diff --git a/bundler/bundle.go b/bundler/bundle.go
index 4a00076ec..f13e51db5 100644
--- a/bundler/bundle.go
+++ b/bundler/bundle.go
@@ -3,6 +3,7 @@ package bundler
 import (
 	"bytes"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/rsa"
 	"crypto/x509"
 	"crypto/x509/pkix"
@@ -13,6 +14,7 @@ import (
 	"time"
 
 	"github.com/cloudflare/cfssl/helpers"
+	"github.com/cloudflare/cfssl/helpers/derhelpers"
 )
 
 // A Bundle contains a certificate and its trust chain. It is intended
@@ -108,6 +110,8 @@ func (b *Bundle) MarshalJSON() ([]byte, error) {
 		keyType = fmt.Sprintf("%d-bit RSA", keyLength)
 	case x509.DSA:
 		keyType = "DSA"
+	case x509.Ed25519:
+		keyType = "Ed25519"
 	default:
 		keyType = "Unknown"
 	}
@@ -119,6 +123,9 @@ func (b *Bundle) MarshalJSON() ([]byte, error) {
 	case *ecdsa.PrivateKey:
 		keyBytes, _ = x509.MarshalECPrivateKey(key)
 		keyString = PemBlockToString(&pem.Block{Type: "EC PRIVATE KEY", Bytes: keyBytes})
+	case ed25519.PrivateKey:
+		keyBytes, _ = derhelpers.MarshalEd25519PrivateKey(key)
+		keyString = PemBlockToString(&pem.Block{Type: "Ed25519 PRIVATE KEY", Bytes: keyBytes})
 	case fmt.Stringer:
 		keyString = key.String()
 	}
diff --git a/bundler/bundle_from_file_test.go b/bundler/bundle_from_file_test.go
index 1e5bc1685..a750540c3 100644
--- a/bundler/bundle_from_file_test.go
+++ b/bundler/bundle_from_file_test.go
@@ -260,12 +260,12 @@ var fileTests = []fileTest{
 	},
 
 	// DSA is NOT supported.
-	// Keyless bundling, expect private key error "NotRSAOrECC"
+	// Keyless bundling, expect private key error "NotRSAOrECCOrEd25519"
 	{
 		cert:          certDSA2048,
 		caBundleFile:  testCFSSLRootBundle,
 		intBundleFile: testCFSSLIntBundle,
-		errorCallback: ExpectErrorMessages([]string{`"code":2200,`, `"message":"Private key algorithm is not RSA or ECC"`}),
+		errorCallback: ExpectErrorMessages([]string{`"code":2200,`, `"message":"Private key algorithm is not RSA or ECC or Ed25519"`}),
 	},
 	// Bundling with DSA private key, expect error "Failed to parse private key"
 	{
diff --git a/bundler/bundler.go b/bundler/bundler.go
index a2014c58c..b5b2fbc56 100644
--- a/bundler/bundler.go
+++ b/bundler/bundler.go
@@ -6,6 +6,7 @@ import (
 	"bytes"
 	"crypto"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/rsa"
 	"crypto/tls"
 	"crypto/x509"
@@ -555,7 +556,7 @@ func (b *Bundler) fetchIntermediates(certs []*x509.Certificate) (err error) {
 
