Skip to content

Commit

Permalink
crypto/kz4844: pass blobs by ref (ethereum#29050)
Browse files Browse the repository at this point in the history
This change makes use of the following underlying changes to the kzg-libraries in order to avoid passing large things on the stack:

- c-kzg: ethereum/c-kzg-4844#393 and
- go-kzg: https://github.com/crate-crypto/go-kzg-4844/pull/63
  • Loading branch information
holiman authored and jorgemmsilva committed Jun 17, 2024
1 parent 1b90e34 commit 5edf5aa
Show file tree
Hide file tree
Showing 13 changed files with 51 additions and 50 deletions.
4 changes: 2 additions & 2 deletions cmd/devp2p/internal/ethtest/suite.go
Original file line number Diff line number Diff line change
Expand Up @@ -754,8 +754,8 @@ func makeSidecar(data ...byte) *types.BlobTxSidecar {
)
for i := range blobs {
blobs[i][0] = data[i]
c, _ := kzg4844.BlobToCommitment(blobs[i])
p, _ := kzg4844.ComputeBlobProof(blobs[i], c)
c, _ := kzg4844.BlobToCommitment(&blobs[i])
p, _ := kzg4844.ComputeBlobProof(&blobs[i], c)
commitments = append(commitments, c)
proofs = append(proofs, p)
}
Expand Down
4 changes: 2 additions & 2 deletions core/txpool/blobpool/blobpool_test.go
Original file line number Diff line number Diff line change
Expand Up @@ -48,7 +48,7 @@ import (
)

var (
emptyBlob = kzg4844.Blob{}
emptyBlob = new(kzg4844.Blob)
emptyBlobCommit, _ = kzg4844.BlobToCommitment(emptyBlob)
emptyBlobProof, _ = kzg4844.ComputeBlobProof(emptyBlob, emptyBlobCommit)
emptyBlobVHash = kzg4844.CalcBlobHashV1(sha256.New(), &emptyBlobCommit)
Expand Down Expand Up @@ -198,7 +198,7 @@ func makeUnsignedTx(nonce uint64, gasTipCap uint64, gasFeeCap uint64, blobFeeCap
BlobHashes: []common.Hash{emptyBlobVHash},
Value: uint256.NewInt(100),
Sidecar: &types.BlobTxSidecar{
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: []kzg4844.Blob{*emptyBlob},
Commitments: []kzg4844.Commitment{emptyBlobCommit},
Proofs: []kzg4844.Proof{emptyBlobProof},
},
Expand Down
2 changes: 1 addition & 1 deletion core/txpool/validation.go
Original file line number Diff line number Diff line change
Expand Up @@ -162,7 +162,7 @@ func validateBlobSidecar(hashes []common.Hash, sidecar *types.BlobTxSidecar) err
// Blob commitments match with the hashes in the transaction, verify the
// blobs themselves via KZG
for i := range sidecar.Blobs {
if err := kzg4844.VerifyBlobProof(sidecar.Blobs[i], sidecar.Commitments[i], sidecar.Proofs[i]); err != nil {
if err := kzg4844.VerifyBlobProof(&sidecar.Blobs[i], sidecar.Commitments[i], sidecar.Proofs[i]); err != nil {
return fmt.Errorf("invalid blob %d: %v", i, err)
}
}
Expand Down
4 changes: 2 additions & 2 deletions core/types/tx_blob_test.go
Original file line number Diff line number Diff line change
Expand Up @@ -59,7 +59,7 @@ func TestBlobTxSize(t *testing.T) {
}

var (
emptyBlob = kzg4844.Blob{}
emptyBlob = new(kzg4844.Blob)
emptyBlobCommit, _ = kzg4844.BlobToCommitment(emptyBlob)
emptyBlobProof, _ = kzg4844.ComputeBlobProof(emptyBlob, emptyBlobCommit)
)
Expand All @@ -72,7 +72,7 @@ func createEmptyBlobTx(key *ecdsa.PrivateKey, withSidecar bool) *Transaction {

func createEmptyBlobTxInner(withSidecar bool) *BlobTx {
sidecar := &BlobTxSidecar{
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: []kzg4844.Blob{*emptyBlob},
Commitments: []kzg4844.Commitment{emptyBlobCommit},
Proofs: []kzg4844.Proof{emptyBlobProof},
}
Expand Down
8 changes: 4 additions & 4 deletions crypto/kzg4844/kzg4844.go
Original file line number Diff line number Diff line change
Expand Up @@ -105,7 +105,7 @@ func UseCKZG(use bool) error {
}

