cf2f92da444fb6c2a924608d53179faa769208",
+                    "0x36e92c46c29c5cfdc2d6a6691b7d48a8bf6b3466dbab33267558f7900a7c008",
+                    "0x2e13f587b69472503a13ec01ed09142915fc3a5b3b3019875823895c7cac67fc",
+                    "0x2ec8578b9fb84503a2e961da085075a860c11cad87618fbc5fba9b8fc31a6f24",
+                    "0xe0b06b86430540dd7ac3a1cb52c39466c20663c2cf9be67cda838b63bcbe74f",
+                    "0x22d2a56c8c395cf502a68bf8727ea91447cf3b7dffe9c9eeb28630fc7837ebb3",
+                    "0xb7900caf5871894e8a22545d60d50dcca4f54e352b5a75bd23a5d41b5debc14",
+                    "0x1ed00bc1d7b90d33d86ec865adaee7e8a80ed796482a37a08eb44eb7975abf9f",
+                    "0xb331cf3edcce5f25787730b8a094149e9493566b3870613af14e982c4ce1556",
+                    "0x21b964c0cc7d5e7628a7d07f67f21382574d4463b04861952559f4bfe462c665",
+                    "0x12c87ce30b817ee601d6258d5dec00f51913b29ee97538f156c4b6d8d0a98d15",
+                    "0x1d63c257b188c4ace7e5da08195e584be093d886962c99ba9c18d4aee4782869",
+                    "0xbc8dafd12870fcfb99e0bc96e5287ee76c65549eb3bc743ed802d56391f055b",
+                    "0x2a5b188afffb06830b271dd562424911b0dd2002353d850d855aff5174cf92d9",
+                    "0xdd3816af2caae3b889dc84ae508f6125c8926c7c650cc6e8b9f20c2d9388a69",
+                    "0x1fe21c35e3983b91ac73c222ed8a94fe96e63b513a4b4b8217ed16e07a40da19",
+                    "0x256511ec8c5cad455f9a725f9e5cd06c3c1c097a78faae48b4dce2ff720ecab8",
+                    "0x1ec7e90f35a1817bb934ac62c795208768832231f5a8d4bd48991e43b3ad9dde",
+                    "0x18e9cb13eef395e8c713e09ae21e89dcac0dd2ed554f49777db1c5e52aeffe78",
+                    "0x122ae704f38513ad407b5af1feb3e67e8741197c01b93fc9563d9a1bb0adc12",
+                    "0x20c1e31b067b3928cdf4b0f9589f81ee99b1a73682c25b5b5a07d19904815ca9",
+                    "0x101447ff22d9335af9603b611d4350dd669830dc61dbcf2824685ed2fb082037",
+                    "0x106f8766691948f513ce1f89764ba83fdb8884486e1dd227b08296ce5a47d572",
+                    "0x19ae7efbc64b4afd73348a78d0569ea64e55072355bb05daa1c242643e0f73c3",
+                    "0x72c0941bb612caddbfaa8c252ee839be123aa3ba3772a9b97c267e6cc58941",
+                    "0x238d13b7b8fdefaea4820d5bee6453455263b7825faa430a54e39af92dd9096d",
+                    "0x4da51b8d5608a1ee6c53f95718239d10d214d1dba91aeac56fd3de5c0b0035",
+                    "0x10d209b10b68fb1e02ad46bcc48ce152fae866f923953c4719cd73846a5a98d5",
+                    "0x12c9739b128d45ac6a7981d0839acf9b9953692d9ef067371fe66bbea3a15e35",
+                    "0x6d539a5e1a76a45cc05c7f74ff48a34728ad241af4dae2de22a0fe353d4eceb",
+                    "0x1ad3b282678cc8095e4ef59ed19dedf7637ab1ac091c232ff48fba69144f151d",
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@@ -31177,41048 +70059,2130 @@
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-                    "0x108c5a07c05d72d63b4281debefddf8f11b532ee8f6c537630a750ef5560ad0b",
-                    "0x87704bc83132eb680cb4c6ba35206ce1cd99a67b5686a32afe651936e22472c",
-                    "0x9670250bcf007bdcf9182e401005349d604f6d3fc3789c68f63fb46769c4815",
-                    "0x3cdf960ac7369d555be3c473a05c51e8cf408f32cb2261a2956a9bf15fbcf46",
-                    "0x2b5196042302f2675ce068e3f5744d056658a9eddbb722bf303b921b81283a29",
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-                    "0x192a042328197c1bb3eae002589087536b484938fa6f2832f27075066b77db",
-                    "0x116cd44e7fa0f00ab90f59e27a3b5d1b1ba7843da6a81ca90a22a8d742abd67a",
-                    "0x34ed7738e8cb1a42628f24002db8fca9ac0c64f9afb5e93fa26becbabe18b03",
-                    "0x6796980e98fb6f838b27a58bf402c3ec359eb1951aa9cbe2a05db320e936722",
-                    "0x2aa8812d2e9a14c950f301377441db57ca5ad0c2cd1db373f4feb1d85903b043",
-                    "0x11e3db1f3d83d5bdf48806836c685802dcf49e88f331edd402480b05522b760",
-                    "0x2f9f4945307a09cf7683ca474da016c5e4bbe43979f983a58e2a09b8259bd438",
-                    "0x165b93520caf1fb63109aed908f979fffc09242d50b58df4824983edf277f0cd",
-                    "0x15b9a919f4101b94656385fd4e540365ab428e8e86442da879afa379e211073a",
-                    "0xdb6232a1a833d6be0a0fe224de3294fd5deb7ab22e90ffc1f548611e7de710a",
-                    "0x6fcf2581706d8c2bb2f73b2bf7c7411988ea72343847957da445eb9aae8d284",
-                    "0x21921a79a68c1dc97503b3c32b7a5591d2a4fb6b07130827bc86ebdc889f1ecc",
-                    "0x1a7f11c7a14d342286a14a45606041cceafb509dca15a360f98bec6af73e22f1",
-                    "0x2789e7f0701aba284e4e6dc67f07baee28a6e8d2a452c3ac2d4318a748a13fca",
-                    "0xe3991d4c42453d5850946681da059b52ede49a923392777924054138d10f390",
-                    "0x3c04a10da0d4b29c09c4babd104cf94f7746d94e6730a03f4600855aae111ac",
-                    "0x30135eaa54dca18145b48d6c76bfd7224372a6a080aef0364e4017060c107190",
-                    "0x209477fcdb1c54de86fa90c6edaf7ce7a7faa1ef4ad7746f4c95b5493c598aa4",
-                    "0x2249936a729dd89f3e21f8bb87e4a77e130069cb2655ee74fff60859e8a3f05",
-                    "0x26506e18bce38d3e8ec8336af681985266fbda778310dcfb395e1c4dc6889787",
-                    "0x9231599a7a22e0e71224158eba1d46990abe854bec3010a0c4d46df309942dc",
-                    "0x1d52643a8227629cf7213641a8002e71434ed3e2e7bcb15805e404f5b49b1392",
-                    "0xcdf78acef04b87a0a38e8ffffbb3c1bf685820a156c152b7f7ed18d84f1a3ec",
-                    "0x1b710e0073c30a20a74283a2e17dd1a6b9e743593f30ef218f907181dad318d3",
-                    "0x197d02d9e3f546e2b754b057b09c3ca21f8eca75751f97d429f1c613259015da",
-                    "0x2b683ee23a44265d7baba33fc1658e0103422b3c44a5858e9a9073dde5a6fffb",
-                    "0x2892ba7e409e619df0655d528bcca937f861efb864ee311b9ffb104909c3632f",
-                    "0xb63c4e5797cc12b230407cdede78609b8256581ff6c36e6d6c7ce5990b40809",
-                    "0x1e91e74c6f976dde7047f79e931e70c177982ade19c9f1453094e99cb7f8383f",
-                    "0x83cd702282463d572c3f1f41abb2ca5fe9b391662cdc6ca76da5fd27652a9ad",
-                    "0x2779cbd531a14a648b189d77472b45a334128bda555625a1996d53c0bd681c2f",
-                    "0xc45e1e67506ee094a30ed5f822da799437cc9130c9690e46c336d32d2579bc6",
-                    "0x551286887074ca01660b25306c14c2717c5033b4df654f49cb18abbbaa5189f",
-                    "0x128d86813e07759c434a36df2ea3188d37c5bd14933d97a1f07d7d30a2d4ebc1",
-                    "0x1732222048c7e3e49b4425ec8ea053cb29d30ae5d68a0725579f4875017260e7",
-                    "0x1c125102f134ce1339df4f89b0d88a0c21fcee7ff9f353e53c224d6277cf6bc",
-                    "0x253c7c2748b69b111d96137bf99fcb11285cff8697e55ef0878de4e4d4d813c8",
-                    "0x20ecc208559e72a3841012a80eb17a87636b36dc79c1eea0b4548ad3a46bd233",
-                    "0x13652ab8ab2c40f846b0c0a41ddcbed73245a0e0ae505035999068a0026c28ed",
-                    "0x23bc1d12a8333dcf9414de63826414fe8da6bc1b58fe5a20a12b81ef80a60b8",
-                    "0x977b2288773f922bc6a40a3057d04a78f1ec2aad67aaff45307212bc3f8a8d3",
-                    "0x2f6eadfd492d1a6e303ca4b1e3d040ba7b71e570a53443421883c11c77aa54be",
-                    "0x1bbb33e59e505a766e84877b55d24bdc4cea947c93f91d57eecd094a4fb0ee8e",
-                    "0x17df1f78cd89b8868d21e7d5fac7b6a1bea3d1487809a05c79d0422c6b00323",
-                    "0xf3c85de9b37ee2c58d55484ff1d288fbbd786328807986ed824ae5fce501fd6",
-                    "0x18be60085fd6698388d510aaa97eee1ce9d3c69b157d3b1e7e04dce19d70f0dc",
-                    "0x2640c140d43386f9c7a731d0b404547099323a37eeac2e0231ea09d041618ca6",
-                    "0x1f4446b68b3a72cb7a029bf16b3cf735e3170df5d3fe2d42fd0c189450cbfe49",
-                    "0x3a3b07afee4d9d137f2dbbabad8b2386aac46b986918842772461253ca1a21a",
-                    "0x20511918db7ec0b0d279543e07942187987e7a7b4db4097bdf37008ef552002c",
-                    "0x2459bf7b1b9d01db13ba9fbc2a11b28473293a2b8a984e440c2505d33d44ac9e",
-                    "0x1504970c9891a25f4edae0035eb2a0b65011acf9b939b8a4a7dd71adbfa38be8",
-                    "0xa39783ec8b4543bdef08ed79fae2286f1e3522bc963af2deed2ad6917827f9c",
-                    "0x191e528a00772dfc81a9b94ec5d6c4bae1ca532150bd975919acd280b5a0e4a8",
-                    "0xe47ffa50d7d203ce43315e9b5faf53e4bdc2f5f88d961c7d4f234c86fd5c9d3",
-                    "0x18e7c8da6587e6a6c7e1bff9ea000e18a01ec7c222c9567c3e05d87e7225c8c4",
-                    "0x130224dbf9a79e7f79416e8938be2900c6a390a4e20db4df9bd6d89d3c1ecba0"
-                ]
-            ]
-        },
-        {
-            "params": {
-                "seed": 5,
-                "logTwoDegree": 12,
-                "logTwoBound": 7,
-                "maxNbElementsToHash": 10
-            },
-            "expected": [
-                [
-                    "0x15cd9b065ea5c613a43a2643a315dc2b7c2f46bf07a402d86de2e3ff74e8abd8",
-                    "0x2119b4c1f61d1cb194e8145e88321aab1ee44a69754f3ff8c62fa4c61a06c71a",
-                    "0x14439f1cc176f95fa95ee9f9b7c8c785760fb7864feaedbd3e449eea9cf9d818",
-                    "0x2c35899ede36c165925c20ce380c62615571b1e2af1ff3cf5d18d019bc0cd70b",
-                    "0x14f453b086b5ca6367c804f47c695c278f9e5147fab82b0d0ffed6d034e3c594",
-                    "0x143950716b963b536b81cd6d8834da1df691f92eadf44a96d598d8997247e47d",
-                    "0x1fa69fb578b08967aba7400f6c9708f561f7beb70ed362170137f81e4faa4bb4",
-                    "0x150992b09f277bbc620c5fcd9ad702ce9cea6ac89218074fac23d133109f3e79",
-                    "0x1cd25033b99856686412cf9e8df5d9f18d619706e60761413108b68135e7d7b9",
-                    "0x195571c1cf03b614d9005ad40d6752777d278d47038431057a8132c5412e1faa",
-                    "0x117b6493f10eae7dc5de2ff987b1256f4272c9cf69e2f5a115a0e10904a1f6da",
-                    "0x92608ea3b516a427e93ce525d80431b99c15a6a99125caa8800288afafe317a",
-                    "0x237afa500c8a1f055b616ff57c20b799a434325942a0292185f6302453f94a99",
-                    "0x1a81692f4ad13d3c945c1f4087e7a99c71b02deda3c443c943d1d3712fda3e87",
-                    "0x28e8793a3debe2db5e8a6d386011b2d75cf611a80de7c0fe1185541a64e380d4",
-                    "0x2d7001a2044438e432047d0bb8595bf5b3274db0a72788da654cf83f1a1e09b6",
-                    "0xabd9a8bf5e8c2f6ed7bc7104ef341889d4c9847c11124341869dd1c6bf8b477",
-                    "0x11b93922ac297a3ed9519628f6452b9aa8c942f65bff595b375782740d7dc623",
-                    "0x3ced72a9c66852121c6e47dec964c2546d72ca695f32d6e508cace21051f243",
-                    "0x27400c4d92aeef9c0b7a30c5243d73d972b57140b77874e4de2e9102aae567c",
-                    "0x2f70cfa7fc1b1be02776c2cb1849d518c3c0fdbc16cc45a97e6a8ee919f5cd28",
-                    "0x10dd279b8c7dc96eb083fd69873d0b7c831b487f4746d515e3490f3f80f38ca7",
-                    "0x256b7c8326f59f3f6d4cbf9f35f14f942c27ee313905a5c19a38dd1b83d8d8d5",
-                    "0xba57f66a96935181a6721e7b8be4ba3ece0a4b170e9f1dbdc72713f0195c523",
-                    "0x1d2d01d5b1e51e53062de3c5cf3b083f45b71a975864c346258b7db84007a61a",
-                    "0x2f340563a7cecee47a2a72c0af819393eddd58133e91ca50707c14efba6eff79",
-                    "0x1d15642b2a3fe9f362e1b9385e7fc42b16838189a21d6544c8d0f7a479b987ad",
-                    "0x1a5747a137641704dadf2da5b2983ef43eee211368384551e240a987d98bda6e",
-                    "0x184daa5d11cac6b4b3c9abb37388369787a374d5d9b507221be4c48b2d877d89",
-                    "0x2652dd9778c865ebb656f6cafc7bf5e5c49b84ee6130293e0cb0f466635c8872",
-                    "0x2750aff21931006c586c24e3d9fb4ff066cd6cb9ba59fbd63c67b04a6dc52ff7",
-                    "0x5d760115f6d3bd6f3ac109009fb824e6b97507152603b90120facfd43291831",
-                    "0x137759185d989d6b9de74feb983d2c264ffd442d3c910e9056968bc9d10d5a56",
-                    "0x1f33ea2a039fd7c8701cfd59b1e9aeb759a01a89fc3d405b7b28d26eea153b1a",
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-                    "0xf011a81f189c36cfca0e887021d25149cfcddb6176b690f04b182854ef8a7e0",
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-                    "0xf2cbc908d433e4375a1508f12102861d4979e47c11d74a0441e6e30a223c65e",
-                    "0x9c5ec544f7f87f9afbcf1fa8a20e66bc9b6a4a0899609e67175750f17a3fd0b",
-                    "0x180e70c7b0161ebfded2ddb0ad9bdadb130ccb8105cfadcb76c8a27aa5af27b3",
-                    "0x194f0191e09516d4d881d877a2050327bf74937b9ab1828cb5b95e1b8277980d",
-                    "0x606d2ca8297fb87a826700331a2c052cc3fcd4b8c9fe17777b3c7b5e0f5c7dc",
-                    "0xef6c6354a48834d94ed45150b79244dd352d6c135aaced50b78bd564eafd721",
-                    "0x2488c11b238f2578cb5cef5ae376757f9ccc0a44433ba8f44bd20daba186590",
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-                    "0x277b97e71c4e5f95c9e798d1441cfbbfb0d7b8749c8c1225b81f6a577939d039",
-                    "0x740cfa11a1d4a2a95abc2acc73acd2f1046cbba03cf89904a291ca38a1ffb27",
-                    "0x28f3cc2d4b88ca1661f2c18337dc3f2b60cc4aa28d9c908b98587d5e56b7c43",
-                    "0x2ab99fe8d847e11329a6b0add2f4b7b9b60e4ebb9142b15341f055c15196758e",
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-                    "0x10bb0031bd62ebc5f84e68dceb394bddec558213d84ecc63a2e7cfbe11a006df",
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-                    "0xf329c17d9e6fb18acfea893ffa699756c4ebe64ad9e6757619d6e9ab652639a",
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-                    "0xc7ed2c2b0a1885035b1eb5728586302c46807094a2135f912323fc500f70f4",
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-                    "0x1cc9d2ebb4903153881a491c9311a93f810e23ab45c75615caebdcf6ca9f7548",
-                    "0x4a6a0b2664add7377bead4ad2cac0324f5cde28767cbf058aab8a334178fd63",
-                    "0x88b896f80c016cd5fa8d699506e781ca3bfd3c8aaed461db5ba6a5f8c83f6d1",
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-                    "0x24a132d770221ff30f80094d94335d93c789ca00b91e7f9dad1e6689a0459b5f",
-                    "0xbe9d117cbea3615f25b156518243bba6bf772e025c7d54ddd218d427cf2b8f1",
-                    "0x33239a6fda84a388d4f9f4e5bb27f24906a2faae85fd62473ad894891485d21",
-                    "0x16766966d732048908e387cdd79f1d2988546e04d52b74088978cfac90815d29",
-                    "0x22a77b31395760052b16623dbc597297e1079c90610e395131ee8ca52010a8a6",
-                    "0x10ae2f9051ff21b52e48d3406d465682a0341fe7338ee92abd10e0958e76ad9f",
-                    "0xe3f764bf744be7d8e8ddc8a3126b87bc60fd9261fe9e1aecaa6063a9661d9f9",
-                    "0xc6a716884cd55ff5662632e5e07322a5987cb94b5be491b0271290d67b5d7e",
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+                    "0x26aa78cfa5b5166ceb14631ab224f25ff3fb84ea90674c2bd14e65af86452dd7",
+                    "0x2197c9ddb9cdbc93ee9b141f41ba6f6adec0bd42bdb12797ea7db7425a991f45",
+                    "0x2e810e3c065faff624cb7f7ad1a908957dee3713bf1a903122a99f8d0f6dce9a",
+                    "0x211a0dd3f866e40aaff1d0792890b158835744951e6029138a10d0c7bb12b7ff",
+                    "0x1494649a8a31ed1e1c9f84b04db42c585fde004ecd99e2c964eca7c852bb19fe",
+                    "0xae7df689ac3dc7976a7e0a1af322512da409a60cd21bd2eee2274351910773f",
+                    "0x25609b7012d85f40914c801229b89a9a2f3ef7381d5406f499871c94ee8eb933",
+                    "0x29a605f4ad20fa5435edd61d1749b87ea75e85506f3fd1238d4bf477fd8e30b4",
+                    "0x22f561a6ac31d55f9c1e52569584dbf3298246107af068041fdbd2792b416f05",
+                    "0x89bc34795c88cd2be65813ff9eca7a6f0f65d684e22c5c835eb74561a632d63",
+                    "0x20de90fe458250af10339a416e608b9cbd4d65ffd976b610105e955350f6d568",
+                    "0x6fb4c4ddfdc5dcde16c2499e3ab3e27fe6c5d51f18e8719853936efd71e193b",
+                    "0x218ddba59f02fa1d4ed2be27a27e8c5a2f106614f7c10701c29ade4a36af0fe6",
+                    "0x2615c1101ea2bd08b21d5a541dcd543e717f765249a87bf61ad28591ee8f8753",
+                    "0x10f79004550cb75f68a50046f9e8dfd32485ee0b35272c0fe2ec4b6aa705c58c",
+                    "0x2b787070403219fe94c4f73e79486c495369fd715088ea22bf4d0c500e1e10c0",
+                    "0x2f3774ed95e5d54fff6af18f1e306048a5f615f6293818975c63c2c245478e72",
+                    "0x2818d2bab0a293a09873975739260b864db17a42f2c84fdb016ed10cfcb04955",
+                    "0x16f27b414910eb883e783abc0b6dbdfa52aa8fc0fb7a5a9e5a786f656dea9f93",
+                    "0x247caf25f7a2f8ade647c2947f6b0e7252d48dea92bcb63d757cc91929010dcf",
+                    "0x2db22272aa8880712d0a5a46c7a636815b5784e353c8341e94c6b29afb9a7309",
+                    "0x6db32b9ca826cafe97d209d59ada635a82054ed007d814a05fca7417f88fa93",
+                    "0x21310163d80d29982e7afa37594513d6bf1c7082847b0eb6327f443d0fbfea1d",
+                    "0x237bef0b985585a21c70e74e109ae55ee894d0f3b93f749a8c71589408edead",
+                    "0x12c370a66c9d42b29cb1715b5aea04c92f5f583d138dfca3e0aec431e29919d5",
+                    "0x17f760ef50df56d16e46a424a3484569e1d8eb53f439248f2ea18b06ed3ba155",
+                    "0x1e2b4328004c86d64a0ae275c2aa421d34964f25ec924b8f76e65462ca4b6d4d",
+                    "0x27d591eae91e0d562cead7105324b21c9e08555f65d4813bed69fd850ca092f7",
+                    "0x14ed9bf8b3d059e8160813f71bcce002d353dc97e1dab847fc0c5e77da4fd328",
+                    "0x123f7e867bbedea72270d94530487df79a71de46200a0804973125f7cd11fe8f",
+                    "0x121e05bb4e46ba1bf947f9e0e4580ff7a371f07419ee9ee574511e95da998a06",
+                    "0x22d4e39975ac959484d27cd2ef05ccae4edcb11b068f3dd7762450baa68f8abd",
+                    "0x5799c7af00962bc9cea98f757e2771514b1c9852c4d192ba5e858db4a4fc847",
+                    "0xb2c864a667743dd4cdc987542f02fdc5d61591de983809bf3083da35cce3661",
+                    "0x2662163afd77d6fee1f71f373c299acc71f4b2364214e903c41fe7d0691cc33c",
+                    "0x2b33da2794eb477d08e7817a2c8832fe58510aa3765a09bf26d08c0a5048cda8",
+                    "0x2852d1753be867e07a7c5bfbd8f32b34fabf58abe8443d46d74f27d4f8c89a46",
+                    "0x255fe3ebf2c31a5f5c5455f1563ecaa5b6423647bebf4c8e74b102de33b73405",
+                    "0x2b5f33068f79fd5d94516fac7c742fc7055f125ea0b643a4ade164802af99412",
+                    "0x1d7b379e1d1a4d8c53d25f2466915540672786bb7e856aa2518a95ec30f80a37",
+                    "0x12b1245c683effb823dca4ede765f76ebac9c5cd94c8ce3bf059ea4d6d8f5948",
+                    "0x172e52f50478b4efa35d796cdcd57271e7143d3c6f245112eb9fffd9628b5342",
+                    "0x9ea2da2fab2b9f72c1e289013687fe65d54358cd38a94a35395882fa9c9ebd2",
+                    "0x21c6c80256d12c4df3833a1e6690deba15ffbffd4b58c2c493f75385d7422ae9",
+                    "0x2fb827a550bd072479e49fba76e5d4edda5f3ca21e69524dc467dbcd57cec896",
+                    "0x112f51a49fe5f9c976664f3b9c174e9b4faa39604499266eaac769f418576096",
+                    "0x8d98192251957c4ed289fbb4d712ce35a29bffd6555e6176e8ec2506845fb17",
+                    "0x2531f4bea2b1efe55818e8e4333b108294eb5098368b2a79918ff679820948f1",
+                    "0x11dec4fbf3a8ca2ebd1525edc32df53f5048effd83cafee0ff7ce55f44d97307",
+                    "0x8804b1f9cde33f9e62429a13a5f232f812115cbbec998cf31164b3cd2c7783f",
+                    "0x1e2de654b2ae09b755bffa5873377f86722ae5be856fda7ebf304a3f3fc22c7d",
+                    "0xf139b87bef33aec9e93bab599dfcb315640a44af0814ce51e2bd771c3c7c908",
+                    "0x96325800f400907a059ba16c2d165c96a959286bbbfef1946a35757afac80d6",
+                    "0x20a100f6dbd006268d0f6f349ece4f850f293ee442889d2e3cfc86ee49cf6949",
+                    "0x1a01e7111c881748eb2d4b1ac04d52212d38c15661470d7bf2f95ac8f95229a",
+                    "0x2c242764ee04326400cc3d143277743b685cb8536f6a29f5c23529548f1f5d6a",
+                    "0x1e547369b9089311370b62ce2d776d2bf696869e91d865ce3e3e2cb8c3e43252",
+                    "0x2b729a9591a9f27b10c9e50d1b35bebfac886ccc80e58e9bde56d7f4f9f3e2fb",
+                    "0xfab78b8ff13c8dd0469c9b80418643edbf52a454186eb3f1afd8c0c8ad8c93e",
+                    "0x226f1463aaa2824e47c6c88d0c2b8173a11477b253dc57f2174e60f97fcdaf47",
+                    "0x2d61f759a07065a1acd47793d1f0a4b039a57068f44a6e570e4021aba7dded97",
+                    "0x26762c8709ed98acba40d00944bdb95699dcd0c6e30369a8c22689d3d6665d34",
+                    "0x207ec1f00f6352ebb88a32b40b55c2924509fdc48a1c5b5fbdec14066cbe31c6",
+                    "0x5fdc129cc998003e7838e7f7d92dbc9b2fc445f52181621d14b1fdc588a8ed7",
+                    "0x2e211a467959147c788145caf7a3bde2eb54185c0307fa6d265707a08b82e8dc",
+                    "0x6c5fb9158b92fd645f4d2e408ddeecc03e168b0738ffd3c0f0426e24b6115dd",
+                    "0x28cebee96534ba16ae7c76563eef3b44971c4dc56c9ec576367fc5e328d94cd8",
+                    "0x1649a49a33abb779fe3e1ffba0f7a21ad11c20ed6c23d449cb2bc3fd7fc4f50b",
+                    "0x182c5c797da65ec088b1f7bb83d2e79143cb1c6e5b022ab7cfaf52b1d92bbb8e",
+                    "0xe363a5b4d18fc79d6b036a5297e77d31d4c54c2295489a1750189bede4ff17b",
+                    "0x2255df96d6d39c05af7f8d86d4caaf69ee0405ef4921fd17d52ef485e94e49dd",
+                    "0xf2f2ae648dd84c428fa9096eb5a4a866f3e04b97e3aee8243e356099e15ebe5",
+                    "0xf970e2ead9b254f20163300b6570b77aecd0df8a3f13e06c025fbba521d349c",
+                    "0x27f955428b3477d3db7db7637a6d955a309c9751229c1e8e19c6dee9e5e3a4e9",
+                    "0xa215c663e145b99276e66f5d44638ea3f60bb96537572607a46e5d1df05b997",
+                    "0x2a00328878bad61e4367d1cf4e13e2d5093322b534a5186c0a6350881047393e",
+                    "0x242355caa61e48a9bc9e84d865f92a9b43de00a587fecdea2761be8492a294f1",
+                    "0x1ec90bde50c66a5c78cbc94c755015bf53143e57655b6c546e62d77236d2df4a",
+                    "0x277971e075adec830e8bfd220be85e845c8277f5e04d9323142f81c5122ee310",
+                    "0x93de6a6ce100e5e8d1c45f45950409a1bfe183ab7cc83e2fcc3f62f23bbdb87",
+                    "0xb317746ec49e9f0e179a784cf91e870b277f1e1c1509e6688da490057b8c79d",
+                    "0x180332dcd63aa5971195a9bc55ce17d64457a7f2a3de431002bc409851bdb7e3",
+                    "0x2b92d79f6582ddb44437fea21e27c00450bc2c07a8a1449a014e54c3b6d0ad51",
+                    "0x18a7fc1aed453c0b30cb8530a19ac5948c6c0f15e10e575add430b035691d406",
+                    "0x2e72ac51466154279639f36a1fed4a02996c2181fac6f4507c4d46dea7ae33b7",
+                    "0x119a0fc9d7dd4f7d2577fcd9dfd739fd078a0c437a3670b229b1023d7a887a8b",
+                    "0x2d14b15219d578c28e730418dd64ceab29c603bdf6dfb8904507913fa74ff5ec",
+                    "0x19ac59a705103b1c5ae873e54b878de2071b260ada400e3bb58c5ed66d3a5f38",
+                    "0x1ea4bb0b6a82901ae92b2c8791b9a878f23d430fb08ed18d53bf1bd80740e7ad",
+                    "0xc4efae2774cf74a45916cbf0d0a2a82790ac519ea47fec4d1cac9b032cb136",
+                    "0x147e62267499ad7fb3bd1de6c5795018684d9cedaac1b3a6ee0adf2aa58b3bc8",
+                    "0x14411a35fe1fc70ab86709ad50ae43a4629a4b4650a0bbbf4683f5a84a9f5065",
+                    "0xd05fbf4cdf70d012af1f24fdbcccf895e461051d30b122e0b926a8a278c77a7",
+                    "0x303f7d4fc51f8f7ec3203a488e65fd520c24691ef4fd08a28bd51d5d0c56d850",
+                    "0x9ded28cc5a2427eb5b859f8bbf94ccd3897ad0a33dc13752b4ab919d3b57aa3",
+                    "0x1bba997c6597466bc0efe9e44a9e1969948ff682114c77c0a0ed2e193e7a95a6",
+                    "0x10b1267a993e9122de9a45a5f963efe47d575885ef31748434aba52175285c94",
+                    "0x98de9d1d329bc74735e95860205d2dc6c679130dd2e3fb898a66cc3382d9dd0",
+                    "0x1128737b3731fdca47ae27c0c1345d33a614c4bbcccad17d07c77209f6652405",
+                    "0x1e4c40caa5486faeeb61a9c816b530347c6f3c375555c33179964cd9c2c6c7c2"
                 ]
             ]
         }
diff --git a/ecc/bn254/g1.go b/ecc/bn254/g1.go
index 718abd6f2..b3d16cc60 100644
--- a/ecc/bn254/g1.go
+++ b/ecc/bn254/g1.go
@@ -92,6 +92,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bn254/g2.go b/ecc/bn254/g2.go
index 49615c541..da0b89b9c 100644
--- a/ecc/bn254/g2.go
+++ b/ecc/bn254/g2.go
@@ -81,6 +81,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bn254/hash_to_g1.go b/ecc/bn254/hash_to_g1.go
index 50d40cd0e..5a2d63f23 100644
--- a/ecc/bn254/hash_to_g1.go
+++ b/ecc/bn254/hash_to_g1.go
@@ -20,10 +20,10 @@ import (
 	"github.com/consensys/gnark-crypto/ecc/bn254/fp"
 )
 