 // Bundle takes an X509 certificate (already in the
 // Certificate structure), a private key as crypto.Signer in one of the appropriate
-// formats (i.e. *rsa.PrivateKey or *ecdsa.PrivateKey, or even a opaque key), using them to
+// formats (i.e. *rsa.PrivateKey, *ecdsa.PrivateKey or ed25519.PrivateKey, or even a opaque key), using them to
 // build a certificate bundle.
 func (b *Bundler) Bundle(certs []*x509.Certificate, key crypto.Signer, flavor BundleFlavor) (*Bundle, error) {
 	log.Infof("bundling certificate for %+v", certs[0].Subject)
@@ -576,7 +577,6 @@ func (b *Bundler) Bundle(certs []*x509.Certificate, key crypto.Signer, flavor Bu
 	if key != nil {
 		switch {
 		case cert.PublicKeyAlgorithm == x509.RSA:
-
 			var rsaPublicKey *rsa.PublicKey
 			if rsaPublicKey, ok = key.Public().(*rsa.PublicKey); !ok {
 				return nil, errors.New(errors.PrivateKeyError, errors.KeyMismatch)
@@ -592,15 +592,24 @@ func (b *Bundler) Bundle(certs []*x509.Certificate, key crypto.Signer, flavor Bu
 			if cert.PublicKey.(*ecdsa.PublicKey).X.Cmp(ecdsaPublicKey.X) != 0 {
 				return nil, errors.New(errors.PrivateKeyError, errors.KeyMismatch)
 			}
+		case cert.PublicKeyAlgorithm == x509.Ed25519:
+			var ed25519PublicKey ed25519.PublicKey
+			if ed25519PublicKey, ok = key.Public().(ed25519.PublicKey); !ok {
+				return nil, errors.New(errors.PrivateKeyError, errors.KeyMismatch)
+			}
+			if !(bytes.Equal(cert.PublicKey.(ed25519.PublicKey), ed25519PublicKey)) {
+				return nil, errors.New(errors.PrivateKeyError, errors.KeyMismatch)
+			}
 		default:
-			return nil, errors.New(errors.PrivateKeyError, errors.NotRSAOrECC)
+			return nil, errors.New(errors.PrivateKeyError, errors.NotRSAOrECCOrEd25519)
 		}
 	} else {
 		switch {
 		case cert.PublicKeyAlgorithm == x509.RSA:
 		case cert.PublicKeyAlgorithm == x509.ECDSA:
+		case cert.PublicKeyAlgorithm == x509.Ed25519:
 		default:
-			return nil, errors.New(errors.PrivateKeyError, errors.NotRSAOrECC)
+			return nil, errors.New(errors.PrivateKeyError, errors.NotRSAOrECCOrEd25519)
 		}
 	}
 
diff --git a/cmd/multirootca/ca.go b/cmd/multirootca/ca.go
index 3689032f5..93f5cc937 100644
--- a/cmd/multirootca/ca.go
+++ b/cmd/multirootca/ca.go
@@ -2,6 +2,7 @@ package main
 
 import (
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/rsa"
 	"errors"
 	"flag"
@@ -25,7 +26,7 @@ import (
 func parseSigner(root *config.Root) (signer.Signer, error) {
 	privateKey := root.PrivateKey
 	switch priv := privateKey.(type) {
-	case *rsa.PrivateKey, *ecdsa.PrivateKey:
+	case *rsa.PrivateKey, *ecdsa.PrivateKey, ed25519.PrivateKey:
 		s, err := local.NewSigner(priv, root.Certificate, signer.DefaultSigAlgo(priv), nil)
 		if err != nil {
 			return nil, err
diff --git a/csr/csr.go b/csr/csr.go
index 0ca250994..e8d899285 100644
--- a/csr/csr.go
+++ b/csr/csr.go
@@ -4,6 +4,7 @@ package csr
 import (
 	"crypto"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/elliptic"
 	"crypto/rand"
 	"crypto/rsa"
@@ -13,6 +14,7 @@ import (
 	"encoding/pem"
 	"errors"
 	"fmt"
+	"io"
 	"net"
 	"net/mail"
 	"net/url"
@@ -21,6 +23,7 @@ import (
 
 	cferr "github.com/cloudflare/cfssl/errors"
 	"github.com/cloudflare/cfssl/helpers"
+	"github.com/cloudflare/cfssl/helpers/derhelpers"
 	"github.com/cloudflare/cfssl/log"
 )
 