// BlobToCommitment creates a small commitment out of a data blob.
func BlobToCommitment(blob Blob) (Commitment, error) {
func BlobToCommitment(blob *Blob) (Commitment, error) {
if useCKZG.Load() {
return ckzgBlobToCommitment(blob)
}
Expand All @@ -114,7 +114,7 @@ func BlobToCommitment(blob Blob) (Commitment, error) {

// ComputeProof computes the KZG proof at the given point for the polynomial
// represented by the blob.
func ComputeProof(blob Blob, point Point) (Proof, Claim, error) {
func ComputeProof(blob *Blob, point Point) (Proof, Claim, error) {
if useCKZG.Load() {
return ckzgComputeProof(blob, point)
}
Expand All @@ -134,15 +134,15 @@ func VerifyProof(commitment Commitment, point Point, claim Claim, proof Proof) e
// the commitment.
//
// This method does not verify that the commitment is correct with respect to blob.
func ComputeBlobProof(blob Blob, commitment Commitment) (Proof, error) {
func ComputeBlobProof(blob *Blob, commitment Commitment) (Proof, error) {
if useCKZG.Load() {
return ckzgComputeBlobProof(blob, commitment)
}
return gokzgComputeBlobProof(blob, commitment)
}

// VerifyBlobProof verifies that the blob data corresponds to the provided commitment.
func VerifyBlobProof(blob Blob, commitment Commitment, proof Proof) error {
func VerifyBlobProof(blob *Blob, commitment Commitment, proof Proof) error {
if useCKZG.Load() {
return ckzgVerifyBlobProof(blob, commitment, proof)
}
Expand Down
16 changes: 8 additions & 8 deletions crypto/kzg4844/kzg4844_ckzg_cgo.go
Original file line number Diff line number Diff line change
Expand Up @@ -61,10 +61,10 @@ func ckzgInit() {
}

// ckzgBlobToCommitment creates a small commitment out of a data blob.
func ckzgBlobToCommitment(blob Blob) (Commitment, error) {
func ckzgBlobToCommitment(blob *Blob) (Commitment, error) {
ckzgIniter.Do(ckzgInit)

commitment, err := ckzg4844.BlobToKZGCommitment((ckzg4844.Blob)(blob))
commitment, err := ckzg4844.BlobToKZGCommitment((*ckzg4844.Blob)(blob))
if err != nil {
return Commitment{}, err
}
Expand All @@ -73,10 +73,10 @@ func ckzgBlobToCommitment(blob Blob) (Commitment, error) {

// ckzgComputeProof computes the KZG proof at the given point for the polynomial
// represented by the blob.
func ckzgComputeProof(blob Blob, point Point) (Proof, Claim, error) {
func ckzgComputeProof(blob *Blob, point Point) (Proof, Claim, error) {
ckzgIniter.Do(ckzgInit)

proof, claim, err := ckzg4844.ComputeKZGProof((ckzg4844.Blob)(blob), (ckzg4844.Bytes32)(point))
proof, claim, err := ckzg4844.ComputeKZGProof((*ckzg4844.Blob)(blob), (ckzg4844.Bytes32)(point))
if err != nil {
return Proof{}, Claim{}, err
}
Expand All @@ -102,21 +102,21 @@ func ckzgVerifyProof(commitment Commitment, point Point, claim Claim, proof Proo
// the commitment.
//
// This method does not verify that the commitment is correct with respect to blob.
func ckzgComputeBlobProof(blob Blob, commitment Commitment) (Proof, error) {
func ckzgComputeBlobProof(blob *Blob, commitment Commitment) (Proof, error) {
ckzgIniter.Do(ckzgInit)

proof, err := ckzg4844.ComputeBlobKZGProof((ckzg4844.Blob)(blob), (ckzg4844.Bytes48)(commitment))
proof, err := ckzg4844.ComputeBlobKZGProof((*ckzg4844.Blob)(blob), (ckzg4844.Bytes48)(commitment))
if err != nil {
return Proof{}, err
}
return (Proof)(proof), nil
}