-// mapToCurve1 implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
+// MapToCurve1 implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
 // No cofactor clearing or isogeny
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#straightline-svdw
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 	var tv1, tv2, tv3, tv4 fp.Element
 	var x1, x2, x3, gx1, gx2, gx, x, y fp.Element
 	var one fp.Element
@@ -112,7 +112,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SVDW map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	return res
 }
 
@@ -128,7 +128,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	return res, nil
 }
@@ -143,8 +143,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	var _Q0, _Q1 G1Jac
 	_Q0.FromAffine(&Q0)
diff --git a/ecc/bn254/hash_to_g1_test.go b/ecc/bn254/hash_to_g1_test.go
index da1b1312d..0a18db90f 100644
--- a/ecc/bn254/hash_to_g1_test.go
+++ b/ecc/bn254/hash_to_g1_test.go
@@ -57,7 +57,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !g.IsOnCurve() {
 				t.Log("SVDW output not on curve")
@@ -74,18 +74,18 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
 
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
 }
diff --git a/ecc/bn254/hash_to_g2.go b/ecc/bn254/hash_to_g2.go
index 7cf07eeac..5c7dec4d4 100644
--- a/ecc/bn254/hash_to_g2.go
+++ b/ecc/bn254/hash_to_g2.go
@@ -21,10 +21,10 @@ import (
 	"github.com/consensys/gnark-crypto/ecc/bn254/internal/fptower"
 )
 
-// mapToCurve2 implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
+// MapToCurve2 implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
 // No cofactor clearing or isogeny
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#straightline-svdw
-func mapToCurve2(u *fptower.E2) G2Affine {
+func MapToCurve2(u *fptower.E2) G2Affine {
 	var tv1, tv2, tv3, tv4 fptower.E2
 	var x1, x2, x3, gx1, gx2, gx, x, y fptower.E2
 	var one fptower.E2
@@ -143,7 +143,7 @@ func g2Sgn0(z *fptower.E2) uint64 {
 
 // MapToG2 invokes the SVDW map, and guarantees that the result is in g2
 func MapToG2(u fptower.E2) G2Affine {
-	res := mapToCurve2(&u)
+	res := MapToCurve2(&u)
 	res.ClearCofactor(&res)
 	return res
 }
@@ -160,7 +160,7 @@ func EncodeToG2(msg, dst []byte) (G2Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve2(&fptower.E2{
+	res = MapToCurve2(&fptower.E2{
 		A0: u[0],
 		A1: u[1],
 	})
@@ -179,11 +179,11 @@ func HashToG2(msg, dst []byte) (G2Affine, error) {
 		return G2Affine{}, err
 	}
 
-	Q0 := mapToCurve2(&fptower.E2{
+	Q0 := MapToCurve2(&fptower.E2{
 		A0: u[0],
 		A1: u[1],
 	})
-	Q1 := mapToCurve2(&fptower.E2{
+	Q1 := MapToCurve2(&fptower.E2{
 		A0: u[2+0],
 		A1: u[2+1],
 	})
diff --git a/ecc/bn254/hash_to_g2_test.go b/ecc/bn254/hash_to_g2_test.go
index 33e231c67..9804d4713 100644
--- a/ecc/bn254/hash_to_g2_test.go
+++ b/ecc/bn254/hash_to_g2_test.go
@@ -59,7 +59,7 @@ func TestMapToCurve2(t *testing.T) {
 	properties.Property("[G2] mapping output must be on curve", prop.ForAll(
 		func(a fptower.E2) bool {
 
-			g := mapToCurve2(&a)
+			g := MapToCurve2(&a)
 
 			if !g.IsOnCurve() {
 				t.Log("SVDW output not on curve")
@@ -76,18 +76,18 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range encodeToG2Vector.cases {
 		var u fptower.E2
 		g2CoordSetString(&u, c.u)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
 
 	for _, c := range hashToG2Vector.cases {
 		var u fptower.E2
 		g2CoordSetString(&u, c.u0)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g2CoordSetString(&u, c.u1)
-		q = mapToCurve2(&u)
+		q = MapToCurve2(&u)
 		g2TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
 }
diff --git a/ecc/bn254/internal/fptower/e12.go b/ecc/bn254/internal/fptower/e12.go
index 8fa8345ec..35961e009 100644
--- a/ecc/bn254/internal/fptower/e12.go
+++ b/ecc/bn254/internal/fptower/e12.go
@@ -230,15 +230,17 @@ func (z *E12) DecompressKarabina(x *E12) *E12 {
 	var one E2
 	one.SetOne()
 
-	// g3 == 0
-	if x.C1.B2.IsZero() {
+	if x.C1.B2.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.C0.B1, &x.C1.B2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.C0.B2)
 
-		// g3 != 0
-	} else {
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
+
 		// t0 = g1^2
 		t[0].Square(&x.C0.B1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -302,20 +304,24 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t0 := make([]E2, n)
 	t1 := make([]E2, n)
 	t2 := make([]E2, n)
+	zeroes := make([]bool, n)
 
 	var one E2
 	one.SetOne()
 
 	for i := 0; i < n; i++ {
-		// g3 == 0
-		if x[i].C1.B2.IsZero() {
+		if x[i].C1.B2.IsZero() /* g3 == 0 */ {
 			t0[i].Mul(&x[i].C0.B1, &x[i].C1.B2).
 				Double(&t0[i])
 			// t1 = g2
 			t1[i].Set(&x[i].C0.B2)
 
-			// g3 != 0
-		} else {
+			if t1[i].IsZero() /* g3 == g2 == 0 */ {
+				x[i].SetOne()
+				zeroes[i] = true
+				continue
+			}
+		} else /* g3 != 0 */ {
 			// t0 = g1^2
 			t0[i].Square(&x[i].C0.B1)
 			// t1 = 3 * g1^2 - 2 * g2
@@ -335,6 +341,10 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t1 = BatchInvertE2(t1) // costs 1 inverse
 
 	for i := 0; i < n; i++ {
+		if zeroes[i] {
+			continue
+		}
+
 		// z4 = g4
 		x[i].C1.B1.Mul(&t0[i], &t1[i])
 
diff --git a/ecc/bn254/marshal.go b/ecc/bn254/marshal.go
index fe66b9a92..c11de4526 100644
--- a/ecc/bn254/marshal.go
+++ b/ecc/bn254/marshal.go
@@ -44,7 +44,10 @@ const (
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bn254 object values to an output stream
 type Encoder struct {
@@ -97,6 +100,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -129,6 +150,7 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -149,6 +171,7 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -180,6 +203,7 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -239,6 +263,7 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -392,6 +417,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -495,6 +522,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -580,6 +609,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 32
 
@@ -592,7 +640,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -842,7 +890,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
diff --git a/ecc/bn254/pairing.go b/ecc/bn254/pairing.go
index 44a87ca61..ec342fe80 100644
--- a/ecc/bn254/pairing.go
+++ b/ecc/bn254/pairing.go
@@ -77,6 +77,12 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	t[0].Mul(&t[0], &result)
 	result.FrobeniusSquare(&t[0]).Mul(&result, &t[0])
 
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
 	// Hard part (up to permutation)
 	// 2x₀(6x₀²+3x₀+1)(p⁴-p²+1)/r
 	// Duquesne and Ghammam
diff --git a/ecc/bw6-633/fr/kzg/kzg.go b/ecc/bw6-633/fr/kzg/kzg.go
index dfb5565a1..461b4be1c 100644
--- a/ecc/bw6-633/fr/kzg/kzg.go
+++ b/ecc/bw6-633/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bw6633.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bw6633.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bw6633.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bw6633.G2Affine // [G₂, [α]G₂ ]
+	G1 bw6633.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bw6633.G1Affine, size)
+	srs.Pk.G1 = make([]bw6633.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bw6633.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bw6633.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bw6633.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bw6633.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bw6633.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bw6633.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bw6633.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bw6633.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bw6633.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bw6633.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bw6633.PairingCheck(
-		[]bw6633.G1Affine{fminusfaG1Aff, negH},
-		[]bw6633.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bw6633.G1Affine{totalG1Aff, negH},
+		[]bw6633.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bw6633.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bw6633.PairingCheck(
 		[]bw6633.G1Affine{foldedDigests, foldedQuotients},
-		[]bw6633.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bw6633.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bw6-633/fr/kzg/kzg_test.go b/ecc/bw6-633/fr/kzg/kzg_test.go
index 55daca27b..0d0ddedcb 100644
--- a/ecc/bw6-633/fr/kzg/kzg_test.go
+++ b/ecc/bw6-633/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bw6633.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bw6-633/fr/kzg/marshal.go b/ecc/bw6-633/fr/kzg/marshal.go
index c9b0f9dbe..4ef19b91a 100644
--- a/ecc/bw6-633/fr/kzg/marshal.go
+++ b/ecc/bw6-633/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bw6633.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bw6633.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bw6633.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bw6633.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bw6633.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bw6633.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bw6633.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bw6633.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bw6-633/fr/pedersen/pedersen.go b/ecc/bw6-633/fr/pedersen/pedersen.go
index 1c5f269bf..a680a17c6 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bw6-633"
+	curve "github.com/consensys/gnark-crypto/ecc/bw6-633"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bw6633.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bw6633.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bw6633.G1Affine
-	basisExpSigma []bw6633.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bw6633.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bw6633.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bw6633.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bw6633.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bw6633.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bw6633.G1Affine, knowledgeProof bw6633.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bw6633.G1Affine, knowledge
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bw6633.G1Affine, knowledgeProof bw6633.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bw6633.Pair([]bw6633.G1Affine{commitment, knowledgeProof}, []bw6633.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bw6633.G1Affine, knowledgeProof bw
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bw6-633/fr/pedersen/pedersen_test.go b/ecc/bw6-633/fr/pedersen/pedersen_test.go
index 17c1f9aa2..f2b9bb6e4 100644
--- a/ecc/bw6-633/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-633/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bw6-633"
+	curve "github.com/consensys/gnark-crypto/ecc/bw6-633"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bw6633.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bw6633.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bw6633.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bw6633.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bw6633.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bw6-633/fr/permutation/permutation.go b/ecc/bw6-633/fr/permutation/permutation.go
index 98f772f08..5dcde6250 100644
--- a/ecc/bw6-633/fr/permutation/permutation.go
+++ b/ecc/bw6-633/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bw6-633/fr/permutation/permutation_test.go b/ecc/bw6-633/fr/permutation/permutation_test.go
index 54232fc40..80b4ddd5f 100644
--- a/ecc/bw6-633/fr/permutation/permutation_test.go
+++ b/ecc/bw6-633/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bw6-633/fr/plookup/plookup_test.go b/ecc/bw6-633/fr/plookup/plookup_test.go
index f143f21a8..a1672a2d4 100644
--- a/ecc/bw6-633/fr/plookup/plookup_test.go
+++ b/ecc/bw6-633/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bw6-633/fr/plookup/table.go b/ecc/bw6-633/fr/plookup/table.go
index 517afaf3a..737cf3d44 100644
--- a/ecc/bw6-633/fr/plookup/table.go
+++ b/ecc/bw6-633/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bw6-633/fr/plookup/vector.go b/ecc/bw6-633/fr/plookup/vector.go
index 1495b4e45..06b556191 100644
--- a/ecc/bw6-633/fr/plookup/vector.go
+++ b/ecc/bw6-633/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bw6-633/g1.go b/ecc/bw6-633/g1.go
index f6398338b..65c7176f5 100644
--- a/ecc/bw6-633/g1.go
+++ b/ecc/bw6-633/g1.go
@@ -97,6 +97,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bw6-633/g2.go b/ecc/bw6-633/g2.go
index 1bab9608a..66ff5c998 100644
--- a/ecc/bw6-633/g2.go
+++ b/ecc/bw6-633/g2.go
@@ -76,6 +76,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bw6-633/hash_to_g1.go b/ecc/bw6-633/hash_to_g1.go
index 45921b9ce..2c6710c48 100644
--- a/ecc/bw6-633/hash_to_g1.go
+++ b/ecc/bw6-633/hash_to_g1.go
@@ -169,9 +169,9 @@ func g1MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve1 implements the SSWU map
+// MapToCurve1 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{12925890271846221020, 6355149021182850637, 12305199997029221454, 3176370205483940054, 1111744716227392272, 1674946515969267914, 9082444721826297409, 17859522351279563418, 11442187008395780520, 4206825732020662}
 	var sswuIsoCurveCoeffB = fp.Element{1447342806075484185, 5642327672839545870, 16783436050687675045, 2630023864181351186, 5909133526915342434, 1057352115267779153, 1923190814798170064, 13280701548970829092, 3305076617946573429, 29606717104036842}
@@ -271,7 +271,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SSWU map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	//this is in an isogenous curve
 	g1Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -290,7 +290,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	//this is in an isogenous curve
 	g1Isogeny(&res)
@@ -308,8 +308,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g1Isogeny(&Q0)
diff --git a/ecc/bw6-633/hash_to_g1_test.go b/ecc/bw6-633/hash_to_g1_test.go
index 8d299c729..7e8814aa3 100644
--- a/ecc/bw6-633/hash_to_g1_test.go
+++ b/ecc/bw6-633/hash_to_g1_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !isOnE1Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bw6-633/hash_to_g2.go b/ecc/bw6-633/hash_to_g2.go
index 94d0f1f11..46a756e02 100644
--- a/ecc/bw6-633/hash_to_g2.go
+++ b/ecc/bw6-633/hash_to_g2.go
@@ -143,9 +143,9 @@ func g2MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve2 implements the SSWU map
+// MapToCurve2 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve2(u *fp.Element) G2Affine {
+func MapToCurve2(u *fp.Element) G2Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{13503940466125084703, 3000707982748310797, 1529397070312683242, 9240962296298654443, 4577258595340312235, 16046828875439788343, 7236093083337192433, 2860564553402019540, 5160479239841632821, 65394042426465165}
 	var sswuIsoCurveCoeffB = fp.Element{4170590011558214244, 9101648159034903675, 4256739633972552875, 7483080556638609334, 12430228215152656439, 9977400640742476476, 15847011074743951739, 17768582661138350292, 10869631430819016060, 64187107279947172}
@@ -245,7 +245,7 @@ func g2Sgn0(z *fp.Element) uint64 {
 
 // MapToG2 invokes the SSWU map, and guarantees that the result is in g2
 func MapToG2(u fp.Element) G2Affine {
-	res := mapToCurve2(&u)
+	res := MapToCurve2(&u)
 	//this is in an isogenous curve
 	g2Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -264,7 +264,7 @@ func EncodeToG2(msg, dst []byte) (G2Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve2(&u[0])
+	res = MapToCurve2(&u[0])
 
 	//this is in an isogenous curve
 	g2Isogeny(&res)
@@ -282,8 +282,8 @@ func HashToG2(msg, dst []byte) (G2Affine, error) {
 		return G2Affine{}, err
 	}
 