@@ -64,7 +67,7 @@ func (kr *KeyRequest) Size() int {
 }
 
 // Generate generates a key as specified in the request. Currently,
-// only ECDSA and RSA are supported.
+// only ECDSA, RSA and ed25519 algorithms are supported.
 func (kr *KeyRequest) Generate() (crypto.PrivateKey, error) {
 	log.Debugf("generate key from request: algo=%s, size=%d", kr.Algo(), kr.Size())
 	switch kr.Algo() {
@@ -89,6 +92,12 @@ func (kr *KeyRequest) Generate() (crypto.PrivateKey, error) {
 			return nil, errors.New("invalid curve")
 		}
 		return ecdsa.GenerateKey(curve, rand.Reader)
+	case "ed25519":
+		seed := make([]byte, ed25519.SeedSize)
+		if _, err := io.ReadFull(rand.Reader, seed); err != nil {
+			return nil, err
+		}
+		return ed25519.NewKeyFromSeed(seed), nil
 	default:
 		return nil, errors.New("invalid algorithm")
 	}
@@ -120,6 +129,8 @@ func (kr *KeyRequest) SigAlgo() x509.SignatureAlgorithm {
 		default:
 			return x509.ECDSAWithSHA1
 		}
+	case "ed25519":
+		return x509.PureEd25519
 	default:
 		return x509.UnknownSignatureAlgorithm
 	}
@@ -249,6 +260,17 @@ func ParseRequest(req *CertificateRequest) (csr, key []byte, err error) {
 			Bytes: key,
 		}
 		key = pem.EncodeToMemory(&block)
+	case ed25519.PrivateKey:
+		key, err = derhelpers.MarshalEd25519PrivateKey(priv)
+		if err != nil {
+			err = cferr.Wrap(cferr.PrivateKeyError, cferr.Unknown, err)
+			return
+		}
+		block := pem.Block{
+			Type:  "Ed25519 PRIVATE KEY",
+			Bytes: key,
+		}
+		key = pem.EncodeToMemory(&block)
 	default:
 		panic("Generate should have failed to produce a valid key.")
 	}
diff --git a/csr/csr_test.go b/csr/csr_test.go
index f6cd54f34..e125ac0a0 100644
--- a/csr/csr_test.go
+++ b/csr/csr_test.go
@@ -3,6 +3,7 @@ package csr
 import (
 	"crypto"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/elliptic"
 	"crypto/rsa"
 	"crypto/x509"
@@ -42,6 +43,10 @@ func TestKeyRequest(t *testing.T) {
 		if kr.Algo() != "ecdsa" {
 			t.Fatal("ECDSA key generated, but expected", kr.Algo())
 		}
+	case ed25519.PrivateKey:
+		if kr.Algo() != "ed25519" {
+			t.Fatal("Ed25519 key generated, but expected", kr.Algo())
+		}
 	}
 }
 
@@ -311,6 +316,21 @@ func TestECGeneration(t *testing.T) {
 	}
 }
 
+func TestED25519Generation(t *testing.T) {
+	kr := &KeyRequest{A: "ed25519"}
+	priv, err := kr.Generate()
+	if err != nil {
+		t.Fatalf("%v", err)
+	}
+	_, ok := priv.(ed25519.PrivateKey)
+	if !ok {
+		t.Fatal("Expected ed25519 key")
+	}
+	if sa := kr.SigAlgo(); sa == x509.UnknownSignatureAlgorithm {
+		t.Fatal("Invalid signature algorithm!")
+	}
+}
+
 func TestRSAKeyGeneration(t *testing.T) {
 	var rsakey *rsa.PrivateKey
 
@@ -404,6 +424,10 @@ func TestDefaultKeyRequest(t *testing.T) {
 		if DefaultKeyRequest.Algo() != "ecdsa" {
 			t.Fatal("Invalid default key request.")
 		}
+	case "Ed25519 PRIVATE KEY":
+		if DefaultKeyRequest.Algo() != "ed25519" {
+			t.Fatal("Invalid default key request.")
+		}
 	}
 }
 