// ckzgVerifyBlobProof verifies that the blob data corresponds to the provided commitment.
func ckzgVerifyBlobProof(blob Blob, commitment Commitment, proof Proof) error {
func ckzgVerifyBlobProof(blob *Blob, commitment Commitment, proof Proof) error {
ckzgIniter.Do(ckzgInit)

valid, err := ckzg4844.VerifyBlobKZGProof((ckzg4844.Blob)(blob), (ckzg4844.Bytes48)(commitment), (ckzg4844.Bytes48)(proof))
valid, err := ckzg4844.VerifyBlobKZGProof((*ckzg4844.Blob)(blob), (ckzg4844.Bytes48)(commitment), (ckzg4844.Bytes48)(proof))
if err != nil {
return err
}
Expand Down
8 changes: 4 additions & 4 deletions crypto/kzg4844/kzg4844_ckzg_nocgo.go
Original file line number Diff line number Diff line change
Expand Up @@ -32,13 +32,13 @@ func ckzgInit() {
}

// ckzgBlobToCommitment creates a small commitment out of a data blob.
func ckzgBlobToCommitment(blob Blob) (Commitment, error) {
func ckzgBlobToCommitment(blob *Blob) (Commitment, error) {
panic("unsupported platform")
}

// ckzgComputeProof computes the KZG proof at the given point for the polynomial
// represented by the blob.
func ckzgComputeProof(blob Blob, point Point) (Proof, Claim, error) {
func ckzgComputeProof(blob *Blob, point Point) (Proof, Claim, error) {
panic("unsupported platform")
}

Expand All @@ -52,11 +52,11 @@ func ckzgVerifyProof(commitment Commitment, point Point, claim Claim, proof Proo
// the commitment.
//
// This method does not verify that the commitment is correct with respect to blob.
func ckzgComputeBlobProof(blob Blob, commitment Commitment) (Proof, error) {
func ckzgComputeBlobProof(blob *Blob, commitment Commitment) (Proof, error) {
panic("unsupported platform")
}

// ckzgVerifyBlobProof verifies that the blob data corresponds to the provided commitment.
func ckzgVerifyBlobProof(blob Blob, commitment Commitment, proof Proof) error {
func ckzgVerifyBlobProof(blob *Blob, commitment Commitment, proof Proof) error {
panic("unsupported platform")
}
16 changes: 8 additions & 8 deletions crypto/kzg4844/kzg4844_gokzg.go
Original file line number Diff line number Diff line change
Expand Up @@ -46,10 +46,10 @@ func gokzgInit() {
}

// gokzgBlobToCommitment creates a small commitment out of a data blob.
func gokzgBlobToCommitment(blob Blob) (Commitment, error) {
func gokzgBlobToCommitment(blob *Blob) (Commitment, error) {
gokzgIniter.Do(gokzgInit)

commitment, err := context.BlobToKZGCommitment((gokzg4844.Blob)(blob), 0)
commitment, err := context.BlobToKZGCommitment((*gokzg4844.Blob)(blob), 0)
if err != nil {
return Commitment{}, err
}
Expand All @@ -58,10 +58,10 @@ func gokzgBlobToCommitment(blob Blob) (Commitment, error) {