-	Q0 := mapToCurve2(&u[0])
-	Q1 := mapToCurve2(&u[1])
+	Q0 := MapToCurve2(&u[0])
+	Q1 := MapToCurve2(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g2Isogeny(&Q0)
diff --git a/ecc/bw6-633/hash_to_g2_test.go b/ecc/bw6-633/hash_to_g2_test.go
index 130f43a0a..44371b4dd 100644
--- a/ecc/bw6-633/hash_to_g2_test.go
+++ b/ecc/bw6-633/hash_to_g2_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve2(t *testing.T) {
 	properties.Property("[G2] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve2(&a)
+			g := MapToCurve2(&a)
 
 			if !isOnE2Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range encodeToG2Vector.cases {
 		var u fp.Element
 		g2CoordSetString(&u, c.u)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range hashToG2Vector.cases {
 		var u fp.Element
 		g2CoordSetString(&u, c.u0)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g2CoordSetString(&u, c.u1)
-		q = mapToCurve2(&u)
+		q = MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bw6-633/internal/fptower/e6.go b/ecc/bw6-633/internal/fptower/e6.go
index 0a5c22e97..5a86ac770 100644
--- a/ecc/bw6-633/internal/fptower/e6.go
+++ b/ecc/bw6-633/internal/fptower/e6.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
@@ -231,15 +229,16 @@ func (z *E6) DecompressKarabina(x *E6) *E6 {
 	var one fp.Element
 	one.SetOne()
 
-	// g3 == 0
-	if x.B1.A0.IsZero() {
+	if x.B1.A0.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.B0.A1, &x.B1.A2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.B0.A2)
 
-		// g3 != 0
-	} else {
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
 		// t0 = g1^2
 		t[0].Square(&x.B0.A1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -688,7 +687,6 @@ func (z *E6) SetBytes(e []byte) error {
 	z.B0.A1.SetBytes(e[offset : offset+sizeOfFp])
 	offset += sizeOfFp
 	z.B0.A0.SetBytes(e[offset : offset+sizeOfFp])
-	offset += sizeOfFp
 
 	return nil
 }
@@ -698,7 +696,7 @@ func (z *E6) IsInSubGroup() bool {
 	var tmp, a, _a, b E6
 	var t [13]E6
 
-	// check z^(Phi_k(p)) == 1
+	// check z^(phi_k(p)) == 1
 	a.Frobenius(z)
 	b.Frobenius(&a).Mul(&b, z)
 
diff --git a/ecc/bw6-633/internal/fptower/e6_test.go b/ecc/bw6-633/internal/fptower/e6_test.go
index 09ed30cfe..7f8d04257 100644
--- a/ecc/bw6-633/internal/fptower/e6_test.go
+++ b/ecc/bw6-633/internal/fptower/e6_test.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
diff --git a/ecc/bw6-633/marshal.go b/ecc/bw6-633/marshal.go
index 4325dbc38..fd13100e0 100644
--- a/ecc/bw6-633/marshal.go
+++ b/ecc/bw6-633/marshal.go
@@ -32,25 +32,27 @@ import (
 // To encode G1Affine and G2Affine points, we mask the most significant bits with these bits to specify without ambiguity
 // metadata needed for point (de)compression
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
 	mUncompressed         byte = 0b000 << 5
+	_                     byte = 0b001 << 5 // invalid
 	mUncompressedInfinity byte = 0b010 << 5
+	_                     byte = 0b011 << 5 // invalid
 	mCompressedSmallest   byte = 0b100 << 5
 	mCompressedLargest    byte = 0b101 << 5
 	mCompressedInfinity   byte = 0b110 << 5
+	_                     byte = 0b111 << 5 // invalid
 )
 
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bw6-633 object values to an output stream
 type Encoder struct {
@@ -103,6 +105,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -135,6 +155,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -155,6 +182,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -186,6 +220,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -245,6 +286,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -315,6 +363,12 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return
 }
 
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
 	return !((mData == mUncompressed) || (mData == mUncompressedInfinity))
@@ -398,6 +452,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -501,6 +557,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -586,6 +644,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 80
 
@@ -598,7 +675,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -682,6 +759,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG1AffineUncompressed {
@@ -854,7 +936,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -938,6 +1020,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG2AffineUncompressed {
diff --git a/ecc/bw6-633/marshal_test.go b/ecc/bw6-633/marshal_test.go
index bd047f0d7..beec029d4 100644
--- a/ecc/bw6-633/marshal_test.go
+++ b/ecc/bw6-633/marshal_test.go
@@ -216,6 +216,26 @@ func TestIsCompressed(t *testing.T) {
 
 }
 
+func TestG1AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG1AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G1Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG1AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -309,6 +329,26 @@ func TestG1AffineSerialization(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestG2AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG2AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G2Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG2AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
diff --git a/ecc/bw6-633/pairing.go b/ecc/bw6-633/pairing.go
index 27fb49be9..2f6fc9102 100644
--- a/ecc/bw6-633/pairing.go
+++ b/ecc/bw6-633/pairing.go
@@ -79,6 +79,12 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	result.Frobenius(&buf).
 		Mul(&result, &buf)
 
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
 	// Hard part (up to permutation)
 	// El Housni and Guillevic
 	// https://eprint.iacr.org/2021/1359.pdf
diff --git a/ecc/bw6-756/fr/kzg/kzg.go b/ecc/bw6-756/fr/kzg/kzg.go
index 9a03e34df..fd7f72447 100644
--- a/ecc/bw6-756/fr/kzg/kzg.go
+++ b/ecc/bw6-756/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bw6756.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bw6756.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bw6756.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bw6756.G2Affine // [G₂, [α]G₂ ]
+	G1 bw6756.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bw6756.G1Affine, size)
+	srs.Pk.G1 = make([]bw6756.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bw6756.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bw6756.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bw6756.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bw6756.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bw6756.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bw6756.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bw6756.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bw6756.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bw6756.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bw6756.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bw6756.PairingCheck(
-		[]bw6756.G1Affine{fminusfaG1Aff, negH},
-		[]bw6756.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bw6756.G1Affine{totalG1Aff, negH},
+		[]bw6756.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bw6756.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bw6756.PairingCheck(
 		[]bw6756.G1Affine{foldedDigests, foldedQuotients},
-		[]bw6756.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bw6756.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bw6-756/fr/kzg/kzg_test.go b/ecc/bw6-756/fr/kzg/kzg_test.go
index f86a9235e..92446f9d7 100644
--- a/ecc/bw6-756/fr/kzg/kzg_test.go
+++ b/ecc/bw6-756/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bw6756.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bw6-756/fr/kzg/marshal.go b/ecc/bw6-756/fr/kzg/marshal.go
index 2f61ed281..2c91e15e2 100644
--- a/ecc/bw6-756/fr/kzg/marshal.go
+++ b/ecc/bw6-756/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bw6756.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bw6756.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bw6756.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bw6756.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bw6756.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bw6756.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bw6756.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bw6756.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bw6-756/fr/pedersen/pedersen.go b/ecc/bw6-756/fr/pedersen/pedersen.go
index a670f6ac5..e6377e136 100644
--- a/ecc/bw6-756/fr/pedersen/pedersen.go
+++ b/ecc/bw6-756/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bw6-756"
+	curve "github.com/consensys/gnark-crypto/ecc/bw6-756"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bw6756.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bw6756.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bw6756.G1Affine
-	basisExpSigma []bw6756.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bw6756.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bw6756.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bw6756.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bw6756.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bw6756.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bw6756.G1Affine, knowledgeProof bw6756.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bw6756.G1Affine, knowledge
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bw6756.G1Affine, knowledgeProof bw6756.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bw6756.Pair([]bw6756.G1Affine{commitment, knowledgeProof}, []bw6756.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bw6756.G1Affine, knowledgeProof bw
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bw6-756/fr/pedersen/pedersen_test.go b/ecc/bw6-756/fr/pedersen/pedersen_test.go
index a4b5387c5..62319db8a 100644
--- a/ecc/bw6-756/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-756/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bw6-756"
+	curve "github.com/consensys/gnark-crypto/ecc/bw6-756"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bw6756.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bw6756.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bw6756.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bw6756.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bw6756.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bw6-756/fr/permutation/permutation.go b/ecc/bw6-756/fr/permutation/permutation.go
index 5cfe45c87..c30462fc9 100644
--- a/ecc/bw6-756/fr/permutation/permutation.go
+++ b/ecc/bw6-756/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bw6-756/fr/permutation/permutation_test.go b/ecc/bw6-756/fr/permutation/permutation_test.go
index 9f56b94c6..9dbf17890 100644
--- a/ecc/bw6-756/fr/permutation/permutation_test.go
+++ b/ecc/bw6-756/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-756/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bw6-756/fr/plookup/plookup_test.go b/ecc/bw6-756/fr/plookup/plookup_test.go
index c33c0d1cb..8c4acdb07 100644
--- a/ecc/bw6-756/fr/plookup/plookup_test.go
+++ b/ecc/bw6-756/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bw6-756/fr/plookup/table.go b/ecc/bw6-756/fr/plookup/table.go
index 0caeceef6..68abe9104 100644
--- a/ecc/bw6-756/fr/plookup/table.go
+++ b/ecc/bw6-756/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bw6-756/fr/plookup/vector.go b/ecc/bw6-756/fr/plookup/vector.go
index 3096ba9b1..3a034baef 100644
--- a/ecc/bw6-756/fr/plookup/vector.go
+++ b/ecc/bw6-756/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bw6-756/g1.go b/ecc/bw6-756/g1.go
index 28fd27815..de931f160 100644
--- a/ecc/bw6-756/g1.go
+++ b/ecc/bw6-756/g1.go
@@ -97,6 +97,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bw6-756/g2.go b/ecc/bw6-756/g2.go
index 641b798cd..40c786ce8 100644
--- a/ecc/bw6-756/g2.go
+++ b/ecc/bw6-756/g2.go
@@ -76,6 +76,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bw6-756/hash_to_g1.go b/ecc/bw6-756/hash_to_g1.go
index bf4a9ba3a..c7b678b2f 100644
--- a/ecc/bw6-756/hash_to_g1.go
+++ b/ecc/bw6-756/hash_to_g1.go
@@ -168,9 +168,9 @@ func g1MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve1 implements the SSWU map
+// MapToCurve1 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{6087387690755251612, 7643068232434215576, 6195945763281467660, 97569654519975969, 1505434147110560758, 12342644747290341982, 14059794106692380317, 15229664573794943703, 16908793757593141664, 1949816925291208189, 9451095697369482684, 234190359239853}
 	var sswuIsoCurveCoeffB = fp.Element{18446744073709458379, 881299893533802495, 4886355625346099349, 6225448195760991771, 6629400315996169345, 12607886696045185322, 7201730065066775519, 1932403901886200506, 8616600553259348813, 6369175937589644082, 7499857803942196586, 3773119276850162}
@@ -270,7 +270,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SSWU map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	//this is in an isogenous curve
 	g1Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -289,7 +289,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	//this is in an isogenous curve
 	g1Isogeny(&res)
@@ -307,8 +307,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g1Isogeny(&Q0)
diff --git a/ecc/bw6-756/hash_to_g1_test.go b/ecc/bw6-756/hash_to_g1_test.go
index 7a7b2dbcf..230a841d9 100644
--- a/ecc/bw6-756/hash_to_g1_test.go
+++ b/ecc/bw6-756/hash_to_g1_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !isOnE1Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bw6-756/hash_to_g2.go b/ecc/bw6-756/hash_to_g2.go
index f3246ede4..d314f0cfa 100644
--- a/ecc/bw6-756/hash_to_g2.go
+++ b/ecc/bw6-756/hash_to_g2.go
@@ -240,9 +240,9 @@ func g2MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve2 implements the SSWU map
+// MapToCurve2 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve2(u *fp.Element) G2Affine {
+func MapToCurve2(u *fp.Element) G2Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{11188695195863236139, 18339800635248689929, 13644954250665578253, 16122525194076552550, 1985822167495960177, 11021218035968661748, 12951199075167016614, 18080500199774882647, 3065668365127963650, 1810223365641727596, 18249180996905802984, 4351293214471385}
 	var sswuIsoCurveCoeffB = fp.Element{3597427888115195847, 8485485194496420669, 9451115945982544412, 10217463679676360079, 3023875305953960937, 5866766270380139867, 15059909646037855295, 1065687373540957157, 12978541562777068958, 18112033168403904062, 11632286302244735111, 1469792042332206}
@@ -342,7 +342,7 @@ func g2Sgn0(z *fp.Element) uint64 {
 
 // MapToG2 invokes the SSWU map, and guarantees that the result is in g2
 func MapToG2(u fp.Element) G2Affine {
-	res := mapToCurve2(&u)
+	res := MapToCurve2(&u)
 	//this is in an isogenous curve
 	g2Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -361,7 +361,7 @@ func EncodeToG2(msg, dst []byte) (G2Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve2(&u[0])
+	res = MapToCurve2(&u[0])
 
 	//this is in an isogenous curve
 	g2Isogeny(&res)
@@ -379,8 +379,8 @@ func HashToG2(msg, dst []byte) (G2Affine, error) {
 		return G2Affine{}, err
 	}
 
-	Q0 := mapToCurve2(&u[0])
-	Q1 := mapToCurve2(&u[1])
+	Q0 := MapToCurve2(&u[0])
+	Q1 := MapToCurve2(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g2Isogeny(&Q0)
diff --git a/ecc/bw6-756/hash_to_g2_test.go b/ecc/bw6-756/hash_to_g2_test.go
index 4ec5aa85b..77d526ffa 100644
--- a/ecc/bw6-756/hash_to_g2_test.go
+++ b/ecc/bw6-756/hash_to_g2_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve2(t *testing.T) {
 	properties.Property("[G2] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve2(&a)
+			g := MapToCurve2(&a)
 
 			if !isOnE2Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range encodeToG2Vector.cases {
 		var u fp.Element
 		g2CoordSetString(&u, c.u)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range hashToG2Vector.cases {
 		var u fp.Element
 		g2CoordSetString(&u, c.u0)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g2CoordSetString(&u, c.u1)
-		q = mapToCurve2(&u)
+		q = MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bw6-756/internal/fptower/e6.go b/ecc/bw6-756/internal/fptower/e6.go
index 547b6ec23..71f2b305c 100644
--- a/ecc/bw6-756/internal/fptower/e6.go
+++ b/ecc/bw6-756/internal/fptower/e6.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
@@ -230,15 +228,18 @@ func (z *E6) DecompressKarabina(x *E6) *E6 {
 	var one fp.Element
 	one.SetOne()
 
-	// g3 == 0
-	if x.B1.A0.IsZero() {
+	if x.B1.A0.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.B0.A1, &x.B1.A2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.B0.A2)
 
 		// g3 != 0
-	} else {
+
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
 		// t0 = g1²
 		t[0].Square(&x.B0.A1)
 		// t1 = 3 * g1² - 2 * g2
@@ -608,7 +609,6 @@ func (z *E6) SetBytes(e []byte) error {
 	z.B0.A1.SetBytes(e[offset : offset+fp.Bytes])
 	offset += fp.Bytes
 	z.B0.A0.SetBytes(e[offset : offset+fp.Bytes])
-	offset += fp.Bytes
 
 	return nil
 }
@@ -618,7 +618,7 @@ func (z *E6) IsInSubGroup() bool {
 	var tmp, a, _a, b E6
 	var t [6]E6
 
-	// check z^(Phi_k(p)) == 1
+	// check z^(phi_k(p)) == 1
 	a.Frobenius(z)
 	b.Frobenius(&a).Mul(&b, z)
 
diff --git a/ecc/bw6-756/internal/fptower/e6_test.go b/ecc/bw6-756/internal/fptower/e6_test.go
index c32630a40..cd69cbff5 100644
--- a/ecc/bw6-756/internal/fptower/e6_test.go
+++ b/ecc/bw6-756/internal/fptower/e6_test.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
diff --git a/ecc/bw6-756/marshal.go b/ecc/bw6-756/marshal.go
index 868b34577..31046c5f7 100644
--- a/ecc/bw6-756/marshal.go
+++ b/ecc/bw6-756/marshal.go
@@ -32,25 +32,27 @@ import (
 // To encode G1Affine and G2Affine points, we mask the most significant bits with these bits to specify without ambiguity
 // metadata needed for point (de)compression
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
 	mUncompressed         byte = 0b000 << 5
+	_                     byte = 0b001 << 5 // invalid
 	mUncompressedInfinity byte = 0b010 << 5
+	_                     byte = 0b011 << 5 // invalid
 	mCompressedSmallest   byte = 0b100 << 5
 	mCompressedLargest    byte = 0b101 << 5
 	mCompressedInfinity   byte = 0b110 << 5
+	_                     byte = 0b111 << 5 // invalid
 )
 
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bw6-756 object values to an output stream
 type Encoder struct {
@@ -103,6 +105,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -135,6 +155,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -155,6 +182,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -186,6 +220,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -245,6 +286,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -315,6 +363,12 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return
 }
 
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
 	return !((mData == mUncompressed) || (mData == mUncompressedInfinity))
@@ -398,6 +452,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -501,6 +557,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -586,6 +644,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 96
 
@@ -598,7 +675,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -682,6 +759,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG1AffineUncompressed {
@@ -854,7 +936,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -938,6 +1020,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG2AffineUncompressed {
diff --git a/ecc/bw6-756/marshal_test.go b/ecc/bw6-756/marshal_test.go
index b17c560f4..c706745f4 100644
--- a/ecc/bw6-756/marshal_test.go
+++ b/ecc/bw6-756/marshal_test.go
@@ -216,6 +216,26 @@ func TestIsCompressed(t *testing.T) {
 
 }
 
+func TestG1AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG1AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G1Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG1AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -309,6 +329,26 @@ func TestG1AffineSerialization(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestG2AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG2AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G2Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG2AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
diff --git a/ecc/bw6-756/pairing.go b/ecc/bw6-756/pairing.go
index 9a3bc5b4c..d4e1b2945 100644
--- a/ecc/bw6-756/pairing.go
+++ b/ecc/bw6-756/pairing.go
@@ -79,9 +79,15 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	result.Frobenius(&buf).
 		Mul(&result, &buf)
 
-		// Hard part (up to permutation)
-		// El Housni and Guillevic
-		// https://eprint.iacr.org/2020/351.pdf
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
+	// Hard part (up to permutation)
+	// El Housni and Guillevic
+	// https://eprint.iacr.org/2020/351.pdf
 	var m1, _m1, m2, _m2, m3, f0, f0_36, g0, g1, _g1, g2, g3, _g3, g4, _g4, g5, _g5, g6, gA, gB, g034, _g1g2, gC, h1, h2, h2g2C, h4 GT
 	m1.Expt(&result)
 	_m1.Conjugate(&m1)
diff --git a/ecc/bw6-761/fr/kzg/kzg.go b/ecc/bw6-761/fr/kzg/kzg.go
index f6636b994..d90d4c7f3 100644
--- a/ecc/bw6-761/fr/kzg/kzg.go
+++ b/ecc/bw6-761/fr/kzg/kzg.go
@@ -32,6 +32,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -41,12 +42,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = bw6761.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
-	G1 []bw6761.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
+	G1 []bw6761.G1Affine // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]bw6761.G2Affine // [G₂, [α]G₂ ]
+	G1 bw6761.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -69,17 +82,17 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]bw6761.G1Affine, size)
+	srs.Pk.G1 = make([]bw6761.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := bw6761.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -87,7 +100,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := bw6761.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -116,9 +129,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -128,7 +141,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -137,8 +150,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -155,7 +168,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -165,13 +178,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff bw6761.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac bw6761.G1Jac
@@ -182,28 +195,19 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH bw6761.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac bw6761.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 bw6761.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
-
-	// [α-a]G₂
-	var xminusaG2Aff bw6761.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
-
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff bw6761.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff bw6761.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := bw6761.PairingCheck(
-		[]bw6761.G1Affine{fminusfaG1Aff, negH},
-		[]bw6761.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]bw6761.G1Affine{totalG1Aff, negH},
+		[]bw6761.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -215,12 +219,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -231,7 +235,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -252,8 +256,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -262,8 +269,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -299,7 +304,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -317,13 +322,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -332,7 +337,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -353,7 +361,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -361,8 +369,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -373,16 +381,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -402,9 +415,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -424,7 +436,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit bw6761.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -451,7 +463,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := bw6761.PairingCheck(
 		[]bw6761.G1Affine{foldedDigests, foldedQuotients},
-		[]bw6761.G2Affine{srs.G2[0], srs.G2[1]},
+		[]bw6761.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -472,7 +484,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -495,18 +507,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/ecc/bw6-761/fr/kzg/kzg_test.go b/ecc/bw6-761/fr/kzg/kzg_test.go
index 67c2025f6..a48206647 100644
--- a/ecc/bw6-761/fr/kzg/kzg_test.go
+++ b/ecc/bw6-761/fr/kzg/kzg_test.go
@@ -17,23 +17,24 @@
 package kzg
 
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -63,7 +64,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -78,32 +79,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -115,7 +96,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -129,7 +110,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit bw6761.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -145,7 +126,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -153,7 +134,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -173,7 +154,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -183,7 +164,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -196,14 +177,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -213,21 +194,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -235,7 +216,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -245,12 +226,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -264,7 +244,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -274,9 +254,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -284,18 +264,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -304,7 +284,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -316,7 +296,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -327,16 +307,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -362,10 +340,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -374,15 +350,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -390,28 +364,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -422,7 +390,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -433,12 +401,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -452,7 +420,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -461,14 +429,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/ecc/bw6-761/fr/kzg/marshal.go b/ecc/bw6-761/fr/kzg/marshal.go
index 92cb2a1a7..2215fc6c5 100644
--- a/ecc/bw6-761/fr/kzg/marshal.go
+++ b/ecc/bw6-761/fr/kzg/marshal.go
@@ -21,15 +21,34 @@ import (
 	"io"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := bw6761.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, bw6761.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*bw6761.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := bw6761.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -41,15 +60,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := bw6761.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := bw6761.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -61,6 +102,18 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn + vn, err
+}
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := bw6761.NewEncoder(w)
@@ -118,7 +171,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := bw6761.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/ecc/bw6-761/fr/pedersen/pedersen.go b/ecc/bw6-761/fr/pedersen/pedersen.go
index 4af6559c9..f22b49970 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen.go
@@ -20,62 +20,68 @@ import (
 	"crypto/rand"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc"
-	"github.com/consensys/gnark-crypto/ecc/bw6-761"
+	curve "github.com/consensys/gnark-crypto/ecc/bw6-761"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"io"
 	"math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-	g             bw6761.G2Affine // TODO @tabaie: does this really have to be randomized?
-	gRootSigmaNeg bw6761.G2Affine //gRootSigmaNeg = g^{-1/σ}
-	basis         []bw6761.G1Affine
-	basisExpSigma []bw6761.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() (bw6761.G2Affine, error) { // TODO: Add to G2.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bw6761.G2Affine{}, err
+type VerifyingKey struct {
+	g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+	gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+	res := make([]byte, fr.Bytes)
+	_, err := rand.Read(res)
+	return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G2Affine{}, err
+	} else {
+		return curve.HashToG2(gBytes, []byte("random on g2"))
 	}
-	return bw6761.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []bw6761.G1Affine) (Key, error) {
-	var (
-		k   Key
-		err error
-	)
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-	if k.g, err = randomOnG2(); err != nil {
-		return k, err
+	if vk.g, err = randomOnG2(); err != nil {
+		return
 	}
 
 	var modMinusOne big.Int
 	modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
 	var sigma *big.Int
 	if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-		return k, err
+		return
 	}
 	sigma.Add(sigma, big.NewInt(1))
 
 	var sigmaInvNeg big.Int
 	sigmaInvNeg.ModInverse(sigma, fr.Modulus())
 	sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-	k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+	vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-	k.basisExpSigma = make([]bw6761.G1Affine, len(basis))
+	pk.basisExpSigma = make([]curve.G1Affine, len(basis))
 	for i := range basis {
-		k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+		pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
 	}
 