@@ -430,6 +454,29 @@ func TestRSACertRequest(t *testing.T) {
 	}
 }
 
+// TestED25519CertRequest validates parsing a certificate request with an
+// ED25519 key.
+func TestED25519CertRequest(t *testing.T) {
+	var req = &CertificateRequest{
+		Names: []Name{
+			{
+				C:  "US",
+				ST: "California",
+				L:  "San Francisco",
+				O:  "CloudFlare",
+				OU: "Systems Engineering",
+			},
+		},
+		CN:         "cloudflare.com",
+		Hosts:      []string{"cloudflare.com", "www.cloudflare.com", "jdoe@example.com", "https://www.cloudflare.com"},
+		KeyRequest: &KeyRequest{A: "ed25519"},
+	}
+	_, _, err := ParseRequest(req)
+	if err != nil {
+		t.Fatalf("%v", err)
+	}
+}
+
 // TestBadCertRequest checks for failure conditions of ParseRequest.
 func TestBadCertRequest(t *testing.T) {
 	var req = &CertificateRequest{
diff --git a/errors/error.go b/errors/error.go
index 9715a7cfb..22850931e 100644
--- a/errors/error.go
+++ b/errors/error.go
@@ -113,10 +113,10 @@ const (
 	// these keys.
 	Encrypted Reason = 100 * (iota + 1) //21XX
 
-	// NotRSAOrECC indicates that they key is not an RSA or ECC
+	// NotRSAOrECCOrEd25519 indicates that they key is not an RSA or ECC or Ed25519
 	// private key; these are the only two private key types supported
 	// at this time by CFSSL.
-	NotRSAOrECC //22XX
+	NotRSAOrECCOrEd25519 //22XX
 
 	// KeyMismatch indicates that the private key does not match
 	// the public key or certificate being presented with the key.
@@ -273,8 +273,8 @@ func New(category Category, reason Reason) *Error {
 			msg = "Failed to parse private key"
 		case Encrypted:
 			msg = "Private key is encrypted."
-		case NotRSAOrECC:
-			msg = "Private key algorithm is not RSA or ECC"
+		case NotRSAOrECCOrEd25519:
+			msg = "Private key algorithm is not RSA or ECC or Ed25519"
 		case KeyMismatch:
 			msg = "Private key does not match public key"
 		case GenerationFailed:
diff --git a/errors/error_test.go b/errors/error_test.go
index 51bdf7d37..330793368 100644
--- a/errors/error_test.go
+++ b/errors/error_test.go
@@ -87,7 +87,7 @@ func TestNew(t *testing.T) {
 	if code != 2100 {
 		t.Fatal("Improper error code")
 	}
-	code = New(PrivateKeyError, NotRSAOrECC).ErrorCode
+	code = New(PrivateKeyError, NotRSAOrECCOrEd25519).ErrorCode
 	if code != 2200 {
 		t.Fatal("Improper error code")
 	}
diff --git a/helpers/helpers.go b/helpers/helpers.go
index f45e63a3d..5ab26bfb1 100644
--- a/helpers/helpers.go
+++ b/helpers/helpers.go
@@ -6,6 +6,7 @@ import (
 	"bytes"
 	"crypto"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/elliptic"
 	"crypto/rsa"
 	"crypto/tls"
@@ -61,7 +62,7 @@ var Jul2012 = InclusiveDate(2012, time.July, 01)
 // issuing certificates valid for more than 39 months.
 var Apr2015 = InclusiveDate(2015, time.April, 01)
 
-// KeyLength returns the bit size of ECDSA or RSA PublicKey
+// KeyLength returns the bit size of ECDSA, RSA or Ed25519 PublicKey
 func KeyLength(key interface{}) int {
 	if key == nil {
 		return 0
@@ -70,6 +71,8 @@ func KeyLength(key interface{}) int {
 		return ecdsaKey.Curve.Params().BitSize
 	} else if rsaKey, ok := key.(*rsa.PublicKey); ok {
 		return rsaKey.N.BitLen()
+	} else if _, ok := key.(ed25519.PublicKey); ok {
+		return ed25519.PublicKeySize
 	}
 
 	return 0
@@ -154,12 +157,14 @@ func SignatureString(alg x509.SignatureAlgorithm) string {
 		return "ECDSAWithSHA384"
 	case x509.ECDSAWithSHA512:
 		return "ECDSAWithSHA512"
+	case x509.PureEd25519:
+		return "Ed25519"
 	default:
 		return "Unknown Signature"
 	}
 }
 