// gokzgComputeProof computes the KZG proof at the given point for the polynomial
// represented by the blob.
func gokzgComputeProof(blob Blob, point Point) (Proof, Claim, error) {
func gokzgComputeProof(blob *Blob, point Point) (Proof, Claim, error) {
gokzgIniter.Do(gokzgInit)

proof, claim, err := context.ComputeKZGProof((gokzg4844.Blob)(blob), (gokzg4844.Scalar)(point), 0)
proof, claim, err := context.ComputeKZGProof((*gokzg4844.Blob)(blob), (gokzg4844.Scalar)(point), 0)
if err != nil {
return Proof{}, Claim{}, err
}
Expand All @@ -80,19 +80,19 @@ func gokzgVerifyProof(commitment Commitment, point Point, claim Claim, proof Pro
// the commitment.
//
// This method does not verify that the commitment is correct with respect to blob.
func gokzgComputeBlobProof(blob Blob, commitment Commitment) (Proof, error) {
func gokzgComputeBlobProof(blob *Blob, commitment Commitment) (Proof, error) {
gokzgIniter.Do(gokzgInit)

proof, err := context.ComputeBlobKZGProof((gokzg4844.Blob)(blob), (gokzg4844.KZGCommitment)(commitment), 0)
proof, err := context.ComputeBlobKZGProof((*gokzg4844.Blob)(blob), (gokzg4844.KZGCommitment)(commitment), 0)
if err != nil {
return Proof{}, err
}
return (Proof)(proof), nil
}

// gokzgVerifyBlobProof verifies that the blob data corresponds to the provided commitment.
func gokzgVerifyBlobProof(blob Blob, commitment Commitment, proof Proof) error {
func gokzgVerifyBlobProof(blob *Blob, commitment Commitment, proof Proof) error {
gokzgIniter.Do(gokzgInit)

return context.VerifyBlobKZGProof((gokzg4844.Blob)(blob), (gokzg4844.KZGCommitment)(commitment), (gokzg4844.KZGProof)(proof))
return context.VerifyBlobKZGProof((*gokzg4844.Blob)(blob), (gokzg4844.KZGCommitment)(commitment), (gokzg4844.KZGProof)(proof))
}
4 changes: 2 additions & 2 deletions crypto/kzg4844/kzg4844_test.go
Original file line number Diff line number Diff line change
Expand Up @@ -36,13 +36,13 @@ func randFieldElement() [32]byte {
return gokzg4844.SerializeScalar(r)
}

func randBlob() Blob {
func randBlob() *Blob {
var blob Blob
for i := 0; i < len(blob); i += gokzg4844.SerializedScalarSize {
fieldElementBytes := randFieldElement()
copy(blob[i:i+gokzg4844.SerializedScalarSize], fieldElementBytes[:])
}
return blob
return &blob
}