-	k.basis = basis
-	return k, err
+	pk.basis = basis
+	return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment bw6761.G1Affine, knowledgeProof bw6761.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-	if len(values) != len(k.basis) {
+	if len(values) != len(pk.basis) {
 		err = fmt.Errorf("unexpected number of values")
 		return
 	}
@@ -86,23 +92,23 @@ func (k *Key) Commit(values []fr.Element) (commitment bw6761.G1Affine, knowledge
 		NbTasks: 1, // TODO Experiment
 	}
 
-	if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+	if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
 		return
 	}
 
-	_, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+	_, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
 	return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment bw6761.G1Affine, knowledgeProof bw6761.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
 	if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
 		return fmt.Errorf("subgroup check failed")
 	}
 
-	product, err := bw6761.Pair([]bw6761.G1Affine{commitment, knowledgeProof}, []bw6761.G2Affine{k.g, k.gRootSigmaNeg})
+	product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
 	if err != nil {
 		return err
 	}
@@ -111,3 +117,56 @@ func (k *Key) VerifyKnowledgeProof(commitment bw6761.G1Affine, knowledgeProof bw
 	}
 	return fmt.Errorf("proof rejected")
 }
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+	if err := enc.Encode(pk.basis); err != nil {
+		return enc.BytesWritten(), err
+	}
+
+	err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+	if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+	if err := dec.Decode(&pk.basisExpSigma); err != nil {
+		return dec.BytesRead(), err
+	}
+
+	if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+		return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+	}
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
diff --git a/ecc/bw6-761/fr/pedersen/pedersen_test.go b/ecc/bw6-761/fr/pedersen/pedersen_test.go
index 1747d3a0b..646cf0e9b 100644
--- a/ecc/bw6-761/fr/pedersen/pedersen_test.go
+++ b/ecc/bw6-761/fr/pedersen/pedersen_test.go
@@ -17,10 +17,10 @@
 package pedersen
 
 import (
-	"github.com/consensys/gnark-crypto/ecc/bw6-761"
+	curve "github.com/consensys/gnark-crypto/ecc/bw6-761"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -44,37 +44,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() (bw6761.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return bw6761.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return bw6761.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]bw6761.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key             Key
+		pk              ProvingKey
+		vk              VerifyingKey
 		err             error
-		commitment, pok bw6761.G1Affine
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -88,3 +94,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
diff --git a/ecc/bw6-761/fr/permutation/permutation.go b/ecc/bw6-761/fr/permutation/permutation.go
index d56d9a6d2..31e851656 100644
--- a/ecc/bw6-761/fr/permutation/permutation.go
+++ b/ecc/bw6-761/fr/permutation/permutation.go
@@ -132,7 +132,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -167,11 +167,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -185,7 +185,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -223,7 +223,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -250,7 +250,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -261,7 +261,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -273,7 +273,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -330,7 +330,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -338,7 +338,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/ecc/bw6-761/fr/permutation/permutation_test.go b/ecc/bw6-761/fr/permutation/permutation_test.go
index 04cfd736e..4cdb905ce 100644
--- a/ecc/bw6-761/fr/permutation/permutation_test.go
+++ b/ecc/bw6-761/fr/permutation/permutation_test.go
@@ -20,16 +20,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -43,12 +43,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -75,7 +75,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -88,7 +88,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/ecc/bw6-761/fr/plookup/plookup_test.go b/ecc/bw6-761/fr/plookup/plookup_test.go
index dce85a34f..a9224f6a4 100644
--- a/ecc/bw6-761/fr/plookup/plookup_test.go
+++ b/ecc/bw6-761/fr/plookup/plookup_test.go
@@ -35,19 +35,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -57,12 +57,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -72,7 +72,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,12 +92,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -106,12 +106,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -124,7 +124,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -135,6 +135,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/ecc/bw6-761/fr/plookup/table.go b/ecc/bw6-761/fr/plookup/table.go
index 7036fac08..203e3eb3b 100644
--- a/ecc/bw6-761/fr/plookup/table.go
+++ b/ecc/bw6-761/fr/plookup/table.go
@@ -60,7 +60,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -116,7 +116,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -131,7 +131,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -164,20 +164,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -221,13 +221,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/ecc/bw6-761/fr/plookup/vector.go b/ecc/bw6-761/fr/plookup/vector.go
index 34da3f373..25be7af31 100644
--- a/ecc/bw6-761/fr/plookup/vector.go
+++ b/ecc/bw6-761/fr/plookup/vector.go
@@ -353,7 +353,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // before generating a lookup proof), the commitment needs to be done on the
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -401,11 +401,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -431,11 +431,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -456,7 +456,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -500,7 +500,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -529,7 +529,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -551,7 +551,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -561,7 +561,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -603,7 +603,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -622,7 +622,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/ecc/bw6-761/g1.go b/ecc/bw6-761/g1.go
index ab29f2f24..958fe7450 100644
--- a/ecc/bw6-761/g1.go
+++ b/ecc/bw6-761/g1.go
@@ -97,6 +97,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/bw6-761/g2.go b/ecc/bw6-761/g2.go
index 9687efef3..73a3a9ba8 100644
--- a/ecc/bw6-761/g2.go
+++ b/ecc/bw6-761/g2.go
@@ -76,6 +76,16 @@ func (p *G2Affine) Add(a, b *G2Affine) *G2Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G2Affine) Double(a *G2Affine) *G2Affine {
+	var p1 G2Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G2Affine) Sub(a, b *G2Affine) *G2Affine {
diff --git a/ecc/bw6-761/hash_to_g1.go b/ecc/bw6-761/hash_to_g1.go
index a26f10d83..2dd3fd0d0 100644
--- a/ecc/bw6-761/hash_to_g1.go
+++ b/ecc/bw6-761/hash_to_g1.go
@@ -131,9 +131,9 @@ func g1MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve1 implements the SSWU map
+// MapToCurve1 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{12169852093062392636, 3867460573998792965, 2540986171999662608, 3377838107874487171, 6313266756742099767, 5994530928773814047, 5007141583730923456, 2345996307867737670, 7096861766432061441, 10014420324597579745, 8416419844935780388, 63340978449966806}
 	var sswuIsoCurveCoeffB = fp.Element{9514135687797572479, 9972495974968977338, 17954535578332286571, 7437044986470910914, 13903267017721129281, 1871129682978723308, 13401268269932482209, 739043012311877982, 12116264695643437343, 1632209977726909861, 3621981106970059143, 65605772132525947}
@@ -233,7 +233,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SSWU map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	//this is in an isogenous curve
 	g1Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -252,7 +252,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	//this is in an isogenous curve
 	g1Isogeny(&res)
@@ -270,8 +270,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g1Isogeny(&Q0)
diff --git a/ecc/bw6-761/hash_to_g1_test.go b/ecc/bw6-761/hash_to_g1_test.go
index a268f8b0e..ddfc96c56 100644
--- a/ecc/bw6-761/hash_to_g1_test.go
+++ b/ecc/bw6-761/hash_to_g1_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !isOnE1Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1Isogeny(&q)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bw6-761/hash_to_g2.go b/ecc/bw6-761/hash_to_g2.go
index f0bc4678e..4b2080736 100644
--- a/ecc/bw6-761/hash_to_g2.go
+++ b/ecc/bw6-761/hash_to_g2.go
@@ -307,9 +307,9 @@ func g2MulByZ(z *fp.Element, x *fp.Element) {
 }
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve2 implements the SSWU map
+// MapToCurve2 implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve2(u *fp.Element) G2Affine {
+func MapToCurve2(u *fp.Element) G2Affine {
 
 	var sswuIsoCurveCoeffA = fp.Element{13704010396169241312, 14330175345318364589, 4449492585807198633, 9884564993510771995, 16507506367033405761, 12171409358426895620, 3759742122315801393, 6972450370136308820, 13649992927502603798, 15742083997009939515, 4062268800652448528, 42571325818609943}
 	var sswuIsoCurveCoeffB = fp.Element{17251063859315847117, 13422534455279952781, 15626212001505409941, 8548929388122544483, 12216093319907597521, 15761783579263790289, 10925761432004348632, 8228665107915194054, 13147767302058909808, 5735540302608306489, 5152863309501448410, 45595036249636616}
@@ -409,7 +409,7 @@ func g2Sgn0(z *fp.Element) uint64 {
 
 // MapToG2 invokes the SSWU map, and guarantees that the result is in g2
 func MapToG2(u fp.Element) G2Affine {
-	res := mapToCurve2(&u)
+	res := MapToCurve2(&u)
 	//this is in an isogenous curve
 	g2Isogeny(&res)
 	res.ClearCofactor(&res)
@@ -428,7 +428,7 @@ func EncodeToG2(msg, dst []byte) (G2Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve2(&u[0])
+	res = MapToCurve2(&u[0])
 
 	//this is in an isogenous curve
 	g2Isogeny(&res)
@@ -446,8 +446,8 @@ func HashToG2(msg, dst []byte) (G2Affine, error) {
 		return G2Affine{}, err
 	}
 
-	Q0 := mapToCurve2(&u[0])
-	Q1 := mapToCurve2(&u[1])
+	Q0 := MapToCurve2(&u[0])
+	Q1 := MapToCurve2(&u[1])
 
 	//TODO (perf): Add in E' first, then apply isogeny
 	g2Isogeny(&Q0)
diff --git a/ecc/bw6-761/hash_to_g2_test.go b/ecc/bw6-761/hash_to_g2_test.go
index 246016b4c..a030e271b 100644
--- a/ecc/bw6-761/hash_to_g2_test.go
+++ b/ecc/bw6-761/hash_to_g2_test.go
@@ -93,7 +93,7 @@ func TestMapToCurve2(t *testing.T) {
 	properties.Property("[G2] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve2(&a)
+			g := MapToCurve2(&a)
 
 			if !isOnE2Prime(g) {
 				t.Log("Mapping output not on E' curve")
@@ -116,7 +116,7 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range encodeToG2Vector.cases {
 		var u fp.Element
 		g2CoordSetString(&u, c.u)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
@@ -124,12 +124,12 @@ func TestMapToCurve2(t *testing.T) {
 	for _, c := range hashToG2Vector.cases {
 		var u fp.Element
 		g2CoordSetString(&u, c.u0)
-		q := mapToCurve2(&u)
+		q := MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g2CoordSetString(&u, c.u1)
-		q = mapToCurve2(&u)
+		q = MapToCurve2(&u)
 		g2Isogeny(&q)
 		g2TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
diff --git a/ecc/bw6-761/internal/fptower/e6.go b/ecc/bw6-761/internal/fptower/e6.go
index 12167e26c..046e3eec5 100644
--- a/ecc/bw6-761/internal/fptower/e6.go
+++ b/ecc/bw6-761/internal/fptower/e6.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
@@ -230,15 +228,18 @@ func (z *E6) DecompressKarabina(x *E6) *E6 {
 	var one fp.Element
 	one.SetOne()
 
-	// g3 == 0
-	if x.B1.A0.IsZero() {
+	if x.B1.A0.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.B0.A1, &x.B1.A2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.B0.A2)
 
 		// g3 != 0
-	} else {
+
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
 		// t0 = g1^2
 		t[0].Square(&x.B0.A1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -608,7 +609,6 @@ func (z *E6) SetBytes(e []byte) error {
 	z.B0.A1.SetBytes(e[offset : offset+fp.Bytes])
 	offset += fp.Bytes
 	z.B0.A0.SetBytes(e[offset : offset+fp.Bytes])
-	offset += fp.Bytes
 
 	return nil
 }
@@ -618,7 +618,7 @@ func (z *E6) IsInSubGroup() bool {
 	var tmp, a, _a, b E6
 	var t [6]E6
 
-	// check z^(Phi_k(p)) == 1
+	// check z^(phi_k(p)) == 1
 	a.Frobenius(z)
 	b.Frobenius(&a).Mul(&b, z)
 
diff --git a/ecc/bw6-761/internal/fptower/e6_test.go b/ecc/bw6-761/internal/fptower/e6_test.go
index cb96e6847..1cf291d88 100644
--- a/ecc/bw6-761/internal/fptower/e6_test.go
+++ b/ecc/bw6-761/internal/fptower/e6_test.go
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by consensys/gnark-crypto DO NOT EDIT
-
 package fptower
 
 import (
diff --git a/ecc/bw6-761/marshal.go b/ecc/bw6-761/marshal.go
index 54bf3ed50..a116dbbc2 100644
--- a/ecc/bw6-761/marshal.go
+++ b/ecc/bw6-761/marshal.go
@@ -32,25 +32,27 @@ import (
 // To encode G1Affine and G2Affine points, we mask the most significant bits with these bits to specify without ambiguity
 // metadata needed for point (de)compression
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
 	mUncompressed         byte = 0b000 << 5
+	_                     byte = 0b001 << 5 // invalid
 	mUncompressedInfinity byte = 0b010 << 5
+	_                     byte = 0b011 << 5 // invalid
 	mCompressedSmallest   byte = 0b100 << 5
 	mCompressedLargest    byte = 0b101 << 5
 	mCompressedInfinity   byte = 0b110 << 5
+	_                     byte = 0b111 << 5 // invalid
 )
 
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding         = errors.New("invalid point encoding")
+)
 
 // Encoder writes bw6-761 object values to an output stream
 type Encoder struct {
@@ -103,6 +105,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -135,6 +155,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -155,6 +182,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+
 		// most significant byte contains metadata
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -186,6 +220,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -245,6 +286,13 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+
 			// most significant byte contains metadata
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -315,6 +363,12 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return
 }
 
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
 	return !((mData == mUncompressed) || (mData == mUncompressedInfinity))
@@ -398,6 +452,8 @@ func (enc *Encoder) encode(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -501,6 +557,8 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -586,6 +644,25 @@ func (enc *Encoder) encodeRaw(v interface{}) (err error) {
 	}
 }
 
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
 // SizeOfG1AffineCompressed represents the size in bytes that a G1Affine need in binary form, compressed
 const SizeOfG1AffineCompressed = 96
 
@@ -598,7 +675,7 @@ func (p *G1Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G1Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -682,6 +759,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG1AffineUncompressed {
@@ -854,7 +936,7 @@ func (p *G2Affine) Marshal() []byte {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *G2Affine) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err
@@ -938,6 +1020,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) {
 	// most significant byte
 	mData := buf[0] & mMask
 
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+
 	// check buffer size
 	if (mData == mUncompressed) || (mData == mUncompressedInfinity) {
 		if len(buf) < SizeOfG2AffineUncompressed {
diff --git a/ecc/bw6-761/marshal_test.go b/ecc/bw6-761/marshal_test.go
index fe66a6741..452f68177 100644
--- a/ecc/bw6-761/marshal_test.go
+++ b/ecc/bw6-761/marshal_test.go
@@ -216,6 +216,26 @@ func TestIsCompressed(t *testing.T) {
 
 }
 
+func TestG1AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG1AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G1Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG1AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -309,6 +329,26 @@ func TestG1AffineSerialization(t *testing.T) {
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
+func TestG2AffineInvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOfG2AffineCompressed]byte
+	rand.Read(buf[:])
+
+	var p G2Affine
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+
 func TestG2AffineSerialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
diff --git a/ecc/bw6-761/pairing.go b/ecc/bw6-761/pairing.go
index a5bad7733..e37bcf079 100644
--- a/ecc/bw6-761/pairing.go
+++ b/ecc/bw6-761/pairing.go
@@ -78,6 +78,12 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
 	result.Frobenius(&buf).
 		Mul(&result, &buf)
 
+	var one GT
+	one.SetOne()
+	if result.Equal(&one) {
+		return result
+	}
+
 	// Hard part (up to permutation)
 	// El Housni and Guillevic
 	// https://eprint.iacr.org/2020/351.pdf
diff --git a/ecc/secp256k1/ecdsa/ecdsa.go b/ecc/secp256k1/ecdsa/ecdsa.go
index e71985e3e..742add4b9 100644
--- a/ecc/secp256k1/ecdsa/ecdsa.go
+++ b/ecc/secp256k1/ecdsa/ecdsa.go
@@ -140,20 +140,14 @@ func RecoverP(v uint, r *big.Int) (*secp256k1.G1Affine, error) {
 	if y.ModSqrt(y, fp.Modulus()) == nil {
 		return nil, errors.New("no square root")
 	}
-	// y2 is -y
-	y2 := new(big.Int).Sub(fp.Modulus(), y)
-	// if yChoice == 0, return min(y, y2), else max(y, y2)
-	if (y.Cmp(y2) < 0) == (yChoice == 0) {
-		return &secp256k1.G1Affine{
-			X: *new(fp.Element).SetBigInt(x),
-			Y: *new(fp.Element).SetBigInt(y),
-		}, nil
-	} else {
-		return &secp256k1.G1Affine{
-			X: *new(fp.Element).SetBigInt(x),
-			Y: *new(fp.Element).SetBigInt(y2),
-		}, nil
+	// check that y has same oddity as defined by v
+	if y.Bit(0) != yChoice {
+		y = y.Sub(fp.Modulus(), y)
 	}
+	return &secp256k1.G1Affine{
+		X: *new(fp.Element).SetBigInt(x),
+		Y: *new(fp.Element).SetBigInt(y),
+	}, nil
 }
 
 type zr struct{}
@@ -241,8 +235,6 @@ func (privKey *PrivateKey) Public() signature.PublicKey {
 //
 // SEC 1, Version 2.0, Section 4.1.3
 func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v uint, r, s *big.Int, err error) {
-	halfp := new(big.Int).Sub(fp.Modulus(), big.NewInt(1))
-	halfp.Div(halfp, big.NewInt(2))
 	r, s = new(big.Int), new(big.Int)
 
 	scalar, kInv := new(big.Int), new(big.Int)
@@ -265,10 +257,8 @@ func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v ui
 			P.X.BigInt(r)
 			// set how many times we overflow the scalar field
 			v |= (uint(new(big.Int).Div(r, order).Uint64())) << 1
-			// set if y is small or big
-			if P.Y.BigInt(new(big.Int)).Cmp(halfp) >= 0 {
-				v |= 1
-			}
+			// set if y is even or odd
+			v |= P.Y.BigInt(new(big.Int)).Bit(0)
 
 			r.Mod(r, order)
 			if r.Sign() != 0 {
diff --git a/ecc/secp256k1/ecdsa/marshal.go b/ecc/secp256k1/ecdsa/marshal.go
index 3372368ab..9eb91dc9e 100644
--- a/ecc/secp256k1/ecdsa/marshal.go
+++ b/ecc/secp256k1/ecdsa/marshal.go
@@ -18,6 +18,7 @@ package ecdsa
 
 import (
 	"crypto/subtle"
+	"errors"
 	"io"
 	"math/big"
 
@@ -61,6 +62,12 @@ func (pk *PublicKey) SetBytes(buf []byte) (int, error) {
 // methods sets the current public key to the recovered value. Otherwise returns
 // error and leaves current public key unchanged.
 func (pk *PublicKey) RecoverFrom(msg []byte, v uint, r, s *big.Int) error {
+	if s.Cmp(fr.Modulus()) >= 0 {
+		return errors.New("s is larger than modulus")
+	}
+	if s.Cmp(big.NewInt(0)) <= 0 {
+		return errors.New("s is negative")
+	}
 	P, err := RecoverP(v, r)
 	if err != nil {
 		return err
diff --git a/ecc/secp256k1/g1.go b/ecc/secp256k1/g1.go
index 82c797965..2b677c179 100644
--- a/ecc/secp256k1/g1.go
+++ b/ecc/secp256k1/g1.go
@@ -92,6 +92,16 @@ func (p *G1Affine) Add(a, b *G1Affine) *G1Affine {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *G1Affine) Double(a *G1Affine) *G1Affine {
+	var p1 G1Jac
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *G1Affine) Sub(a, b *G1Affine) *G1Affine {
diff --git a/ecc/secp256k1/hash_to_g1.go b/ecc/secp256k1/hash_to_g1.go
index 8f87a6634..21c2c13a1 100644
--- a/ecc/secp256k1/hash_to_g1.go
+++ b/ecc/secp256k1/hash_to_g1.go
@@ -20,10 +20,10 @@ import (
 	"github.com/consensys/gnark-crypto/ecc/secp256k1/fp"
 )
 
-// mapToCurve1 implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
+// MapToCurve1 implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
 // No cofactor clearing or isogeny
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#straightline-svdw
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 	var tv1, tv2, tv3, tv4 fp.Element
 	var x1, x2, x3, gx1, gx2, gx, x, y fp.Element
 	var one fp.Element
@@ -112,7 +112,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SVDW map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	return res
 }
 
@@ -128,7 +128,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	return res, nil
 }
@@ -143,8 +143,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	var _Q0, _Q1 G1Jac
 	_Q0.FromAffine(&Q0)
diff --git a/ecc/secp256k1/hash_to_g1_test.go b/ecc/secp256k1/hash_to_g1_test.go
index 825264e00..e4d31d0d1 100644
--- a/ecc/secp256k1/hash_to_g1_test.go
+++ b/ecc/secp256k1/hash_to_g1_test.go
@@ -57,7 +57,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !g.IsOnCurve() {
 				t.Log("SVDW output not on curve")
@@ -74,18 +74,18 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
 
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
 }
diff --git a/ecc/stark-curve/ecdsa/ecdsa.go b/ecc/stark-curve/ecdsa/ecdsa.go
index f9d9c5f0b..9746d29ad 100644
--- a/ecc/stark-curve/ecdsa/ecdsa.go
+++ b/ecc/stark-curve/ecdsa/ecdsa.go
@@ -140,20 +140,14 @@ func RecoverP(v uint, r *big.Int) (*starkcurve.G1Affine, error) {
 	if y.ModSqrt(y, fp.Modulus()) == nil {
 		return nil, errors.New("no square root")
 	}
-	// y2 is -y
-	y2 := new(big.Int).Sub(fp.Modulus(), y)
-	// if yChoice == 0, return min(y, y2), else max(y, y2)
-	if (y.Cmp(y2) < 0) == (yChoice == 0) {
-		return &starkcurve.G1Affine{
-			X: *new(fp.Element).SetBigInt(x),
-			Y: *new(fp.Element).SetBigInt(y),
-		}, nil
-	} else {
-		return &starkcurve.G1Affine{
-			X: *new(fp.Element).SetBigInt(x),
-			Y: *new(fp.Element).SetBigInt(y2),
-		}, nil
+	// check that y has same oddity as defined by v
+	if y.Bit(0) != yChoice {
+		y = y.Sub(fp.Modulus(), y)
 	}
+	return &starkcurve.G1Affine{
+		X: *new(fp.Element).SetBigInt(x),
+		Y: *new(fp.Element).SetBigInt(y),
+	}, nil
 }
 
 type zr struct{}
@@ -241,8 +235,6 @@ func (privKey *PrivateKey) Public() signature.PublicKey {
 //
 // SEC 1, Version 2.0, Section 4.1.3
 func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v uint, r, s *big.Int, err error) {
-	halfp := new(big.Int).Sub(fp.Modulus(), big.NewInt(1))
-	halfp.Div(halfp, big.NewInt(2))
 	r, s = new(big.Int), new(big.Int)
 
 	scalar, kInv := new(big.Int), new(big.Int)
@@ -265,10 +257,8 @@ func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v ui
 			P.X.BigInt(r)
 			// set how many times we overflow the scalar field
 			v |= (uint(new(big.Int).Div(r, order).Uint64())) << 1
-			// set if y is small or big
-			if P.Y.BigInt(new(big.Int)).Cmp(halfp) >= 0 {
-				v |= 1
-			}
+			// set if y is even or odd
+			v |= P.Y.BigInt(new(big.Int)).Bit(0)
 
 			r.Mod(r, order)
 			if r.Sign() != 0 {
diff --git a/ecc/stark-curve/ecdsa/marshal.go b/ecc/stark-curve/ecdsa/marshal.go
index 258a5a74b..8cf682d31 100644
--- a/ecc/stark-curve/ecdsa/marshal.go
+++ b/ecc/stark-curve/ecdsa/marshal.go
@@ -18,6 +18,7 @@ package ecdsa
 
 import (
 	"crypto/subtle"
+	"errors"
 	"io"
 	"math/big"
 