-// HashAlgoString returns the hash algorithm name contains in the signature
+// HashAlgoString returns the hash algorithm name contained in the signature
 // method.
 func HashAlgoString(alg x509.SignatureAlgorithm) string {
 	switch alg {
@@ -187,6 +192,8 @@ func HashAlgoString(alg x509.SignatureAlgorithm) string {
 		return "SHA384"
 	case x509.ECDSAWithSHA512:
 		return "SHA512"
+	case x509.PureEd25519:
+		return "Ed25519"
 	default:
 		return "Unknown Hash Algorithm"
 	}
@@ -479,6 +486,8 @@ func SignerAlgo(priv crypto.Signer) x509.SignatureAlgorithm {
 		default:
 			return x509.ECDSAWithSHA1
 		}
+	case ed25519.PublicKey:
+		return x509.PureEd25519
 	default:
 		return x509.UnknownSignatureAlgorithm
 	}
diff --git a/helpers/helpers_test.go b/helpers/helpers_test.go
index dc59bf2c6..bbc74d38e 100644
--- a/helpers/helpers_test.go
+++ b/helpers/helpers_test.go
@@ -3,6 +3,7 @@ package helpers
 import (
 	"bytes"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/elliptic"
 	"crypto/rand"
 	"crypto/rsa"
@@ -106,6 +107,16 @@ func TestKeyLength(t *testing.T) {
 	if expRsa != outRsa {
 		t.Fatal("KeyLength malfunctioning on rsa input")
 	}
+
+	//test the ed25519 branch
+	_, ed25519priv, _ := ed25519.GenerateKey(rand.Reader)
+	ed25519In, _ := ed25519priv.Public().(ed25519.PublicKey)
+	expEd25519 := len(ed25519In)
+	outEd25519 := KeyLength(ed25519In)
+	if expEd25519 != outEd25519 {
+		t.Fatal("KeyLength malfunctioning on ed25519 input")
+	}
+
 }
 
 func TestExpiryTime(t *testing.T) {
@@ -219,6 +230,9 @@ func TestHashAlgoString(t *testing.T) {
 	if HashAlgoString(x509.ECDSAWithSHA512) != "SHA512" {
 		t.Fatal("standin")
 	}
+	if HashAlgoString(x509.PureEd25519) != "Ed25519" {
+		t.Fatal("standin")
+	}
 	if HashAlgoString(math.MaxInt32) != "Unknown Hash Algorithm" {
 		t.Fatal("standin")
 	}
@@ -261,6 +275,9 @@ func TestSignatureString(t *testing.T) {
 	if SignatureString(x509.ECDSAWithSHA512) != "ECDSAWithSHA512" {
 		t.Fatal("Signature String functioning improperly")
 	}
+	if SignatureString(x509.PureEd25519) != "Ed25519" {
+		t.Fatal("Signature String functioning improperly")
+	}
 	if SignatureString(math.MaxInt32) != "Unknown Signature" {
 		t.Fatal("Signature String functioning improperly")
 	}
diff --git a/initca/initca.go b/initca/initca.go
index 40a608502..0ba8f715d 100644
--- a/initca/initca.go
+++ b/initca/initca.go
@@ -3,8 +3,10 @@
 package initca
 
 import (
+	"bytes"
 	"crypto"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/rand"
 	"crypto/rsa"
 	"crypto/x509"
@@ -97,7 +99,6 @@ func New(req *csr.CertificateRequest) (cert, csrPEM, key []byte, err error) {
 	cert, err = s.Sign(signReq)
 
 	return
-
 }
 
 // NewFromPEM creates a new root certificate from the key file passed in.
@@ -210,8 +211,17 @@ func RenewFromSigner(ca *x509.Certificate, priv crypto.Signer) ([]byte, error) {
 		if ca.PublicKey.(*ecdsa.PublicKey).X.Cmp(ecdsaPublicKey.X) != 0 {
 			return nil, cferr.New(cferr.PrivateKeyError, cferr.KeyMismatch)
 		}
+	case ca.PublicKeyAlgorithm == x509.Ed25519:
+		var ed25519PublicKey ed25519.PublicKey
+		var ok bool
+		if ed25519PublicKey, ok = priv.Public().(ed25519.PublicKey); !ok {
+			return nil, cferr.New(cferr.PrivateKeyError, cferr.KeyMismatch)
+		}
+		if !(bytes.Equal(ca.PublicKey.(ed25519.PublicKey), ed25519PublicKey)) {
+			return nil, cferr.New(cferr.PrivateKeyError, cferr.KeyMismatch)
+		}
 	default:
-		return nil, cferr.New(cferr.PrivateKeyError, cferr.NotRSAOrECC)
+		return nil, cferr.New(cferr.PrivateKeyError, cferr.NotRSAOrECCOrEd25519)
 	}
 