func TestCKZGWithPoint(t *testing.T) { testKZGWithPoint(t, true) }
Expand Down
4 changes: 2 additions & 2 deletions go.mod
Original file line number Diff line number Diff line change
Expand Up @@ -16,12 +16,12 @@ require (
github.com/cockroachdb/pebble v1.1.0
github.com/consensys/gnark-crypto v0.12.1
github.com/crate-crypto/go-ipa v0.0.0-20231025140028-3c0104f4b233
github.com/crate-crypto/go-kzg-4844 v0.7.0
github.com/crate-crypto/go-kzg-4844 v1.0.0
github.com/davecgh/go-spew v1.1.1
github.com/deckarep/golang-set/v2 v2.1.0
github.com/donovanhide/eventsource v0.0.0-20210830082556-c59027999da0
github.com/dop251/goja v0.0.0-20230605162241-28ee0ee714f3
github.com/ethereum/c-kzg-4844 v0.4.0
github.com/ethereum/c-kzg-4844 v1.0.0
github.com/fatih/color v1.13.0
github.com/ferranbt/fastssz v0.1.2
github.com/fjl/gencodec v0.0.0-20230517082657-f9840df7b83e
Expand Down
8 changes: 4 additions & 4 deletions go.sum
Original file line number Diff line number Diff line change
Expand Up @@ -129,8 +129,8 @@ github.com/cpuguy83/go-md2man/v2 v2.0.2 h1:p1EgwI/C7NhT0JmVkwCD2ZBK8j4aeHQX2pMHH
github.com/cpuguy83/go-md2man/v2 v2.0.2/go.mod h1:tgQtvFlXSQOSOSIRvRPT7W67SCa46tRHOmNcaadrF8o=
github.com/crate-crypto/go-ipa v0.0.0-20231025140028-3c0104f4b233 h1:d28BXYi+wUpz1KBmiF9bWrjEMacUEREV6MBi2ODnrfQ=
github.com/crate-crypto/go-ipa v0.0.0-20231025140028-3c0104f4b233/go.mod h1:geZJZH3SzKCqnz5VT0q/DyIG/tvu/dZk+VIfXicupJs=
github.com/crate-crypto/go-kzg-4844 v0.7.0 h1:C0vgZRk4q4EZ/JgPfzuSoxdCq3C3mOZMBShovmncxvA=
github.com/crate-crypto/go-kzg-4844 v0.7.0/go.mod h1:1kMhvPgI0Ky3yIa+9lFySEBUBXkYxeOi8ZF1sYioxhc=
github.com/crate-crypto/go-kzg-4844 v1.0.0 h1:TsSgHwrkTKecKJ4kadtHi4b3xHW5dCFUDFnUp1TsawI=
github.com/crate-crypto/go-kzg-4844 v1.0.0/go.mod h1:1kMhvPgI0Ky3yIa+9lFySEBUBXkYxeOi8ZF1sYioxhc=
github.com/creack/pty v1.1.9/go.mod h1:oKZEueFk5CKHvIhNR5MUki03XCEU+Q6VDXinZuGJ33E=
github.com/cyberdelia/templates v0.0.0-20141128023046-ca7fffd4298c/go.mod h1:GyV+0YP4qX0UQ7r2MoYZ+AvYDp12OF5yg4q8rGnyNh4=
github.com/davecgh/go-spew v1.1.0/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
Expand Down Expand Up @@ -160,8 +160,8 @@ github.com/envoyproxy/go-control-plane v0.9.0/go.mod h1:YTl/9mNaCwkRvm6d1a2C3ymF
github.com/envoyproxy/go-control-plane v0.9.1-0.20191026205805-5f8ba28d4473/go.mod h1:YTl/9mNaCwkRvm6d1a2C3ymFceY/DCBVvsKhRF0iEA4=
github.com/envoyproxy/go-control-plane v0.9.4/go.mod h1:6rpuAdCZL397s3pYoYcLgu1mIlRU8Am5FuJP05cCM98=
github.com/envoyproxy/protoc-gen-validate v0.1.0/go.mod h1:iSmxcyjqTsJpI2R4NaDN7+kN2VEUnK/pcBlmesArF7c=
github.com/ethereum/c-kzg-4844 v0.4.0 h1:3MS1s4JtA868KpJxroZoepdV0ZKBp3u/O5HcZ7R3nlY=
github.com/ethereum/c-kzg-4844 v0.4.0/go.mod h1:VewdlzQmpT5QSrVhbBuGoCdFJkpaJlO1aQputP83wc0=
github.com/ethereum/c-kzg-4844 v1.0.0 h1:0X1LBXxaEtYD9xsyj9B9ctQEZIpnvVDeoBx8aHEwTNA=
github.com/ethereum/c-kzg-4844 v1.0.0/go.mod h1:VewdlzQmpT5QSrVhbBuGoCdFJkpaJlO1aQputP83wc0=
github.com/fatih/color v1.13.0 h1:8LOYc1KYPPmyKMuN8QV2DNRWNbLo6LZ0iLs8+mlH53w=
github.com/fatih/color v1.13.0/go.mod h1:kLAiJbzzSOZDVNGyDpeOxJ47H46qBXwg5ILebYFFOfk=
github.com/ferranbt/fastssz v0.1.2 h1:Dky6dXlngF6Qjc+EfDipAkE83N5I5DE68bY6O0VLNPk=
Expand Down
17 changes: 9 additions & 8 deletions internal/ethapi/api_test.go
Original file line number Diff line number Diff line change
Expand Up @@ -1088,7 +1088,8 @@ func TestFillBlobTransaction(t *testing.T) {
Config: params.MergedTestChainConfig,
Alloc: types.GenesisAlloc{},
}