@@ -61,6 +62,12 @@ func (pk *PublicKey) SetBytes(buf []byte) (int, error) {
 // methods sets the current public key to the recovered value. Otherwise returns
 // error and leaves current public key unchanged.
 func (pk *PublicKey) RecoverFrom(msg []byte, v uint, r, s *big.Int) error {
+	if s.Cmp(fr.Modulus()) >= 0 {
+		return errors.New("s is larger than modulus")
+	}
+	if s.Cmp(big.NewInt(0)) <= 0 {
+		return errors.New("s is negative")
+	}
 	P, err := RecoverP(v, r)
 	if err != nil {
 		return err
diff --git a/ecc/stark-curve/hash_to_g1.go b/ecc/stark-curve/hash_to_g1.go
index 1d499e5de..68ac69e5f 100644
--- a/ecc/stark-curve/hash_to_g1.go
+++ b/ecc/stark-curve/hash_to_g1.go
@@ -20,10 +20,10 @@ import (
 	"github.com/consensys/gnark-crypto/ecc/stark-curve/fp"
 )
 
-// mapToCurve1 implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
+// MapToCurve1 implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
 // No cofactor clearing or isogeny
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#straightline-svdw
-func mapToCurve1(u *fp.Element) G1Affine {
+func MapToCurve1(u *fp.Element) G1Affine {
 	var tv1, tv2, tv3, tv4 fp.Element
 	var x1, x2, x3, gx1, gx2, gx, x, y fp.Element
 	var one fp.Element
@@ -112,7 +112,7 @@ func g1Sgn0(z *fp.Element) uint64 {
 
 // MapToG1 invokes the SVDW map, and guarantees that the result is in g1
 func MapToG1(u fp.Element) G1Affine {
-	res := mapToCurve1(&u)
+	res := MapToCurve1(&u)
 	return res
 }
 
@@ -128,7 +128,7 @@ func EncodeToG1(msg, dst []byte) (G1Affine, error) {
 		return res, err
 	}
 
-	res = mapToCurve1(&u[0])
+	res = MapToCurve1(&u[0])
 
 	return res, nil
 }
@@ -143,8 +143,8 @@ func HashToG1(msg, dst []byte) (G1Affine, error) {
 		return G1Affine{}, err
 	}
 
-	Q0 := mapToCurve1(&u[0])
-	Q1 := mapToCurve1(&u[1])
+	Q0 := MapToCurve1(&u[0])
+	Q1 := MapToCurve1(&u[1])
 
 	var _Q0, _Q1 G1Jac
 	_Q0.FromAffine(&Q0)
diff --git a/ecc/stark-curve/hash_to_g1_test.go b/ecc/stark-curve/hash_to_g1_test.go
index d226bb198..b53f89bba 100644
--- a/ecc/stark-curve/hash_to_g1_test.go
+++ b/ecc/stark-curve/hash_to_g1_test.go
@@ -57,7 +57,7 @@ func TestMapToCurve1(t *testing.T) {
 	properties.Property("[G1] mapping output must be on curve", prop.ForAll(
 		func(a fp.Element) bool {
 
-			g := mapToCurve1(&a)
+			g := MapToCurve1(&a)
 
 			if !g.IsOnCurve() {
 				t.Log("SVDW output not on curve")
@@ -74,18 +74,18 @@ func TestMapToCurve1(t *testing.T) {
 	for _, c := range encodeToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
 
 	for _, c := range hashToG1Vector.cases {
 		var u fp.Element
 		g1CoordSetString(&u, c.u0)
-		q := mapToCurve1(&u)
+		q := MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		g1CoordSetString(&u, c.u1)
-		q = mapToCurve1(&u)
+		q = MapToCurve1(&u)
 		g1TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
 }
diff --git a/ecc/stark-curve/pedersen-hash/pedersen_hash.go b/ecc/stark-curve/pedersen-hash/pedersen_hash.go
index 184ef3b96..40f13df3d 100644
--- a/ecc/stark-curve/pedersen-hash/pedersen_hash.go
+++ b/ecc/stark-curve/pedersen-hash/pedersen_hash.go
@@ -7,12 +7,12 @@ import (
 	"github.com/consensys/gnark-crypto/ecc/stark-curve/fp"
 )
 
+const nibbleCount = fp.Bits / 4
+
 var (
-	shiftPoint starkcurve.G1Jac
-	p0         starkcurve.G1Jac
-	p1         starkcurve.G1Jac
-	p2         starkcurve.G1Jac
-	p3         starkcurve.G1Jac
+	shiftPoint   starkcurve.G1Jac
+	pointIndexed [4][nibbleCount][16]*starkcurve.G1Jac
+	p            [4]starkcurve.G1Jac
 )
 
 func init() {
@@ -24,64 +24,89 @@ func init() {
 	shiftPoint.Y.SetString("1713931329540660377023406109199410414810705867260802078187082345529207694986")
 	shiftPoint.Z.SetOne()
 
-	p0.X.SetString("996781205833008774514500082376783249102396023663454813447423147977397232763")
-	p0.Y.SetString("1668503676786377725805489344771023921079126552019160156920634619255970485781")
-	p0.Z.SetOne()
-
-	p1.X.SetString("2251563274489750535117886426533222435294046428347329203627021249169616184184")
-	p1.Y.SetString("1798716007562728905295480679789526322175868328062420237419143593021674992973")
-	p1.Z.SetOne()
-
-	p2.X.SetString("2138414695194151160943305727036575959195309218611738193261179310511854807447")
-	p2.Y.SetString("113410276730064486255102093846540133784865286929052426931474106396135072156")
-	p2.Z.SetOne()
-
-	p3.X.SetString("2379962749567351885752724891227938183011949129833673362440656643086021394946")
-	p3.Y.SetString("776496453633298175483985398648758586525933812536653089401905292063708816422")
-	p3.Z.SetOne()
+	p[0].X.SetString("996781205833008774514500082376783249102396023663454813447423147977397232763")
+	p[0].Y.SetString("1668503676786377725805489344771023921079126552019160156920634619255970485781")
+	p[0].Z.SetOne()
+
+	p[1].X.SetString("2251563274489750535117886426533222435294046428347329203627021249169616184184")
+	p[1].Y.SetString("1798716007562728905295480679789526322175868328062420237419143593021674992973")
+	p[1].Z.SetOne()
+
+	p[2].X.SetString("2138414695194151160943305727036575959195309218611738193261179310511854807447")
+	p[2].Y.SetString("113410276730064486255102093846540133784865286929052426931474106396135072156")
+	p[2].Z.SetOne()
+
+	p[3].X.SetString("2379962749567351885752724891227938183011949129833673362440656643086021394946")
+	p[3].Y.SetString("776496453633298175483985398648758586525933812536653089401905292063708816422")
+	p[3].Z.SetOne()
+
+	var multiplier big.Int
+	for pointIndex, point := range p {
+		var nibbleIndexed [nibbleCount][16]*starkcurve.G1Jac
+		for nibIndex := uint(0); nibIndex < nibbleCount; nibIndex++ {
+			var selectorIndexed [16]*starkcurve.G1Jac
+			for selector := 0; selector < 16; selector++ {
+				multiplier.SetUint64(uint64(selector))
+				multiplier.Lsh(&multiplier, nibIndex*4)
+
+				res := point
+				res.ScalarMultiplication(&res, &multiplier)
+				selectorIndexed[selector] = &res
+			}
+			nibbleIndexed[nibIndex] = selectorIndexed
+		}
+		pointIndexed[pointIndex] = nibbleIndexed
+	}
 }
 
 // PedersenArray implements [Pedersen array hashing].
 //
 // [Pedersen array hashing]: https://docs.starknet.io/documentation/develop/Hashing/hash-functions/#array_hashing
-func PedersenArray(elems ...*fp.Element) *fp.Element {
-	d := new(fp.Element)
+func PedersenArray(elems ...*fp.Element) fp.Element {
+	var d fp.Element
 	for _, e := range elems {
-		d = Pedersen(d, e)
+		d = Pedersen(&d, e)
 	}
-	return Pedersen(d, new(fp.Element).SetUint64(uint64(len(elems))))
+	return Pedersen(&d, new(fp.Element).SetUint64(uint64(len(elems))))
 }
 
 // Pedersen implements the [Pedersen hash] based on the [reference implementation].
 //
 // [Pedersen hash]: https://docs.starknet.io/documentation/develop/Hashing/hash-functions/#pedersen_hash
 // [reference implementation]: https://github.com/starkware-libs/cairo-lang/blob/de741b92657f245a50caab99cfaef093152fd8be/src/starkware/crypto/signature/fast_pedersen_hash.py
-func Pedersen(a *fp.Element, b *fp.Element) *fp.Element {
+func Pedersen(a *fp.Element, b *fp.Element) fp.Element {
+	acc := shiftPoint
+	accumulate := func(bytes []byte, nibbleIndexed [nibbleCount][16]*starkcurve.G1Jac) {
+		for i, val := range bytes {
+			lowNibble := val & 0x0F
+			index := len(bytes) - i - 1
+
+			if lowNibble > 0 {
+				lowNibbleIndex := 2 * index
+				acc.AddAssign(nibbleIndexed[lowNibbleIndex][lowNibble])
+			}
+
+			highNibble := (val & 0xF0) >> 4
+
+			if highNibble > 0 {
+				highNibbleIndex := (2 * index) + 1
+				acc.AddAssign(nibbleIndexed[highNibbleIndex][highNibble])
+			}
+		}
+	}
 
-	result := new(starkcurve.G1Jac).Set(&shiftPoint)
-	result.AddAssign(processElement(a, &p0, &p1))
-	result.AddAssign(processElement(b, &p2, &p3))
+	aBytes := a.Bytes()
+	accumulate(aBytes[1:], pointIndexed[0])
+	accumulate(aBytes[:1], pointIndexed[1])
+	bBytes := b.Bytes()
+	accumulate(bBytes[1:], pointIndexed[2])
+	accumulate(bBytes[:1], pointIndexed[3])
 
 	// recover the affine x coordinate
 	var x fp.Element
-	x.Inverse(&result.Z).
+	x.Inverse(&acc.Z).
 		Square(&x)
-	x.Mul(&result.X, &x)
-
-	return &x
-}
-
-func processElement(a *fp.Element, p1 *starkcurve.G1Jac, p2 *starkcurve.G1Jac) *starkcurve.G1Jac {
-	var bigInt big.Int
-	var aBytes [32]byte
-	a.BigInt(&bigInt).FillBytes(aBytes[:])
-
-	highPart := bigInt.SetUint64(uint64(aBytes[0])) // The top nibble (bits 249-252)
-	lowPart := aBytes[1:]                           // Zero-out the top nibble (bits 249-252)
-
-	m := new(starkcurve.G1Jac).ScalarMultiplication(p2, highPart)
+	x.Mul(&acc.X, &x)
 
-	var n starkcurve.G1Jac
-	n.ScalarMultiplication(p1, bigInt.SetBytes(lowPart))
-	return m.AddAssign(&n)
+	return x
 }
diff --git a/ecc/stark-curve/pedersen-hash/pedersen_hash_test.go b/ecc/stark-curve/pedersen-hash/pedersen_hash_test.go
index 5ac057cc9..638257b99 100644
--- a/ecc/stark-curve/pedersen-hash/pedersen_hash_test.go
+++ b/ecc/stark-curve/pedersen-hash/pedersen_hash_test.go
@@ -114,7 +114,7 @@ func TestPedersenArray(t *testing.T) {
 	}
 }
 
-var feltBench *fp.Element
+var feltBench fp.Element
 
 // go test -bench=. -run=^# -cpu=1,2,4,8,16
 func BenchmarkPedersenArray(b *testing.B) {
@@ -133,7 +133,7 @@ func BenchmarkPedersenArray(b *testing.B) {
 
 	for _, i := range numOfElems {
 		b.Run(fmt.Sprintf("Number of felts: %d", i), func(b *testing.B) {
-			var f *fp.Element
+			var f fp.Element
 			randomFelts := createRandomFelts(i)
 			for n := 0; n < b.N; n++ {
 				f = PedersenArray(randomFelts...)
@@ -154,7 +154,7 @@ func BenchmarkPedersen(b *testing.B) {
 		b.Errorf("Error occured %s", err)
 	}
 
-	var f *fp.Element
+	var f fp.Element
 	for n := 0; n < b.N; n++ {
 		f = Pedersen(e0, e1)
 	}
diff --git a/internal/generator/ecc/template/hash_to_curve.go.tmpl b/internal/generator/ecc/template/hash_to_curve.go.tmpl
index ade6de5fd..c4b0ef74a 100644
--- a/internal/generator/ecc/template/hash_to_curve.go.tmpl
+++ b/internal/generator/ecc/template/hash_to_curve.go.tmpl
@@ -61,7 +61,7 @@ func {{$CurveName}}Sgn0(z *{{$CoordType}}) uint64 {
 
 // MapTo{{$CurveTitle}} invokes the {{.MappingAlgorithm}} map, and guarantees that the result is in {{$CurveName}}
 func MapTo{{$CurveTitle}}(u {{$CoordType}}) {{$AffineType}} {
-    res := mapToCurve{{$CurveIndex}}(&u)
+    res := MapToCurve{{$CurveIndex}}(&u)
     {{- if $isogenyNeeded }}
     //this is in an isogenous curve
         {{$CurveName}}Isogeny(&res)
@@ -85,9 +85,9 @@ func EncodeTo{{$CurveTitle}}(msg, dst []byte) ({{$AffineType}}, error) {
 	}
 
     {{if eq $TowerDegree 1}}
-    res = mapToCurve{{$CurveIndex}}(&u[0])
+    res = MapToCurve{{$CurveIndex}}(&u[0])
     {{else}}
-    res = mapToCurve{{$CurveIndex}}( &{{$CoordType}} {
+    res = MapToCurve{{$CurveIndex}}( &{{$CoordType}} {
         {{range $i := interval 0 $TowerDegree }} {{if eq $TowerDegree 2}}A{{end}}{{$i}}: u[{{$i}}],
     {{end}} })
     {{end}}
@@ -113,13 +113,13 @@ func HashTo{{$CurveTitle}}(msg, dst []byte) ({{$AffineType}}, error) {
 	}
 
 	{{if eq $TowerDegree 1}}
-	Q0 := mapToCurve{{$CurveIndex}}(&u[0])
-	Q1 := mapToCurve{{$CurveIndex}}(&u[1])
+	Q0 := MapToCurve{{$CurveIndex}}(&u[0])
+	Q1 := MapToCurve{{$CurveIndex}}(&u[1])
 	{{else}}
-	Q0 := mapToCurve{{$CurveIndex}}( &{{$CoordType}} {
+	Q0 := MapToCurve{{$CurveIndex}}( &{{$CoordType}} {
 		{{range $i := interval 0 $TowerDegree }} {{if eq $TowerDegree 2}}A{{end}}{{$i}}: u[{{$i}}],
 		{{end}} })
-	Q1 := mapToCurve{{$CurveIndex}}( &{{$CoordType}} {
+	Q1 := MapToCurve{{$CurveIndex}}( &{{$CoordType}} {
         {{range $i := interval 0 $TowerDegree }} {{if eq $TowerDegree 2}}A{{end}}{{$i}}: u[{{$TowerDegree}} + {{$i}}],
         {{end}} })
 	{{end}}
diff --git a/internal/generator/ecc/template/marshal.go.tmpl b/internal/generator/ecc/template/marshal.go.tmpl
index fb1a9aa61..132b1c957 100644
--- a/internal/generator/ecc/template/marshal.go.tmpl
+++ b/internal/generator/ecc/template/marshal.go.tmpl
@@ -25,19 +25,18 @@ import (
 // metadata needed for point (de)compression
 {{- if ge .FpUnusedBits 3}}
 // we follow the BLS12-381 style encoding as specified in ZCash and now IETF
-//
-// The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
-//
-// The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element's encoding should be set to zero.
-//
-// The third-most significant bit is set if (and only if) this point is in compressed form and it is not the point at infinity and its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.
+// see https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/11/
+// Appendix C.  ZCash serialization format for BLS12_381
 const (
 	mMask                 byte = 0b111 << 5
-	mUncompressed         byte = 0b000 << 5
-	mUncompressedInfinity byte = 0b010 << 5
-	mCompressedSmallest   byte = 0b100 << 5
-	mCompressedLargest    byte = 0b101 << 5
-	mCompressedInfinity   byte = 0b110 << 5
+	mUncompressed          byte = 0b000 << 5
+	_ byte						= 0b001 << 5 // invalid
+	mUncompressedInfinity  byte	= 0b010 << 5
+	_ byte						= 0b011 << 5 // invalid
+	mCompressedSmallest    byte	= 0b100 << 5
+	mCompressedLargest     byte	= 0b101 << 5
+	mCompressedInfinity    byte = 0b110 << 5
+	_ byte 						= 0b111 << 5 // invalid
 )
 {{- else}}
 // we have less than 3 bits available on the msw, so we can't follow BLS12-381 style encoding.
@@ -54,7 +53,10 @@ const (
 // SizeOfGT represents the size in bytes that a GT element need in binary form
 const SizeOfGT = fptower.SizeOfGT
 
-var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+var (
+	ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding")
+	ErrInvalidEncoding = errors.New("invalid point encoding")
+)
 
 // Encoder writes {{.Name}} object values to an output stream
 type Encoder struct {
@@ -108,6 +110,24 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 	var read int
 
 	switch t := v.(type) {
+	case *[]uint64:
+		buf64 := buf[:64/8]
+		read, err = io.ReadFull(dec.r, buf64)
+		dec.n += int64(read)
+		if err != nil {
+			return
+		}
+		length := binary.BigEndian.Uint64(buf64)
+		*t = make([]uint64, length)
+		for i := range *t {
+			read, err = io.ReadFull(dec.r, buf64)
+			dec.n += int64(read)
+			if err != nil {
+				return
+			}
+			(*t)[i] = binary.BigEndian.Uint64(buf64)
+		}
+		return
 	case *fr.Element:
 		read, err = io.ReadFull(dec.r, buf[:fr.Bytes])
 		dec.n += int64(read)
@@ -140,6 +160,15 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG1AffineCompressed
+
+		{{ if ge .FpUnusedBits 3}}
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+		{{- end}}
+
 		// most significant byte contains metadata 
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG1AffineUncompressed
@@ -160,6 +189,15 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 			return
 		}
 		nbBytes := SizeOfG2AffineCompressed
+
+		{{ if ge .FpUnusedBits 3}}
+		// 111, 011, 001  --> invalid mask
+		if isMaskInvalid(buf[0]) {
+			err = ErrInvalidEncoding
+			return
+		}
+		{{- end}}
+
 		// most significant byte contains metadata 
 		if !isCompressed(buf[0]) {
 			nbBytes = SizeOfG2AffineUncompressed
@@ -191,6 +229,15 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG1AffineCompressed
+
+			{{ if ge .FpUnusedBits 3}}
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+			{{- end}}
+
 			// most significant byte contains metadata 
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG1AffineUncompressed
@@ -250,6 +297,16 @@ func (dec *Decoder) Decode(v interface{}) (err error) {
 				return
 			}
 			nbBytes := SizeOfG2AffineCompressed
+
+
+			{{ if ge .FpUnusedBits 3}}
+			// 111, 011, 001  --> invalid mask
+			if isMaskInvalid(buf[0]) {
+				err = ErrInvalidEncoding
+				return
+			}
+			{{- end}}
+
 			// most significant byte contains metadata 
 			if !isCompressed(buf[0]) {
 				nbBytes = SizeOfG2AffineUncompressed
@@ -308,8 +365,6 @@ func (dec *Decoder) BytesRead() int64 {
 	return dec.n
 }
 
-
-
 func (dec *Decoder) readUint32() (r uint32, err error) {
 	var read int
 	var buf [4]byte
@@ -322,6 +377,13 @@ func (dec *Decoder) readUint32() (r uint32, err error) {
 	return 
 }
 
+{{ if ge .FpUnusedBits 3}}
+// isMaskInvalid returns true if the mask is invalid
+func isMaskInvalid(msb byte) bool {
+	mData := msb & mMask
+	return ((mData == (0b111 << 5)) || (mData == (0b011 << 5)) || (mData == (0b001 << 5)))
+}
+{{- end}}
 
 func isCompressed(msb byte) bool {
 	mData := msb & mMask
@@ -394,7 +456,24 @@ func isZeroed(firstByte byte, buf []byte) bool {
 {{template "encode" dict "Raw" ""}}
 {{template "encode" dict "Raw" "Raw"}}
 
-
+func (enc *Encoder) writeUint64Slice(t []uint64) error {
+	buff := make([]byte, 64/8)
+	binary.BigEndian.PutUint64(buff, uint64(len(t)))
+	written, err := enc.w.Write(buff)
+	enc.n += int64(written)
+	if err != nil {
+		return err
+	}
+	for i := range t {
+		binary.BigEndian.PutUint64(buff, t[i])
+		written, err = enc.w.Write(buff)
+		enc.n += int64(written)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
 
 {{ define "encode"}}
 
@@ -416,6 +495,8 @@ func (enc *Encoder) encode{{- $.Raw}}(v interface{}) (err error) {
 	var written int
 
 	switch t := v.(type) {
+	case []uint64:
+		return enc.writeUint64Slice(t)
 	case *fr.Element:
 		buf := t.Bytes()
 		written, err = enc.w.Write(buf[:])
@@ -530,7 +611,7 @@ func (p *{{ $.TAffine }}) Marshal() ([]byte) {
 	return b[:]
 }
 
-// Unmarshal is an allias to SetBytes()
+// Unmarshal is an alias to SetBytes()
 func (p *{{ $.TAffine }}) Unmarshal(buf []byte) error {
 	_, err := p.SetBytes(buf)
 	return err 
@@ -686,6 +767,13 @@ func (p *{{ $.TAffine }}) setBytes(buf []byte, subGroupCheck bool) (int, error)
 
 	// most significant byte
 	mData := buf[0] & mMask
+
+	{{if ge .all.FpUnusedBits 3}}
+	// 111, 011, 001  --> invalid mask
+	if isMaskInvalid(mData) {
+		return 0, ErrInvalidEncoding
+	}
+	{{- end}}
 	
 
 	// check buffer size
diff --git a/internal/generator/ecc/template/point.go.tmpl b/internal/generator/ecc/template/point.go.tmpl
index 59bf390c8..bd7344360 100644
--- a/internal/generator/ecc/template/point.go.tmpl
+++ b/internal/generator/ecc/template/point.go.tmpl
@@ -108,6 +108,16 @@ func (p *{{ $TAffine }}) Add(a, b *{{ $TAffine }}) *{{ $TAffine }} {
 	return p
 }
 