 	req := csr.ExtractCertificateRequest(ca)
diff --git a/initca/initca_test.go b/initca/initca_test.go
index 154021ac8..c46c208b9 100644
--- a/initca/initca_test.go
+++ b/initca/initca_test.go
@@ -23,6 +23,7 @@ var validKeyParams = []csr.KeyRequest{
 	{A: "ecdsa", S: 256},
 	{A: "ecdsa", S: 384},
 	{A: "ecdsa", S: 521},
+	{A: "ed25519"},
 }
 
 var validCAConfigs = []csr.CAConfig{
@@ -46,12 +47,15 @@ var csrFiles = []string{
 	"testdata/ecdsa256.csr",
 	"testdata/ecdsa384.csr",
 	"testdata/ecdsa521.csr",
+	"testdata/ed25519.csr",
 }
 
 var testRSACAFile = "testdata/5min-rsa.pem"
 var testRSACAKeyFile = "testdata/5min-rsa-key.pem"
 var testECDSACAFile = "testdata/5min-ecdsa.pem"
 var testECDSACAKeyFile = "testdata/5min-ecdsa-key.pem"
+var testED25519CAFile = "testdata/5min-ed25519.pem"
+var testED25519CAKeyFile = "testdata/5min-ed25519-key.pem"
 
 var invalidCryptoParams = []csr.KeyRequest{
 	// Weak Key
@@ -160,7 +164,7 @@ func TestInitCA(t *testing.T) {
 			}
 			s.SetPolicy(CAPolicy())
 
-			// Sign RSA and ECDSA customer CSRs.
+			// Sign RSA, ECDSA and ed25519 customer CSRs.
 			for _, csrFile := range csrFiles {
 				csrBytes, err := os.ReadFile(csrFile)
 				if err != nil {
@@ -209,7 +213,7 @@ func TestInvalidCAConfig(t *testing.T) {
 
 	_, _, _, err := New(req)
 	if err == nil {
-		t.Fatal("InitCA with bad CAConfig should fail:", err)
+		t.Fatalf("InitCA with bad CAConfig should fail: %v", invalidCAConfig)
 	}
 }
 func TestInvalidCryptoParams(t *testing.T) {
@@ -232,7 +236,7 @@ func TestInvalidCryptoParams(t *testing.T) {
 		}
 		_, _, _, err := New(req)
 		if err == nil {
-			t.Fatal("InitCA with bad params should fail:", err)
+			t.Fatalf("InitCA with bad CAConfig should fail: %v", invalidCAConfig)
 		}
 
 		if !strings.Contains(err.Error(), `"code":2400`) {
@@ -311,6 +315,43 @@ func TestRenewRSA(t *testing.T) {
 	}
 }
 