emptyBlob = kzg4844.Blob{}
emptyBlob = new(kzg4844.Blob)
emptyBlobs = []kzg4844.Blob{*emptyBlob}
emptyBlobCommit, _ = kzg4844.BlobToCommitment(emptyBlob)
emptyBlobProof, _ = kzg4844.ComputeBlobProof(emptyBlob, emptyBlobCommit)
emptyBlobHash common.Hash = kzg4844.CalcBlobHashV1(sha256.New(), &emptyBlobCommit)
Expand Down Expand Up @@ -1171,14 +1172,14 @@ func TestFillBlobTransaction(t *testing.T) {
From: &b.acc.Address,
To: &to,
Value: (*hexutil.Big)(big.NewInt(1)),
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: emptyBlobs,
Commitments: []kzg4844.Commitment{emptyBlobCommit},
Proofs: []kzg4844.Proof{emptyBlobProof},
},
want: &result{
Hashes: []common.Hash{emptyBlobHash},
Sidecar: &types.BlobTxSidecar{
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: emptyBlobs,
Commitments: []kzg4844.Commitment{emptyBlobCommit},
Proofs: []kzg4844.Proof{emptyBlobProof},
},
Expand All @@ -1191,14 +1192,14 @@ func TestFillBlobTransaction(t *testing.T) {
To: &to,
Value: (*hexutil.Big)(big.NewInt(1)),
BlobHashes: []common.Hash{emptyBlobHash},
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: emptyBlobs,
Commitments: []kzg4844.Commitment{emptyBlobCommit},
Proofs: []kzg4844.Proof{emptyBlobProof},
},
want: &result{
Hashes: []common.Hash{emptyBlobHash},
Sidecar: &types.BlobTxSidecar{
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: emptyBlobs,
Commitments: []kzg4844.Commitment{emptyBlobCommit},
Proofs: []kzg4844.Proof{emptyBlobProof},
},
Expand All @@ -1211,7 +1212,7 @@ func TestFillBlobTransaction(t *testing.T) {
To: &to,
Value: (*hexutil.Big)(big.NewInt(1)),
BlobHashes: []common.Hash{{0x01, 0x22}},
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: emptyBlobs,
Commitments: []kzg4844.Commitment{emptyBlobCommit},
Proofs: []kzg4844.Proof{emptyBlobProof},
},
Expand All @@ -1223,12 +1224,12 @@ func TestFillBlobTransaction(t *testing.T) {
From: &b.acc.Address,
To: &to,
Value: (*hexutil.Big)(big.NewInt(1)),
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: emptyBlobs,
},
want: &result{
Hashes: []common.Hash{emptyBlobHash},
Sidecar: &types.BlobTxSidecar{
Blobs: []kzg4844.Blob{emptyBlob},
Blobs: emptyBlobs,
Commitments: []kzg4844.Commitment{emptyBlobCommit},
Proofs: []kzg4844.Proof{emptyBlobProof},
},
Expand Down
6 changes: 3 additions & 3 deletions internal/ethapi/transaction_args.go
Original file line number Diff line number Diff line change
Expand Up @@ -326,12 +326,12 @@ func (args *TransactionArgs) setBlobTxSidecar(ctx context.Context, b Backend) er
commitments := make([]kzg4844.Commitment, n)
proofs := make([]kzg4844.Proof, n)
for i, b := range args.Blobs {
c, err := kzg4844.BlobToCommitment(b)
c, err := kzg4844.BlobToCommitment(&b)
if err != nil {
return fmt.Errorf("blobs[%d]: error computing commitment: %v", i, err)
}
commitments[i] = c
p, err := kzg4844.ComputeBlobProof(b, c)
p, err := kzg4844.ComputeBlobProof(&b, c)
if err != nil {
return fmt.Errorf("blobs[%d]: error computing proof: %v", i, err)
}
Expand All @@ -341,7 +341,7 @@ func (args *TransactionArgs) setBlobTxSidecar(ctx context.Context, b Backend) er
args.Proofs = proofs
} else {
for i, b := range args.Blobs {
if err := kzg4844.VerifyBlobProof(b, args.Commitments[i], args.Proofs[i]); err != nil {
if err := kzg4844.VerifyBlobProof(&b, args.Commitments[i], args.Proofs[i]); err != nil {
return fmt.Errorf("failed to verify blob proof: %v", err)
}
}
Expand Down

0 comments on commit 5edf5aa

Please sign in to comment.