+// Double doubles a point in affine coordinates.
+// This should rarely be used as it is very inefficient compared to Jacobian
+func (p *{{ $TAffine }}) Double(a *{{ $TAffine }}) *{{ $TAffine }} {
+	var p1 {{ $TJacobian }}
+	p1.FromAffine(a)
+	p1.Double(&p1)
+	p.FromJacobian(&p1)
+	return p
+}
+
 // Sub subs two point in affine coordinates.
 // This should rarely be used as it is very inefficient compared to Jacobian
 func (p *{{ $TAffine }}) Sub(a, b *{{ $TAffine }}) *{{ $TAffine }} {
diff --git a/internal/generator/ecc/template/sswu.go.tmpl b/internal/generator/ecc/template/sswu.go.tmpl
index 3db929131..9a8e45515 100644
--- a/internal/generator/ecc/template/sswu.go.tmpl
+++ b/internal/generator/ecc/template/sswu.go.tmpl
@@ -291,9 +291,9 @@ func {{$CurveName}}MulByZ(z *{{$CoordType}}, x *{{$CoordType}}) {
 {{ end }}}
 
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-simplified-swu-method
-// mapToCurve{{$CurveIndex}} implements the SSWU map
+// MapToCurve{{$CurveIndex}} implements the SSWU map
 // No cofactor clearing or isogeny
-func mapToCurve{{$CurveIndex}}(u *{{$CoordType}}) {{$AffineType}} {
+func MapToCurve{{$CurveIndex}}(u *{{$CoordType}}) {{$AffineType}} {
 
     {{if $isogenyNeeded}}
         var {{$sswuCurveACoeff}} = {{$CoordType}} {{asElement .A}}
diff --git a/internal/generator/ecc/template/svdw.go.tmpl b/internal/generator/ecc/template/svdw.go.tmpl
index 7056bf5ad..9628bef6c 100644
--- a/internal/generator/ecc/template/svdw.go.tmpl
+++ b/internal/generator/ecc/template/svdw.go.tmpl
@@ -11,10 +11,10 @@
 {{if $IsG1}}{{$CurveIndex = "1"}}{{$B = "bCurveCoeff"}}{{end}}
 
 
-// mapToCurve{{$CurveIndex}} implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
+// MapToCurve{{$CurveIndex}} implements the Shallue and van de Woestijne method, applicable to any elliptic curve in Weierstrass form
 // No cofactor clearing or isogeny
 // https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#straightline-svdw
-func mapToCurve{{$CurveIndex}}(u *{{$CoordType}}) {{$AffineType}} {
+func MapToCurve{{$CurveIndex}}(u *{{$CoordType}}) {{$AffineType}} {
     var tv1, tv2, tv3, tv4 {{$CoordType}}
     var x1, x2, x3, gx1, gx2, gx, x, y {{$CoordType}}
     var one {{$CoordType}}
diff --git a/internal/generator/ecc/template/tests/hash_to_curve.go.tmpl b/internal/generator/ecc/template/tests/hash_to_curve.go.tmpl
index 053eaf753..5cd6e2f00 100644
--- a/internal/generator/ecc/template/tests/hash_to_curve.go.tmpl
+++ b/internal/generator/ecc/template/tests/hash_to_curve.go.tmpl
@@ -99,7 +99,7 @@ func TestMapToCurve{{$CurveIndex}}(t *testing.T) {
 	properties.Property("[{{$CurveTitle}}] mapping output must be on curve", prop.ForAll(
 		func(a {{$CoordType}}) bool {
 
-			g := mapToCurve{{$CurveIndex}}(&a)
+			g := MapToCurve{{$CurveIndex}}(&a)
 
 			{{if $isogenyNeeded}}
 				if !isOnE{{$CurveIndex}}Prime(g) {
@@ -126,18 +126,18 @@ func TestMapToCurve{{$CurveIndex}}(t *testing.T) {
 	for _, c := range encodeTo{{$CurveTitle}}Vector.cases {
 		var u {{$CoordType}}
 		{{$CurveName}}CoordSetString(&u, c.u)
-		q := mapToCurve{{$CurveIndex}}(&u)
+		q := MapToCurve{{$CurveIndex}}(&u)
 		{{$runIsogeny}}{{$CurveName}}TestMatchPoint(t, "Q", c.msg, c.Q, &q)
 	}
 
 	for _, c := range hashTo{{$CurveTitle}}Vector.cases {
 		var u {{$CoordType}}
 		{{$CurveName}}CoordSetString(&u, c.u0)
-		q := mapToCurve{{$CurveIndex}}(&u)
+		q := MapToCurve{{$CurveIndex}}(&u)
 		{{$runIsogeny}}{{$CurveName}}TestMatchPoint(t, "Q0", c.msg, c.Q0, &q)
 
 		{{$CurveName}}CoordSetString(&u, c.u1)
-		q = mapToCurve{{$CurveIndex}}(&u)
+		q = MapToCurve{{$CurveIndex}}(&u)
 		{{$runIsogeny}}{{$CurveName}}TestMatchPoint(t, "Q1", c.msg, c.Q1, &q)
 	}
 }
diff --git a/internal/generator/ecc/template/tests/marshal.go.tmpl b/internal/generator/ecc/template/tests/marshal.go.tmpl
index ec69a15c1..50ffd5651 100644
--- a/internal/generator/ecc/template/tests/marshal.go.tmpl
+++ b/internal/generator/ecc/template/tests/marshal.go.tmpl
@@ -214,15 +214,39 @@ func TestIsCompressed(t *testing.T) {
 }
 
 {{- $sizeOfFp := mul .Fp.NbWords 8}}
+{{- $FpUnusedBits := .FpUnusedBits}}
 
-{{template "marshalpoint" dict "all" . "sizeOfFp" $sizeOfFp "CoordType" .G1.CoordType "PointName" .G1.PointName "TAffine" $G1TAffine "TJacobian" $G1TJacobian "TJacobianExtended" $G1TJacobianExtended "FrNbWords" .Fr.NbWords "CRange" .G1.CRange}}
-{{template "marshalpoint" dict "all" . "sizeOfFp" $sizeOfFp  "CoordType" .G2.CoordType "PointName" .G2.PointName "TAffine" $G2TAffine "TJacobian" $G2TJacobian "TJacobianExtended" $G2TJacobianExtended "FrNbWords" .Fr.NbWords "CRange" .G2.CRange}}
+{{template "marshalpoint" dict "all" . "sizeOfFp" $sizeOfFp "CoordType" .G1.CoordType "PointName" .G1.PointName "TAffine" $G1TAffine "TJacobian" $G1TJacobian "TJacobianExtended" $G1TJacobianExtended "FrNbWords" .Fr.NbWords "CRange" .G1.CRange "FpUnusedBits" $FpUnusedBits}}
+{{template "marshalpoint" dict "all" . "sizeOfFp" $sizeOfFp  "CoordType" .G2.CoordType "PointName" .G2.PointName "TAffine" $G2TAffine "TJacobian" $G2TJacobian "TJacobianExtended" $G2TJacobianExtended "FrNbWords" .Fr.NbWords "CRange" .G2.CRange "FpUnusedBits" $FpUnusedBits}}
 
 
 {{define "marshalpoint"}}
 
 
 
+{{if ge $.FpUnusedBits 3}}
+func Test{{ $.TAffine }}InvalidBitMask(t *testing.T) {
+	t.Parallel()
+	var buf [SizeOf{{ $.TAffine }}Compressed]byte 
+	rand.Read(buf[:])
+
+	var p {{ $.TAffine }}
+	buf[0] = 0b111 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b011 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+	buf[0] = 0b001 << 5
+	if _, err := p.SetBytes(buf[:]); err != ErrInvalidEncoding {
+		t.Fatal("should error on invalid bit mask")
+	}
+}
+{{- end}}
+
+
 func Test{{ $.TAffine }}Serialization(t *testing.T) {
 	t.Parallel()
 	// test round trip serialization of infinity
@@ -316,8 +340,6 @@ func Test{{ $.TAffine }}Serialization(t *testing.T) {
 		GenFp(),
 	))
 
-
-
 	properties.TestingRun(t, gopter.ConsoleReporter(false))
 }
 
diff --git a/internal/generator/ecdsa/template/ecdsa.go.tmpl b/internal/generator/ecdsa/template/ecdsa.go.tmpl
index 3d5264c98..ff966d73a 100644
--- a/internal/generator/ecdsa/template/ecdsa.go.tmpl
+++ b/internal/generator/ecdsa/template/ecdsa.go.tmpl
@@ -136,20 +136,14 @@ func RecoverP(v uint, r *big.Int) (*{{ .CurvePackage }}.G1Affine, error) {
 	if y.ModSqrt(y, fp.Modulus()) == nil {
 		return nil, errors.New("no square root")
 	}
-	// y2 is -y
-	y2 := new(big.Int).Sub(fp.Modulus(), y)
-	// if yChoice == 0, return min(y, y2), else max(y, y2)
-	if (y.Cmp(y2) < 0) == (yChoice == 0) {
-		return &{{ .CurvePackage }}.G1Affine{
-			X: *new(fp.Element).SetBigInt(x),
-			Y: *new(fp.Element).SetBigInt(y),
-		}, nil
-	} else {
-		return &{{ .CurvePackage }}.G1Affine{
-			X: *new(fp.Element).SetBigInt(x),
-			Y: *new(fp.Element).SetBigInt(y2),
-		}, nil
+	// check that y has same oddity as defined by v
+	if y.Bit(0) != yChoice {
+		y = y.Sub(fp.Modulus(), y)
 	}
+	return &{{ .CurvePackage }}.G1Affine{
+		X: *new(fp.Element).SetBigInt(x),
+		Y: *new(fp.Element).SetBigInt(y),
+	}, nil
 }
 {{- end}}
 
@@ -239,8 +233,6 @@ func (privKey *PrivateKey) Public() signature.PublicKey {
 //
 // SEC 1, Version 2.0, Section 4.1.3
 func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v uint, r, s *big.Int, err error) {
-	halfp := new(big.Int).Sub(fp.Modulus(), big.NewInt(1))
-	halfp.Div(halfp, big.NewInt(2))
 	r, s = new(big.Int), new(big.Int)
 
 	scalar, kInv := new(big.Int), new(big.Int)
@@ -263,10 +255,8 @@ func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v ui
 			P.X.BigInt(r)
 			// set how many times we overflow the scalar field
 			v |= (uint(new(big.Int).Div(r, order).Uint64())) << 1
-			// set if y is small or big
-			if P.Y.BigInt(new(big.Int)).Cmp(halfp) >= 0 {
-				v |= 1
-			}
+			// set if y is even or odd
+			v |= P.Y.BigInt(new(big.Int)).Bit(0)
 
 			r.Mod(r, order)
 			if r.Sign() != 0 {
diff --git a/internal/generator/ecdsa/template/marshal.go.tmpl b/internal/generator/ecdsa/template/marshal.go.tmpl
index 81e2a2a8c..d95d9df21 100644
--- a/internal/generator/ecdsa/template/marshal.go.tmpl
+++ b/internal/generator/ecdsa/template/marshal.go.tmpl
@@ -2,6 +2,7 @@ import (
 	"crypto/subtle"
 	"io"
 	{{- if or (eq .Name "secp256k1") (eq .Name "bn254") (eq .Name "stark-curve") }}
+	"errors"
 	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}"
@@ -50,6 +51,12 @@ func (pk *PublicKey) SetBytes(buf []byte) (int, error) {
 // methods sets the current public key to the recovered value. Otherwise returns
 // error and leaves current public key unchanged.
 func (pk *PublicKey) RecoverFrom(msg []byte, v uint, r, s *big.Int) error {
+	if s.Cmp(fr.Modulus()) >= 0 {
+		return errors.New("s is larger than modulus")
+	}
+	if s.Cmp(big.NewInt(0)) <= 0 {
+		return errors.New("s is negative")
+	}
 	P, err := RecoverP(v, r)
 	if err != nil {
 		return err
diff --git a/internal/generator/kzg/template/kzg.go.tmpl b/internal/generator/kzg/template/kzg.go.tmpl
index 0f42fb5a2..d5918e535 100644
--- a/internal/generator/kzg/template/kzg.go.tmpl
+++ b/internal/generator/kzg/template/kzg.go.tmpl
@@ -14,6 +14,7 @@ import (
 
 var (
 	ErrInvalidNbDigests              = errors.New("number of digests is not the same as the number of polynomials")
+	ErrZeroNbDigests                 = errors.New("number of digests is zero")
 	ErrInvalidPolynomialSize         = errors.New("invalid polynomial size (larger than SRS or == 0)")
 	ErrVerifyOpeningProof            = errors.New("can't verify opening proof")
 	ErrVerifyBatchOpeningSinglePoint = errors.New("can't verify batch opening proof at single point")
@@ -23,12 +24,24 @@ var (
 // Digest commitment of a polynomial.
 type Digest = {{ .CurvePackage }}.G1Affine
 
-// SRS stores the result of the MPC
-type SRS struct {
+// ProvingKey used to create or open commitments
+type ProvingKey struct {
 	G1 []{{ .CurvePackage }}.G1Affine  // [G₁ [α]G₁ , [α²]G₁, ... ]
+}
+
+// VerifyingKey used to verify opening proofs
+type VerifyingKey struct {
 	G2 [2]{{ .CurvePackage }}.G2Affine // [G₂, [α]G₂ ]
+	G1 {{ .CurvePackage }}.G1Affine
+}
+
+// SRS must be computed through MPC and comprises the ProvingKey and the VerifyingKey
+type SRS struct {
+	Pk ProvingKey
+	Vk VerifyingKey
 }
 
+// TODO @Tabaie get rid of this and use the polynomial package
 // eval returns p(point) where p is interpreted as a polynomial
 // ∑_{i<len(p)}p[i]Xⁱ
 func eval(p []fr.Element, point fr.Element) fr.Element {
@@ -46,22 +59,22 @@ func eval(p []fr.Element, point fr.Element) fr.Element {
 // In production, a SRS generated through MPC should be used.
 //
 // implements io.ReaderFrom and io.WriterTo
-func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
+func NewSRS(size uint64, bAlpha *big.Int)  (*SRS, error) {
 
 	if size < 2 {
 		return nil, ErrMinSRSSize
 	}
-
 	var srs SRS
-	srs.G1 = make([]{{ .CurvePackage }}.G1Affine, size)
+	srs.Pk.G1 = make([]{{ .CurvePackage }}.G1Affine, size)
 
 	var alpha fr.Element
 	alpha.SetBigInt(bAlpha)
 
 	_, _, gen1Aff, gen2Aff := {{ .CurvePackage }}.Generators()
-	srs.G1[0] = gen1Aff
-	srs.G2[0] = gen2Aff
-	srs.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
+	srs.Pk.G1[0] = gen1Aff
+	srs.Vk.G1 = gen1Aff
+	srs.Vk.G2[0] = gen2Aff
+	srs.Vk.G2[1].ScalarMultiplication(&gen2Aff, bAlpha)
 
 	alphas := make([]fr.Element, size-1)
 	alphas[0] = alpha
@@ -69,7 +82,7 @@ func NewSRS(size uint64, bAlpha *big.Int) (*SRS, error) {
 		alphas[i].Mul(&alphas[i-1], &alpha)
 	}
 	g1s := {{ .CurvePackage }}.BatchScalarMultiplicationG1(&gen1Aff, alphas)
-	copy(srs.G1[1:], g1s)
+	copy(srs.Pk.G1[1:], g1s)
 
 	return &srs, nil
 }
@@ -98,9 +111,9 @@ type BatchOpeningProof struct {
 
 // Commit commits to a polynomial using a multi exponentiation with the SRS.
 // It is assumed that the polynomial is in canonical form, in Montgomery form.
-func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
+func Commit(p []fr.Element, pk ProvingKey, nbTasks ...int) (Digest, error) {
 
-	if len(p) == 0 || len(p) > len(srs.G1) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return Digest{}, ErrInvalidPolynomialSize
 	}
 
@@ -110,7 +123,7 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 	if len(nbTasks) > 0 {
 		config.NbTasks = nbTasks[0]
 	}
-	if _, err := res.MultiExp(srs.G1[:len(p)], p, config); err != nil {
+	if _, err := res.MultiExp(pk.G1[:len(p)], p, config); err != nil {
 		return Digest{}, err
 	}
 
@@ -119,8 +132,8 @@ func Commit(p []fr.Element, srs *SRS, nbTasks ...int) (Digest, error) {
 
 // Open computes an opening proof of polynomial p at given point.
 // fft.Domain Cardinality must be larger than p.Degree()
-func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
-	if len(p) == 0 || len(p) > len(srs.G1) {
+func Open(p []fr.Element, point fr.Element, pk ProvingKey) (OpeningProof, error) {
+	if len(p) == 0 || len(p) > len(pk.G1) {
 		return OpeningProof{}, ErrInvalidPolynomialSize
 	}
 
@@ -137,7 +150,7 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 	_p = nil // h re-use this memory
 
 	// commit to H
-	hCommit, err := Commit(h, srs)
+	hCommit, err := Commit(h, pk)
 	if err != nil {
 		return OpeningProof{}, err
 	}
@@ -147,13 +160,13 @@ func Open(p []fr.Element, point fr.Element, srs *SRS) (OpeningProof, error) {
 }
 
 // Verify verifies a KZG opening proof at a single point
-func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS) error {
+func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, vk VerifyingKey) error {
 
 	// [f(a)]G₁
 	var claimedValueG1Aff {{ .CurvePackage }}.G1Jac
 	var claimedValueBigInt big.Int
 	proof.ClaimedValue.BigInt(&claimedValueBigInt)
-	claimedValueG1Aff.ScalarMultiplicationAffine(&srs.G1[0], &claimedValueBigInt)
+	claimedValueG1Aff.ScalarMultiplicationAffine(&vk.G1, &claimedValueBigInt)
 
 	// [f(α) - f(a)]G₁
 	var fminusfaG1Jac {{ .CurvePackage }}.G1Jac
@@ -164,28 +177,20 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 	var negH {{ .CurvePackage }}.G1Affine
 	negH.Neg(&proof.H)
 
-	// [α-a]G₂
-	var alphaMinusaG2Jac, genG2Jac, alphaG2Jac {{ .CurvePackage }}.G2Jac
+	// [f(α) - f(a) + a*H(α)]G₁
+	var totalG1 {{ .CurvePackage }}.G1Jac
 	var pointBigInt big.Int
 	point.BigInt(&pointBigInt)
-	genG2Jac.FromAffine(&srs.G2[0])
-	alphaG2Jac.FromAffine(&srs.G2[1])
-	alphaMinusaG2Jac.ScalarMultiplication(&genG2Jac, &pointBigInt).
-		Neg(&alphaMinusaG2Jac).
-		AddAssign(&alphaG2Jac)
+	totalG1.ScalarMultiplicationAffine(&proof.H, &pointBigInt)
+	totalG1.AddAssign(&fminusfaG1Jac)
+	var totalG1Aff {{ .CurvePackage }}.G1Affine
+	totalG1Aff.FromJacobian(&totalG1)
 
-	// [α-a]G₂
-	var xminusaG2Aff {{ .CurvePackage }}.G2Affine
-	xminusaG2Aff.FromJacobian(&alphaMinusaG2Jac)
 
-	// [f(α) - f(a)]G₁
-	var fminusfaG1Aff {{ .CurvePackage }}.G1Affine
-	fminusfaG1Aff.FromJacobian(&fminusfaG1Jac)
-
-	// e([f(α) - f(a)]G₁, G₂).e([-H(α)]G₁, [α-a]G₂) ==? 1
+	// e([f(α)-f(a)+aH(α)]G₁], G₂).e([-H(α)]G₁, [α]G₂) == 1
 	check, err := {{ .CurvePackage }}.PairingCheck(
-		[]{{ .CurvePackage }}.G1Affine{fminusfaG1Aff, negH},
-		[]{{ .CurvePackage }}.G2Affine{srs.G2[0], xminusaG2Aff},
+		[]{{ .CurvePackage }}.G1Affine{totalG1Aff, negH},
+		[]{{ .CurvePackage }}.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -197,12 +202,12 @@ func Verify(commitment *Digest, proof *OpeningProof, point fr.Element, srs *SRS)
 }
 
 // BatchOpenSinglePoint creates a batch opening proof at point of a list of polynomials.
-// It's an interactive protocol, made non interactive using Fiat Shamir.
+// It's an interactive protocol, made non-interactive using Fiat Shamir.
 //
 // * point is the point at which the polynomials are opened.
 // * digests is the list of committed polynomials to open, need to derive the challenge using Fiat Shamir.
 // * polynomials is the list of polynomials to open, they are supposed to be of the same size.
-func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, srs *SRS) (BatchOpeningProof, error) {
+func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr.Element, hf hash.Hash, pk ProvingKey) (BatchOpeningProof, error) {
 
 	// check for invalid sizes
 	nbDigests := len(digests)
@@ -213,7 +218,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	// TODO ensure the polynomials are of the same size
 	largestPoly := -1
 	for _, p := range polynomials {
-		if len(p) == 0 || len(p) > len(srs.G1) {
+		if len(p) == 0 || len(p) > len(pk.G1) {
 			return BatchOpeningProof{}, ErrInvalidPolynomialSize
 		}
 		if len(p) > largestPoly {
@@ -234,8 +239,11 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 		}(i)
 	}
 
+	// wait for polynomial evaluations to be completed (res.ClaimedValues)
+	wg.Wait()
+
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, res.ClaimedValues, hf)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -244,8 +252,6 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	var foldedEvaluations fr.Element
 	chSumGammai := make(chan struct{}, 1)
 	go func() {
-		// wait for polynomial evaluations to be completed (res.ClaimedValues)
-		wg.Wait()
 		foldedEvaluations = res.ClaimedValues[nbDigests-1]
 		for i := nbDigests - 2; i >= 0; i-- {
 			foldedEvaluations.Mul(&foldedEvaluations, &gamma).
@@ -264,7 +270,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	for i := 1 ; i < len(polynomials); i++ {
 		gammas[i].Mul(&gammas[i-1], &gamma)
 	}
-	
+
 	for i := 1; i < len(polynomials); i++ {
 		i := i
 		parallel.Execute(len(polynomials[i]), func(start, end int) {
@@ -281,7 +287,7 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr
 	h := dividePolyByXminusA(foldedPolynomials, foldedEvaluations, point)
 	foldedPolynomials = nil // same memory as h
 
-	res.H, err = Commit(h, srs)
+	res.H, err = Commit(h, pk)
 	if err != nil {
 		return BatchOpeningProof{}, err
 	}
@@ -299,13 +305,13 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 
 	nbDigests := len(digests)
 
-	// check consistancy between numbers of claims vs number of digests
+	// check consistency between numbers of claims vs number of digests
 	if nbDigests != len(batchOpeningProof.ClaimedValues) {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
 
 	// derive the challenge γ, binded to the point and the commitments
-	gamma, err := deriveGamma(point, digests, hf)
+	gamma, err := deriveGamma(point, digests, batchOpeningProof.ClaimedValues, hf)
 	if err != nil {
 		return OpeningProof{}, Digest{}, ErrInvalidNbDigests
 	}
@@ -314,7 +320,10 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 	// gammai = [1,γ,γ²,..,γⁿ⁻¹]
 	gammai := make([]fr.Element, nbDigests)
 	gammai[0].SetOne()
-	for i := 1; i < nbDigests; i++ {
+	if nbDigests > 1 {
+		gammai[1] = gamma
+	}
+	for i := 2; i < nbDigests; i++ {
 		gammai[i].Mul(&gammai[i-1], &gamma)
 	}
 
@@ -335,7 +344,7 @@ func FoldProof(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.
 //
 // * digests list of digests on which opening proof is done
 // * batchOpeningProof proof of correct opening on the digests
-func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, srs *SRS) error {
+func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningProof, point fr.Element, hf hash.Hash, vk VerifyingKey) error {
 
 	// fold the proof
 	foldedProof, foldedDigest, err := FoldProof(digests, batchOpeningProof, point, hf)
@@ -343,8 +352,8 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 		return err
 	}
 
-	// verify the foldedProof againts the foldedDigest
-	err = Verify(&foldedDigest, &foldedProof, point, srs)
+	// verify the foldedProof against the foldedDigest
+	err = Verify(&foldedDigest, &foldedProof, point, vk)
 	return err
 
 }
@@ -355,16 +364,21 @@ func BatchVerifySinglePoint(digests []Digest, batchOpeningProof *BatchOpeningPro
 // * digests list of committed polynomials
 // * proofs list of opening proofs, one for each digest
 // * points the list of points at which the opening are done
-func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, srs *SRS) error {
+func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr.Element, vk VerifyingKey) error {
 
-	// check consistancy nb proogs vs nb digests
+	// check consistency nb proogs vs nb digests
 	if len(digests) != len(proofs) || len(digests) != len(points) {
 		return ErrInvalidNbDigests
 	}
 
+	// len(digests) should be nonzero because of randomNumbers
+	if len(digests) == 0 {
+		return ErrZeroNbDigests
+	}
+
 	// if only one digest, call Verify
 	if len(digests) == 1 {
-		return Verify(&digests[0], &proofs[0], points[0], srs)
+		return Verify(&digests[0], &proofs[0], points[0], vk)
 	}
 
 	// sample random numbers λᵢ for sampling
@@ -384,9 +398,8 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 		quotients[i].Set(&proofs[i].H)
 	}
 	config := ecc.MultiExpConfig{}
-	_, err := foldedQuotients.MultiExp(quotients, randomNumbers, config)
-	if err != nil {
-		return nil
+	if _, err := foldedQuotients.MultiExp(quotients, randomNumbers, config); err != nil {
+		return err
 	}
 
 	// fold digests and evals
@@ -406,7 +419,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	var foldedEvalsCommit {{ .CurvePackage }}.G1Affine
 	var foldedEvalsBigInt big.Int
 	foldedEvals.BigInt(&foldedEvalsBigInt)
-	foldedEvalsCommit.ScalarMultiplication(&srs.G1[0], &foldedEvalsBigInt)
+	foldedEvalsCommit.ScalarMultiplication(&vk.G1, &foldedEvalsBigInt)
 
 	// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
 	foldedDigests.Sub(&foldedDigests, &foldedEvalsCommit)
@@ -433,7 +446,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 	// e([∑ᵢλᵢ(fᵢ(α) - fᵢ(pᵢ) + pᵢHᵢ(α))]G₁, G₂).e([-∑ᵢλᵢ[Hᵢ(α)]G₁), [α]G₂)
 	check, err := {{ .CurvePackage }}.PairingCheck(
 		[]{{ .CurvePackage }}.G1Affine{foldedDigests, foldedQuotients},
-		[]{{ .CurvePackage }}.G2Affine{srs.G2[0], srs.G2[1]},
+		[]{{ .CurvePackage }}.G2Affine{vk.G2[0], vk.G2[1]},
 	)
 	if err != nil {
 		return err
@@ -454,7 +467,7 @@ func BatchVerifyMultiPoints(digests []Digest, proofs []OpeningProof, points []fr
 // * Returns ∑ᵢcᵢdᵢ, ∑ᵢcᵢf(aᵢ)
 func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, error) {
 
-	// length inconsistancy between digests and evaluations should have been done before calling this function
+	// length inconsistency between digests and evaluations should have been done before calling this function
 	nbDigests := len(di)
 
 	// fold the claimed values ∑ᵢcᵢf(aᵢ)
@@ -477,18 +490,23 @@ func fold(di []Digest, fai []fr.Element, ci []fr.Element) (Digest, fr.Element, e
 }
 
 // deriveGamma derives a challenge using Fiat Shamir to fold proofs.
-func deriveGamma(point fr.Element, digests []Digest, hf hash.Hash) (fr.Element, error) {
+func deriveGamma(point fr.Element, digests []Digest, claimedValues []fr.Element, hf hash.Hash) (fr.Element, error) {
 
 	// derive the challenge gamma, binded to the point and the commitments
 	fs := fiatshamir.NewTranscript(hf, "gamma")
 	if err := fs.Bind("gamma", point.Marshal()); err != nil {
 		return fr.Element{}, err
 	}
-	for i := 0; i < len(digests); i++ {
+	for i := range digests {
 		if err := fs.Bind("gamma", digests[i].Marshal()); err != nil {
 			return fr.Element{}, err
 		}
 	}
+	for i := range claimedValues {
+		if err := fs.Bind("gamma", claimedValues[i].Marshal()); err != nil {
+			return fr.Element{}, err
+		}
+	}
 	gammaByte, err := fs.ComputeChallenge("gamma")
 	if err != nil {
 		return fr.Element{}, err
diff --git a/internal/generator/kzg/template/kzg.test.go.tmpl b/internal/generator/kzg/template/kzg.test.go.tmpl
index a0cd06300..31c82727a 100644
--- a/internal/generator/kzg/template/kzg.test.go.tmpl
+++ b/internal/generator/kzg/template/kzg.test.go.tmpl
@@ -1,21 +1,22 @@
 import (
-	"bytes"
 	"crypto/sha256"
+	"github.com/stretchr/testify/assert"
 	"math/big"
-	"reflect"
 	"testing"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+
+	"github.com/consensys/gnark-crypto/utils"
 )
 
-// testSRS re-used accross tests of the KZG scheme
-var testSRS *SRS
+// Test SRS re-used across tests of the KZG scheme
+var testSrs *SRS
 
 func init() {
 	const srsSize = 230
-	testSRS, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
+	testSrs, _ = NewSRS(ecc.NextPowerOfTwo(srsSize), new(big.Int).SetInt64(42))
 }
 
 func TestDividePolyByXminusA(t *testing.T) {
@@ -45,7 +46,7 @@ func TestDividePolyByXminusA(t *testing.T) {
 	pol = nil // h reuses this memory
 
 	if len(h) != 229 {
-		t.Fatal("inconsistant size of quotient")
+		t.Fatal("inconsistent size of quotient")
 	}
 
 	hRandPoint := eval(h, randPoint)
@@ -60,32 +61,12 @@ func TestDividePolyByXminusA(t *testing.T) {
 }
 
 func TestSerializationSRS(t *testing.T) {
-
 	// create a SRS
 	srs, err := NewSRS(64, new(big.Int).SetInt64(42))
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// serialize it...
-	var buf bytes.Buffer
-	_, err = srs.WriteTo(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// reconstruct the SRS
-	var _srs SRS
-	_, err = _srs.ReadFrom(&buf)
-	if err != nil {
-		t.Fatal(err)
-	}
-
-	// compare
-	if !reflect.DeepEqual(srs, &_srs) {
-		t.Fatal("scheme serialization failed")
-	}
-
+	assert.NoError(t, err)
+	t.Run("proving key round-trip", utils.SerializationRoundTrip(&srs.Pk))
+	t.Run("verifying key round-trip", utils.SerializationRoundTrip(&srs.Vk))
+	t.Run("whole SRS round-trip", utils.SerializationRoundTrip(srs))
 }
 
 func TestCommit(t *testing.T) {
@@ -97,7 +78,7 @@ func TestCommit(t *testing.T) {
 	}
 
 	// commit using the method from KZG
-	_kzgCommit, err := Commit(f, testSRS)
+	_kzgCommit, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -111,7 +92,7 @@ func TestCommit(t *testing.T) {
 	var fxbi big.Int
 	fx.BigInt(&fxbi)
 	var manualCommit {{ .CurvePackage }}.G1Affine
-	manualCommit.Set(&testSRS.G1[0])
+	manualCommit.Set(&testSrs.Vk.G1)
 	manualCommit.ScalarMultiplication(&manualCommit, &fxbi)
 
 	// compare both results
@@ -127,7 +108,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	f := randomPolynomial(60)
 
 	// commit the polynomial
-	digest, err := Commit(f, testSRS)
+	digest, err := Commit(f, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -135,7 +116,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := Open(f, point, testSRS)
+	proof, err := Open(f, point, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -147,7 +128,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	}
 
 	// verify correct proof
-	err = Verify(&digest, &proof, point, testSRS)
+	err = Verify(&digest, &proof, point, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -155,7 +136,7 @@ func TestVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValue.Double(&proof.ClaimedValue)
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -165,7 +146,7 @@ func TestVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = Verify(&digest, &proof, point, testSRS)
+		err = Verify(&digest, &proof, point, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -178,14 +159,14 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 
 	// create polynomials
 	f := make([][]fr.Element, 10)
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		f[i] = randomPolynomial(size)
 	}
 
 	// commit the polynomials
-	digests := make([]Digest, 10)
-	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+	digests := make([]Digest, len(f))
+	for i := range f {
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 
 	}
 
@@ -195,21 +176,21 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	// compute opening proof at a random point
 	var point fr.Element
 	point.SetString("4321")
-	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSRS)
+	proof, err := BatchOpenSinglePoint(f, digests, point, hf, testSrs.Pk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// verify the claimed values
-	for i := 0; i < 10; i++ {
+	for i := range f {
 		expectedClaim := eval(f[i], point)
 		if !expectedClaim.Equal(&proof.ClaimedValues[i]) {
-			t.Fatal("inconsistant claimed values")
+			t.Fatal("inconsistent claimed values")
 		}
 	}
 
 	// verify correct proof
-	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+	err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -217,7 +198,7 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 	{
 		// verify wrong proof
 		proof.ClaimedValues[0].Double(&proof.ClaimedValues[0])
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
@@ -227,12 +208,11 @@ func TestBatchVerifySinglePoint(t *testing.T) {
 		// see https://cryptosubtlety.medium.com/00-8d4adcf4d255
 		proof.H.X.SetZero()
 		proof.H.Y.SetZero()
-		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSRS)
+		err = BatchVerifySinglePoint(digests, &proof, point, hf, testSrs.Vk)
 		if err == nil {
 			t.Fatal("verifying wrong proof should have failed")
 		}
 	}
-
 }
 
 func TestBatchVerifyMultiPoints(t *testing.T) {
@@ -246,7 +226,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	// commit the polynomials
 	digests := make([]Digest, 10)
 	for i := 0; i < 10; i++ {
-		digests[i], _ = Commit(f[i], testSRS)
+		digests[i], _ = Commit(f[i], testSrs.Pk)
 	}
 
 	// pick a hash function
@@ -256,9 +236,9 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	points := make([]fr.Element, 2)
 	batchProofs := make([]BatchOpeningProof, 2)
 	points[0].SetRandom()
-	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSRS)
+	batchProofs[0], _ = BatchOpenSinglePoint(f[:5], digests[:5], points[0], hf, testSrs.Pk)
 	points[1].SetRandom()
-	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSRS)
+	batchProofs[1], _ = BatchOpenSinglePoint(f[5:], digests[5:], points[1], hf, testSrs.Pk)
 
 	// fold the 2 batch opening proofs
 	proofs := make([]OpeningProof, 2)
@@ -266,18 +246,18 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 	proofs[0], foldedDigests[0], _ = FoldProof(digests[:5], &batchProofs[0], points[0], hf)
 	proofs[1], foldedDigests[1], _ = FoldProof(digests[5:], &batchProofs[1], points[1], hf)
 
-	// check the the individual batch proofs are correct
-	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSRS)
+	// check that the individual batch proofs are correct
+	err := Verify(&foldedDigests[0], &proofs[0], points[0], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSRS)
+	err = Verify(&foldedDigests[1], &proofs[1], points[1], testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// batch verify correct folded proofs
-	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+	err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -286,7 +266,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		// batch verify tampered folded proofs
 		proofs[0].ClaimedValue.Double(&proofs[0].ClaimedValue)
 
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -298,7 +278,7 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 		proofs[0].H.Y.SetZero()
 		proofs[1].H.X.SetZero()
 		proofs[1].H.Y.SetZero()
-		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSRS)
+		err = BatchVerifyMultiPoints(foldedDigests, proofs, points, testSrs.Vk)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -309,16 +289,14 @@ func TestBatchVerifyMultiPoints(t *testing.T) {
 const benchSize = 1 << 16
 
 func BenchmarkKZGCommit(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Commit(p, benchSRS)
+		_, _ = Commit(p, srs.Pk)
 	}
 }
 
@@ -344,10 +322,8 @@ func BenchmarkDivideByXMinusA(b *testing.B) {
 }
 
 func BenchmarkKZGOpen(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -356,15 +332,13 @@ func BenchmarkKZGOpen(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		_, _ = Open(p, r, benchSRS)
+		_, _ = Open(p, r, srs.Pk)
 	}
 }
 
 func BenchmarkKZGVerify(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// random polynomial
 	p := randomPolynomial(benchSize / 2)
@@ -372,28 +346,22 @@ func BenchmarkKZGVerify(b *testing.B) {
 	r.SetRandom()
 
 	// commit
-	comm, err := Commit(p, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	comm, err := Commit(p, srs.Pk)
+	assert.NoError(b, err)
 
 	// open
-	openingProof, err := Open(p, r, benchSRS)
-	if err != nil {
-		b.Fatal(err)
-	}
+	openingProof, err := Open(p, r, srs.Pk)
+	assert.NoError(b, err)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Verify(&comm, &openingProof, r, benchSRS)
+		Verify(&comm, &openingProof, r, srs.Vk)
 	}
 }
 
 func BenchmarkKZGBatchOpen10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
-	if err != nil {
-		b.Fatal(err)
-	}
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	assert.NoError(b, err)
 
 	// 10 random polynomials
 	var ps [10][]fr.Element
@@ -404,7 +372,7 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -415,12 +383,12 @@ func BenchmarkKZGBatchOpen10(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+		BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	}
 }
 
 func BenchmarkKZGBatchVerify10(b *testing.B) {
-	benchSRS, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
+	srs, err := NewSRS(ecc.NextPowerOfTwo(benchSize), new(big.Int).SetInt64(42))
 	if err != nil {
 		b.Fatal(err)
 	}
@@ -434,7 +402,7 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	// commitments
 	var commitments [10]Digest
 	for i := 0; i < 10; i++ {
-		commitments[i], _ = Commit(ps[i], benchSRS)
+		commitments[i], _ = Commit(ps[i], srs.Pk)
 	}
 
 	// pick a hash function
@@ -443,14 +411,14 @@ func BenchmarkKZGBatchVerify10(b *testing.B) {
 	var r fr.Element
 	r.SetRandom()
 
-	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, benchSRS)
+	proof, err := BatchOpenSinglePoint(ps[:], commitments[:], r, hf, srs.Pk)
 	if err != nil {
 		b.Fatal(err)
 	}
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		BatchVerifySinglePoint(commitments[:], &proof, r, hf, benchSRS)
+		BatchVerifySinglePoint(commitments[:], &proof, r, hf, testSrs.Vk)
 	}
 }
 
diff --git a/internal/generator/kzg/template/marshal.go.tmpl b/internal/generator/kzg/template/marshal.go.tmpl
index d1caf3c86..435f178c8 100644
--- a/internal/generator/kzg/template/marshal.go.tmpl
+++ b/internal/generator/kzg/template/marshal.go.tmpl
@@ -4,15 +4,34 @@ import (
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}"
 )
 
-// WriteTo writes binary encoding of the SRS
-func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
-	// encode the SRS
+// WriteTo writes binary encoding of the ProvingKey
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	// encode the ProvingKey
 	enc := {{ .CurvePackage }}.NewEncoder(w)
+	if err := enc.Encode(pk.G1); err != nil {
+		return enc.BytesWritten(), err
+	}
+	return enc.BytesWritten(), nil
+}
+
+// WriteRawTo writes binary encoding of VerifyingKey to w without point compression
+func (vk *VerifyingKey) WriteRawTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w, {{.CurvePackage}}.RawEncoding())
+}
+
+// WriteTo writes binary encoding of the VerifyingKey
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	return vk.writeTo(w)
+}
+
+func (vk *VerifyingKey) writeTo(w io.Writer, options ...func(*{{.CurvePackage}}.Encoder)) (int64, error) {
+	// encode the VerifyingKey
+	enc := {{ .CurvePackage }}.NewEncoder(w, options...)
 
 	toEncode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toEncode {
@@ -24,15 +43,37 @@ func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
 	return enc.BytesWritten(), nil
 }
 
-// ReadFrom decodes SRS data from reader.
-func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
-	// decode the SRS
+// WriteTo writes binary encoding of the entire SRS
+func (srs *SRS) WriteTo(w io.Writer) (int64, error) {
+	// encode the SRS
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.WriteTo(w); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.WriteTo(w)
+	return pn + vn, err
+}
+
+// ReadFrom decodes ProvingKey data from reader.
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the ProvingKey
+	dec := {{ .CurvePackage }}.NewDecoder(r)
+	if err := dec.Decode(&pk.G1); err != nil {
+		return dec.BytesRead(), err
+	}
+	return dec.BytesRead(), nil
+}
+
+// ReadFrom decodes VerifyingKey data from reader.
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
 	dec := {{ .CurvePackage }}.NewDecoder(r)
 
 	toDecode := []interface{}{
-		&srs.G2[0],
-		&srs.G2[1],
-		&srs.G1,
+		&vk.G2[0],
+		&vk.G2[1],
+		&vk.G1,
 	}
 
 	for _, v := range toDecode {
@@ -44,6 +85,19 @@ func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
 	return dec.BytesRead(), nil
 }
 
+// ReadFrom decodes SRS data from reader.
+func (srs *SRS) ReadFrom(r io.Reader) (int64, error) {
+	// decode the VerifyingKey
+	var pn, vn int64
+	var err error
+	if pn, err = srs.Pk.ReadFrom(r); err != nil {
+		return pn, err
+	}
+	vn, err = srs.Vk.ReadFrom(r)
+	return pn+vn, err
+}
+
+
 // WriteTo writes binary encoding of a OpeningProof
 func (proof *OpeningProof) WriteTo(w io.Writer) (int64, error) {
 	enc := {{ .CurvePackage }}.NewEncoder(w)
@@ -101,7 +155,6 @@ func (proof *BatchOpeningProof) WriteTo(w io.Writer) (int64, error) {
 // ReadFrom decodes BatchOpeningProof data from reader.
 func (proof *BatchOpeningProof) ReadFrom(r io.Reader) (int64, error) {
 	dec := {{ .CurvePackage }}.NewDecoder(r)
-
 	toDecode := []interface{}{
 		&proof.H,
 		&proof.ClaimedValues,
diff --git a/internal/generator/pedersen/template/pedersen.go.tmpl b/internal/generator/pedersen/template/pedersen.go.tmpl
index 19f6c6b9c..6957402e1 100644
--- a/internal/generator/pedersen/template/pedersen.go.tmpl
+++ b/internal/generator/pedersen/template/pedersen.go.tmpl
@@ -2,62 +2,68 @@ import (
     "crypto/rand"
     "fmt"
     "github.com/consensys/gnark-crypto/ecc"
-    "github.com/consensys/gnark-crypto/ecc/{{.Name}}"
+    curve "github.com/consensys/gnark-crypto/ecc/{{.Name}}"
     "github.com/consensys/gnark-crypto/ecc/{{.Name}}/fr"
+	"io"
     "math/big"
 )
 
-// Key for proof and verification
-type Key struct {
-    g             {{.CurvePackage}}.G2Affine // TODO @tabaie: does this really have to be randomized?
-    gRootSigmaNeg {{.CurvePackage}}.G2Affine //gRootSigmaNeg = g^{-1/σ}
-    basis         []{{.CurvePackage}}.G1Affine
-    basisExpSigma []{{.CurvePackage}}.G1Affine
+// ProvingKey for committing and proofs of knowledge
+type ProvingKey struct {
+	basis         []curve.G1Affine
+	basisExpSigma []curve.G1Affine
 }
 
-func randomOnG2() ({{.CurvePackage}}.G2Affine, error) { // TODO: Add to G2.go?
-    gBytes := make([]byte, fr.Bytes)
-    if _, err := rand.Read(gBytes); err != nil {
-        return {{.CurvePackage}}.G2Affine{}, err
+type VerifyingKey struct {
+    g             curve.G2Affine // TODO @tabaie: does this really have to be randomized?
+    gRootSigmaNeg curve.G2Affine //gRootSigmaNeg = g^{-1/σ}
+}
+
+func randomFrSizedBytes() ([]byte, error) {
+    res := make([]byte, fr.Bytes)
+    _, err := rand.Read(res)
+    return res, err
+}
+
+func randomOnG2() (curve.G2Affine, error) { // TODO: Add to G2.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+        return curve.G2Affine{}, err
+	} else {
+        return curve.HashToG2(gBytes, []byte("random on g2"))
     }
-    return {{.CurvePackage}}.HashToG2(gBytes, []byte("random on g2"))
 }
 
-func Setup(basis []{{.CurvePackage}}.G1Affine) (Key, error) {
-    var (
-        k   Key
-        err error
-    )
+func Setup(basis []curve.G1Affine) (pk ProvingKey, vk VerifyingKey, err error) {
 
-    if k.g, err = randomOnG2(); err != nil {
-        return k, err
+    if vk.g, err = randomOnG2(); err != nil {
+        return
     }
 
     var modMinusOne big.Int
     modMinusOne.Sub(fr.Modulus(), big.NewInt(1))
     var sigma *big.Int
     if sigma, err = rand.Int(rand.Reader, &modMinusOne); err != nil {
-        return k, err
+        return
     }
     sigma.Add(sigma, big.NewInt(1))
 
     var sigmaInvNeg big.Int
     sigmaInvNeg.ModInverse(sigma, fr.Modulus())
     sigmaInvNeg.Sub(fr.Modulus(), &sigmaInvNeg)
-    k.gRootSigmaNeg.ScalarMultiplication(&k.g, &sigmaInvNeg)
+    vk.gRootSigmaNeg.ScalarMultiplication(&vk.g, &sigmaInvNeg)
 
-    k.basisExpSigma = make([]{{.CurvePackage}}.G1Affine, len(basis))
+    pk.basisExpSigma = make([]curve.G1Affine, len(basis))
     for i := range basis {
-        k.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
+        pk.basisExpSigma[i].ScalarMultiplication(&basis[i], sigma)
     }
 
-    k.basis = basis
-    return k, err
+    pk.basis = basis
+    return
 }
 
-func (k *Key) Commit(values []fr.Element) (commitment {{.CurvePackage}}.G1Affine, knowledgeProof {{.CurvePackage}}.G1Affine, err error) {
+func (pk *ProvingKey) Commit(values []fr.Element) (commitment curve.G1Affine, knowledgeProof curve.G1Affine, err error) {
 
-    if len(values) != len(k.basis) {
+    if len(values) != len(pk.basis) {
         err = fmt.Errorf("unexpected number of values")
         return
     }
@@ -68,23 +74,23 @@ func (k *Key) Commit(values []fr.Element) (commitment {{.CurvePackage}}.G1Affine
         NbTasks:     1, // TODO Experiment
     }
 
-    if _, err = commitment.MultiExp(k.basis, values, config); err != nil {
+    if _, err = commitment.MultiExp(pk.basis, values, config); err != nil {
         return
     }
 
-    _, err = knowledgeProof.MultiExp(k.basisExpSigma, values, config)
+    _, err = knowledgeProof.MultiExp(pk.basisExpSigma, values, config)
 
     return
 }
 
-// VerifyKnowledgeProof checks if the proof of knowledge is valid
-func (k *Key) VerifyKnowledgeProof(commitment {{.CurvePackage}}.G1Affine, knowledgeProof {{.CurvePackage}}.G1Affine) error {
+// Verify checks if the proof of knowledge is valid
+func (vk *VerifyingKey) Verify(commitment curve.G1Affine, knowledgeProof curve.G1Affine) error {
 
     if !commitment.IsInSubGroup() || !knowledgeProof.IsInSubGroup() {
         return fmt.Errorf("subgroup check failed")
     }
 
-    product, err := {{.CurvePackage}}.Pair([]{{.CurvePackage}}.G1Affine{commitment, knowledgeProof}, []{{.CurvePackage}}.G2Affine{k.g, k.gRootSigmaNeg})
+    product, err := curve.Pair([]curve.G1Affine{commitment, knowledgeProof}, []curve.G2Affine{vk.g, vk.gRootSigmaNeg})
     if err != nil {
         return err
     }
@@ -93,3 +99,57 @@ func (k *Key) VerifyKnowledgeProof(commitment {{.CurvePackage}}.G1Affine, knowle
     }
     return fmt.Errorf("proof rejected")
 }
+
+
+// Marshal
+
+func (pk *ProvingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+
+    if err := enc.Encode(pk.basis); err != nil {
+        return enc.BytesWritten(), err
+    }
+
+    err := enc.Encode(pk.basisExpSigma)
+
+	return enc.BytesWritten(), err
+}
+
+func (pk *ProvingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+
+    if err := dec.Decode(&pk.basis); err != nil {
+		return dec.BytesRead(), err
+	}
+    if err := dec.Decode(&pk.basisExpSigma); err != nil {
+        return dec.BytesRead(), err
+    }
+
+    if cL, pL := len(pk.basis), len(pk.basisExpSigma); cL != pL {
+        return dec.BytesRead(), fmt.Errorf("commitment basis size (%d) doesn't match proof basis size (%d)", cL, pL)
+    }
+
+	return dec.BytesRead(), nil
+}
+
+func (vk *VerifyingKey) WriteTo(w io.Writer) (int64, error) {
+	enc := curve.NewEncoder(w)
+	var err error
+
+	if err = enc.Encode(&vk.g); err != nil {
+		return enc.BytesWritten(), err
+	}
+	err = enc.Encode(&vk.gRootSigmaNeg)
+	return enc.BytesWritten(), err
+}
+
+func (vk *VerifyingKey) ReadFrom(r io.Reader) (int64, error) {
+	dec := curve.NewDecoder(r)
+	var err error
+
+	if err = dec.Decode(&vk.g); err != nil {
+		return dec.BytesRead(), err
+	}
+	err = dec.Decode(&vk.gRootSigmaNeg)
+	return dec.BytesRead(), err
+}
\ No newline at end of file
diff --git a/internal/generator/pedersen/template/pedersen.test.go.tmpl b/internal/generator/pedersen/template/pedersen.test.go.tmpl
index 1df98e4f5..12f6f8002 100644
--- a/internal/generator/pedersen/template/pedersen.test.go.tmpl
+++ b/internal/generator/pedersen/template/pedersen.test.go.tmpl
@@ -1,8 +1,8 @@
 import (
-	"github.com/consensys/gnark-crypto/ecc/{{.Name}}"
+	curve "github.com/consensys/gnark-crypto/ecc/{{.Name}}"
 	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/fr"
+	"github.com/consensys/gnark-crypto/utils"
 	"github.com/stretchr/testify/assert"
-	"math/rand"
 	"testing"
 )
 
@@ -26,37 +26,43 @@ func randomFrSlice(t *testing.T, size int) []interface{} {
 	return res
 }
 
-func randomOnG1() ({{.CurvePackage}}.G1Affine, error) { // TODO: Add to G1.go?
-	gBytes := make([]byte, fr.Bytes)
-	if _, err := rand.Read(gBytes); err != nil {
-		return {{.CurvePackage}}.G1Affine{}, err
+func randomOnG1() (curve.G1Affine, error) { // TODO: Add to G1.go?
+	if gBytes, err := randomFrSizedBytes(); err != nil {
+		return curve.G1Affine{}, err
+	} else {
+		return curve.HashToG1(gBytes, []byte("random on g1"))
 	}
-	return {{.CurvePackage}}.HashToG1(gBytes, []byte("random on g2"))
 }
 
-func testCommit(t *testing.T, values ...interface{}) {
-
-	basis := make([]{{.CurvePackage}}.G1Affine, len(values))
-	for i := range basis {
+func randomG1Slice(t *testing.T, size int) []curve.G1Affine {
+	res := make([]curve.G1Affine, size)
+	for i := range res {
 		var err error
-		basis[i], err = randomOnG1()
+		res[i], err = randomOnG1()
 		assert.NoError(t, err)
 	}
+	return res
+}
+
+func testCommit(t *testing.T, values ...interface{}) {
+
+	basis := randomG1Slice(t, len(values))
 
 	var (
-		key Key
-		err error
-		commitment, pok {{.CurvePackage}}.G1Affine
+		pk              ProvingKey
+		vk              VerifyingKey
+		err 			error
+		commitment, pok curve.G1Affine
 	)
 
-	key, err = Setup(basis)
+	pk, vk, err = Setup(basis)
 	assert.NoError(t, err)
-	commitment, pok, err = key.Commit(interfaceSliceToFrSlice(t, values...))
+	commitment, pok, err = pk.Commit(interfaceSliceToFrSlice(t, values...))
 	assert.NoError(t, err)
-	assert.NoError(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NoError(t, vk.Verify(commitment, pok))
 
 	pok.Neg(&pok)
-	assert.NotNil(t, key.VerifyKnowledgeProof(commitment, pok))
+	assert.NotNil(t, vk.Verify(commitment, pok))
 }
 
 func TestCommitToOne(t *testing.T) {
@@ -70,3 +76,21 @@ func TestCommitSingle(t *testing.T) {
 func TestCommitFiveElements(t *testing.T) {
 	testCommit(t, randomFrSlice(t, 5)...)
 }
+
+func TestMarshal(t *testing.T) {
+	var pk ProvingKey
+	pk.basisExpSigma = randomG1Slice(t, 5)
+	pk.basis = randomG1Slice(t, 5)
+
+	var (
+		vk  VerifyingKey
+		err error
+	)
+	vk.g, err = randomOnG2()
+	assert.NoError(t, err)
+	vk.gRootSigmaNeg, err = randomOnG2()
+	assert.NoError(t, err)
+
+	t.Run("ProvingKey -> Bytes -> ProvingKey must remain identical.", utils.SerializationRoundTrip(&pk))
+	t.Run("VerifyingKey -> Bytes -> VerifyingKey must remain identical.", utils.SerializationRoundTrip(&vk))
+}
\ No newline at end of file
diff --git a/internal/generator/permutation/template/permutation.go.tmpl b/internal/generator/permutation/template/permutation.go.tmpl
index 3bc6815b2..3498c99b1 100644
--- a/internal/generator/permutation/template/permutation.go.tmpl
+++ b/internal/generator/permutation/template/permutation.go.tmpl
@@ -114,7 +114,7 @@ func evaluateSecondPartNumReverse(lz []fr.Element, d *fft.Domain) []fr.Element {
 
 // Prove generates a proof that t1 and t2 are the same but permuted.
 // The size of t1 and t2 should be the same and a power of 2.
-func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
+func Prove(pk kzg.ProvingKey, t1, t2 []fr.Element) (Proof, error) {
 
 	// res
 	var proof Proof
@@ -149,11 +149,11 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	d.FFTInverse(ct2, fft.DIF)
 	fft.BitReverse(ct1)
 	fft.BitReverse(ct2)
-	proof.t1, err = kzg.Commit(ct1, srs)
+	proof.t1, err = kzg.Commit(ct1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.t2, err = kzg.Commit(ct2, srs)
+	proof.t2, err = kzg.Commit(ct2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -167,7 +167,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	// compute Z and commit it
 	cz := evaluateAccumulationPolynomialBitReversed(t1, t2, epsilon)
 	d.FFTInverse(cz, fft.DIT)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -205,7 +205,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 
 	// get the quotient and commit it
 	d.FFTInverse(lsNum, fft.DIT, fft.OnCoset())
-	proof.q, err = kzg.Commit(lsNum, srs)
+	proof.q, err = kzg.Commit(lsNum, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -232,7 +232,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 		},
 		eta,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -243,7 +243,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 	proof.shiftedProof, err = kzg.Open(
 		cz,
 		shiftedEta,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -255,7 +255,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) {
 }
 
 // Verify verifies a permutation proof.
-func Verify(srs *kzg.SRS, proof Proof) error {
+func Verify(vk kzg.VerifyingKey, proof Proof) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -312,7 +312,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 		&proof.batchedProof,
 		eta,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -320,7 +320,7 @@ func Verify(srs *kzg.SRS, proof Proof) error {
 
 	var shiftedEta fr.Element
 	shiftedEta.Mul(&eta, &proof.g)
-	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, srs)
+	err = kzg.Verify(&proof.z, &proof.shiftedProof, shiftedEta, vk)
 	if err != nil {
 		return err
 	}
diff --git a/internal/generator/permutation/template/permutation.test.go.tmpl b/internal/generator/permutation/template/permutation.test.go.tmpl
index b7e98134a..e78a9459d 100644
--- a/internal/generator/permutation/template/permutation.test.go.tmpl
+++ b/internal/generator/permutation/template/permutation.test.go.tmpl
@@ -2,16 +2,16 @@ import (
 	"math/big"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
+
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
 	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr/kzg"
 )
 
 func TestProof(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
-	if err != nil {
-		t.Fatal(err)
-	}
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
+	assert.NoError(t, err)
 
 	a := make([]fr.Element, 8)
 	b := make([]fr.Element, 8)
@@ -25,12 +25,12 @@ func TestProof(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -39,12 +39,12 @@ func TestProof(t *testing.T) {
 	// wrong proof
 	{
 		a[0].SetRandom()
-		proof, err := Prove(srs, a, b)
+		proof, err := Prove(kzgSrs.Pk, a, b)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = Verify(srs, proof)
+		err = Verify(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -57,7 +57,7 @@ func BenchmarkProver(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make([]fr.Element, polySize)
 	c := make([]fr.Element, polySize)
 
@@ -70,7 +70,7 @@ func BenchmarkProver(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		Prove(srs, a, c)
+		Prove(kzgSrs.Pk, a, c)
 	}
 
 }
diff --git a/internal/generator/plookup/template/plookup.test.go.tmpl b/internal/generator/plookup/template/plookup.test.go.tmpl
index 725db2f54..3b9fa918d 100644
--- a/internal/generator/plookup/template/plookup.test.go.tmpl
+++ b/internal/generator/plookup/template/plookup.test.go.tmpl
@@ -17,19 +17,19 @@ func TestLookupVector(t *testing.T) {
 		fvector[i].Set(&lookupVector[(4*i+1)%8])
 	}
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	// correct proof vector
 	{
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -39,12 +39,12 @@ func TestLookupVector(t *testing.T) {
 	{
 		fvector[0].SetRandom()
 
-		proof, err := ProveLookupVector(srs, fvector, lookupVector)
+		proof, err := ProveLookupVector(kzgSrs.Pk, fvector, lookupVector)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupVector(srs, proof)
+		err = VerifyLookupVector(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -54,7 +54,7 @@ func TestLookupVector(t *testing.T) {
 
 func TestLookupTable(t *testing.T) {
 
-	srs, err := kzg.NewSRS(64, big.NewInt(13))
+	kzgSrs, err := kzg.NewSRS(64, big.NewInt(13))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -74,12 +74,12 @@ func TestLookupTable(t *testing.T) {
 
 	// correct proof
 	{
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -88,12 +88,12 @@ func TestLookupTable(t *testing.T) {
 	// wrong proof
 	{
 		fTable[0][0].SetRandom()
-		proof, err := ProveLookupTables(srs, fTable, lookupTable)
+		proof, err := ProveLookupTables(kzgSrs.Pk, fTable, lookupTable)
 		if err != nil {
 			t.Fatal(err)
 		}
 
-		err = VerifyLookupTables(srs, proof)
+		err = VerifyLookupTables(kzgSrs.Vk, proof)
 		if err == nil {
 			t.Fatal(err)
 		}
@@ -106,7 +106,7 @@ func BenchmarkPlookup(b *testing.B) {
 	srsSize := 1 << 15
 	polySize := 1 << 14
 
-	srs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
+	kzgSrs, _ := kzg.NewSRS(uint64(srsSize), big.NewInt(13))
 	a := make(fr.Vector, polySize)
 	c := make(fr.Vector, polySize)
 
@@ -117,6 +117,6 @@ func BenchmarkPlookup(b *testing.B) {
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
-		ProveLookupVector(srs, a, c)
+		ProveLookupVector(kzgSrs.Pk, a, c)
 	}
 }
diff --git a/internal/generator/plookup/template/table.go.tmpl b/internal/generator/plookup/template/table.go.tmpl
index bdef72ad4..46dbe3a29 100644
--- a/internal/generator/plookup/template/table.go.tmpl
+++ b/internal/generator/plookup/template/table.go.tmpl
@@ -42,7 +42,7 @@ type ProofLookupTables struct {
 // that t[:][i] contains the i-th entry of the truth table, so t[0][i] XOR t[1][i] = t[2][i].
 //
 // The fr.Vector in f and t are supposed to be of the same size constant size.
-func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error) {
+func ProveLookupTables(pk kzg.ProvingKey, f, t []fr.Vector) (ProofLookupTables, error) {
 
 	// res
 	proof := ProofLookupTables{}
@@ -98,7 +98,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cfs[i], fft.DIF)
 		fft.BitReverse(cfs[i])
-		proof.fs[i], err = kzg.Commit(cfs[i], srs)
+		proof.fs[i], err = kzg.Commit(cfs[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -113,7 +113,7 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 		}
 		d.FFTInverse(cts[i], fft.DIF)
 		fft.BitReverse(cts[i])
-		proof.ts[i], err = kzg.Commit(cts[i], srs)
+		proof.ts[i], err = kzg.Commit(cts[i], pk)
 		if err != nil {
 			return proof, err
 		}
@@ -146,20 +146,20 @@ func ProveLookupTables(srs *kzg.SRS, f, t []fr.Vector) (ProofLookupTables, error
 	foldedtSorted := make(fr.Vector, nbColumns)
 	copy(foldedtSorted, foldedt)
 	sort.Sort(foldedtSorted)
-	proof.permutationProof, err = permutation.Prove(srs, foldedt, foldedtSorted)
+	proof.permutationProof, err = permutation.Prove(pk, foldedt, foldedtSorted)
 	if err != nil {
 		return proof, err
 	}
 
 	// call plookupVector, on foldedf[:len(foldedf)-1] to ensure that the domain size
 	// in ProveLookupVector is the same as d's
-	proof.foldedProof, err = ProveLookupVector(srs, foldedf[:len(foldedf)-1], foldedt)
+	proof.foldedProof, err = ProveLookupVector(pk, foldedf[:len(foldedf)-1], foldedt)
 
 	return proof, err
 }
 
 // VerifyLookupTables verifies that a ProofLookupTables proof is correct.
-func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
+func VerifyLookupTables(vk kzg.VerifyingKey, proof ProofLookupTables) error {
 
 	// hash function used for Fiat Shamir
 	hFunc := sha256.New()
@@ -203,13 +203,13 @@ func VerifyLookupTables(srs *kzg.SRS, proof ProofLookupTables) error {
 	}
 
 	// check that the folded commitment of the ts is a permutation of proof.FoldedProof.t
-	err = permutation.Verify(srs, proof.permutationProof)
+	err = permutation.Verify(vk, proof.permutationProof)
 	if err != nil {
 		return err
 	}
 
 	// verify the inner proof
-	return VerifyLookupVector(srs, proof.foldedProof)
+	return VerifyLookupVector(vk, proof.foldedProof)
 }
 
 // TODO put that in fiat-shamir package
diff --git a/internal/generator/plookup/template/vector.go.tmpl b/internal/generator/plookup/template/vector.go.tmpl
index 55478d7e0..a506523b4 100644
--- a/internal/generator/plookup/template/vector.go.tmpl
+++ b/internal/generator/plookup/template/vector.go.tmpl
@@ -336,7 +336,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element
 // table sorted. Otherwise the commitment in proof.t will not be the same as
 // the public commitment: it will contain the same values, but permuted.
 //
-func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) {
+func ProveLookupVector(pk kzg.ProvingKey, f, t fr.Vector) (ProofLookupVector, error) {
 
 	// res
 	var proof ProofLookupVector
@@ -384,11 +384,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	domainSmall.FFTInverse(cf, fft.DIF)
 	fft.BitReverse(ct)
 	fft.BitReverse(cf)
-	proof.t, err = kzg.Commit(ct, srs)
+	proof.t, err = kzg.Commit(ct, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.f, err = kzg.Commit(cf, srs)
+	proof.f, err = kzg.Commit(cf, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -414,11 +414,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	fft.BitReverse(ch1)
 	fft.BitReverse(ch2)
 
-	proof.h1, err = kzg.Commit(ch1, srs)
+	proof.h1, err = kzg.Commit(ch1, pk)
 	if err != nil {
 		return proof, err
 	}
-	proof.h2, err = kzg.Commit(ch2, srs)
+	proof.h2, err = kzg.Commit(ch2, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -439,7 +439,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 	copy(cz, lz)
 	domainSmall.FFTInverse(cz, fft.DIF)
 	fft.BitReverse(cz)
-	proof.z, err = kzg.Commit(cz, srs)
+	proof.z, err = kzg.Commit(cz, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -483,7 +483,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		return proof, err
 	}
 	ch := computeQuotientCanonical(alpha, lh, lh0, lhn, lh1h2, domainBig)
-	proof.h, err = kzg.Commit(ch, srs)
+	proof.h, err = kzg.Commit(ch, pk)
 	if err != nil {
 		return proof, err
 	}
@@ -512,7 +512,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -534,7 +534,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 		},
 		nu,
 		hFunc,
-		srs,
+		pk,
 	)
 	if err != nil {
 		return proof, err
@@ -544,7 +544,7 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error)
 }
 
 // VerifyLookupVector verifies that a ProofLookupVector proof is correct
-func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
+func VerifyLookupVector(vk kzg.VerifyingKey, proof ProofLookupVector) error {
 
 	// hash function that is used for Fiat Shamir
 	hFunc := sha256.New()
@@ -586,7 +586,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProof,
 		nu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
@@ -605,7 +605,7 @@ func VerifyLookupVector(srs *kzg.SRS, proof ProofLookupVector) error {
 		&proof.BatchedProofShifted,
 		shiftedNu,
 		hFunc,
-		srs,
+		vk,
 	)
 	if err != nil {
 		return err
diff --git a/internal/generator/tower/template/fq12over6over2/fq12.go.tmpl b/internal/generator/tower/template/fq12over6over2/fq12.go.tmpl
index a2853c37f..eaddb89ff 100644
--- a/internal/generator/tower/template/fq12over6over2/fq12.go.tmpl
+++ b/internal/generator/tower/template/fq12over6over2/fq12.go.tmpl
@@ -209,15 +209,17 @@ func (z *E12) DecompressKarabina(x *E12) *E12 {
     var one E2
     one.SetOne()
 
-	// g3 == 0
-	if x.C1.B2.IsZero() {
+	if x.C1.B2.IsZero() /* g3 == 0 */ {
 		t[0].Mul(&x.C0.B1, &x.C1.B2).
 			Double(&t[0])
 		// t1 = g2
 		t[1].Set(&x.C0.B2)
 
-		// g3 != 0
-	} else {
+		if t[1].IsZero() /* g2 == g3 == 0 */ {
+			return z.SetOne()
+		}
+	} else /* g3 != 0 */ {
+
 		// t0 = g1^2
 		t[0].Square(&x.C0.B1)
 		// t1 = 3 * g1^2 - 2 * g2
@@ -278,20 +280,24 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t0 := make([]E2, n)
 	t1 := make([]E2, n)
 	t2 := make([]E2, n)
+	zeroes := make([]bool, n)
 
 	var one E2
 	one.SetOne()
 
 	for i := 0; i < n; i++ {
-		// g3 == 0
-		if x[i].C1.B2.IsZero() {
+		if x[i].C1.B2.IsZero() /* g3 == 0 */ {
 			t0[i].Mul(&x[i].C0.B1, &x[i].C1.B2).
 				Double(&t0[i])
 			// t1 = g2
 			t1[i].Set(&x[i].C0.B2)
 
-			// g3 != 0
-		} else {
+			if t1[i].IsZero() /* g3 == g2 == 0 */ {
+				x[i].SetOne()
+				zeroes[i] = true
+				continue
+			}
+		} else /* g3 != 0 */ {
 			// t0 = g1^2
 			t0[i].Square(&x[i].C0.B1)
 			// t1 = 3 * g1^2 - 2 * g2
@@ -311,6 +317,10 @@ func BatchDecompressKarabina(x []E12) []E12 {
 	t1 = BatchInvertE2(t1) // costs 1 inverse
 
 	for i := 0; i < n; i++ {
+		if zeroes[i] {
+			continue
+		}
+
 		// z4 = g4
 		x[i].C1.B1.Mul(&t0[i], &t1[i])
 
@@ -731,7 +741,7 @@ func (z *E12) IsInSubGroup() bool {
 {{ else }}
     var a, b E12
 
-    // check z^(Phi_k(p)) == 1
+    // check z^(phi_k(p)) == 1
     a.FrobeniusSquare(z)
     b.FrobeniusSquare(&a).Mul(&b, z)
 
diff --git a/kzg/kzg.go b/kzg/kzg.go
index 8e8886953..fa35382bd 100644
--- a/kzg/kzg.go
+++ b/kzg/kzg.go
@@ -19,12 +19,13 @@ import (
 	kzg_bw6761 "github.com/consensys/gnark-crypto/ecc/bw6-761/fr/kzg"
 )
 
-// SRS ...
-type SRS interface {
+type Serializable interface {
 	io.ReaderFrom
 	io.WriterTo
 }
 
+type SRS Serializable
+
 // NewSRS returns an empty curved-typed SRS object
 // that implements io.ReaderFrom and io.WriterTo interfaces
 func NewSRS(curveID ecc.ID) SRS {
diff --git a/utils/testing.go b/utils/testing.go
new file mode 100644
index 000000000..af2d37c20
--- /dev/null
+++ b/utils/testing.go
@@ -0,0 +1,31 @@
+package utils
+
+import (
+	"bytes"
+	"github.com/stretchr/testify/assert"
+	"io"
+	"reflect"
+	"testing"
+)
+
+type Serializable interface {
+	io.ReaderFrom
+	io.WriterTo
+}
+
+func SerializationRoundTrip(o Serializable) func(*testing.T) {
+	return func(t *testing.T) {
+		// serialize it...
+		var buf bytes.Buffer
+		_, err := o.WriteTo(&buf)
+		assert.NoError(t, err)
+
+		// reconstruct the object
+		_o := reflect.New(reflect.TypeOf(o).Elem()).Interface().(Serializable)
+		_, err = _o.ReadFrom(&buf)
+		assert.NoError(t, err)
+
+		// compare
+		assert.Equal(t, o, _o)
+	}
+}