+func TestRenewED25519(t *testing.T) {
+	certPEM, err := RenewFromPEM(testED25519CAFile, testED25519CAKeyFile)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	// must parse ok
+	cert, err := helpers.ParseCertificatePEM(certPEM)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	if !cert.IsCA {
+		t.Fatal("renewed CA certificate is not CA")
+	}
+
+	// cert expiry must be 5 minutes
+	expiry := cert.NotAfter.Sub(cert.NotBefore).Seconds()
+	if expiry >= 301 || expiry <= 299 {
+		t.Fatal("expiry is not correct:", expiry)
+	}
+
+	// check subject
+
+	if cert.Subject.CommonName != "" {
+		t.Fatal("Bad CommonName")
+	}
+
+	if len(cert.Subject.Country) != 1 || cert.Subject.Country[0] != "US" {
+		t.Fatal("Bad Subject")
+	}
+
+	if len(cert.Subject.Organization) != 1 || cert.Subject.Organization[0] != "CloudFlare, Inc." {
+		t.Fatal("Bad Subject")
+	}
+}
+
 func TestRenewECDSA(t *testing.T) {
 	certPEM, err := RenewFromPEM(testECDSACAFile, testECDSACAKeyFile)
 	if err != nil {
diff --git a/initca/testdata/5min-ed25519-key.pem b/initca/testdata/5min-ed25519-key.pem
new file mode 100644
index 000000000..8521ed701
--- /dev/null
+++ b/initca/testdata/5min-ed25519-key.pem
@@ -0,0 +1,3 @@
+-----BEGIN Ed25519 PRIVATE KEY-----
+MC4CAQAwBQYDK2VwBCIEIO23h+PSszCu1BdPNn2HnmPexKh9p3HA3QxTOZ3cXQqx
+-----END Ed25519 PRIVATE KEY-----
diff --git a/initca/testdata/5min-ed25519.pem b/initca/testdata/5min-ed25519.pem
new file mode 100644
index 000000000..4d99bddb1
--- /dev/null
+++ b/initca/testdata/5min-ed25519.pem
@@ -0,0 +1,13 @@
+-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----
diff --git a/initca/testdata/README.md b/initca/testdata/README.md
index e34ad2af6..e4fade9e4 100644
--- a/initca/testdata/README.md
+++ b/initca/testdata/README.md
@@ -1,11 +1,20 @@
 1. To generate 5min-rsa.pem and 5min-rsa-key.pem
+
 ```
 $ cfssl gencert -initca ca_csr_rsa.json | cfssljson -bare 5min-rsa
 ```
+
 2. To generate 5min-ecdsa.pem and 5min-ecdsa-key.pem
+
 ```
 $ cfssl gencert -initca ca_csr_ecdsa.json | cfssljson -bare 5min-ecdsa
 ```
 
-The above commands will generate 5min-rsa.csr and 5min-ecdsa.csr as well, but those
-files can be ignored.
+2. To generate 5min-ed25519.pem and 5min-ed25519-key.pem
+
+```
+$ cfssl gencert -initca ca_csr_ed25519.json | cfssljson -bare 5min-ed25519
+```
+
+The above commands will generate 5min-rsa.csr, 5min-ecdsa.csr 5min-ed25519.csr
+accordingly, but those files can be ignored.
diff --git a/initca/testdata/ca_csr_ed25519.json b/initca/testdata/ca_csr_ed25519.json
new file mode 100644
index 000000000..461011d8c
--- /dev/null
+++ b/initca/testdata/ca_csr_ed25519.json
@@ -0,0 +1,17 @@
+{
+  "key": {
+    "algo": "ed25519"
+  },
+  "names": [
+    {
+    "C": "US",
+    "L": "San Francisco",
+    "ST": "California",
+    "O": "CloudFlare, Inc.",
+    "OU": "Test Certificate Authority"
+    }
+  ],
+  "ca": {
+    "expiry": "5m"
+  }
+}
diff --git a/initca/testdata/ed25519.csr b/initca/testdata/ed25519.csr
new file mode 100644
index 000000000..a4b49b262
--- /dev/null
+++ b/initca/testdata/ed25519.csr
@@ -0,0 +1,8 @@
+-----BEGIN CERTIFICATE REQUEST-----
+MIIBFzCBygIBADBqMQswCQYDVQQGEwJVUzETMBEGA1UECBMKQ2FsaWZvcm5pYTEW
+MBQGA1UEBxMNU2FuIEZyYW5jaXNjbzEUMBIGA1UEChMLZXhhbXBsZS5jb20xGDAW
+BgNVBAMTD3d3dy5leGFtcGxlLmNvbTAqMAUGAytlcAMhAIvEIdwMxpLmXW+ZKI+u
+hb4/H/1qaEOCSbWmWF95m1HzoC0wKwYJKoZIhvcNAQkOMR4wHDAaBgNVHREEEzAR
+gg93d3cuZXhhbXBsZS5jb20wBQYDK2VwA0EA/FCjbBOJT6z5wdBLgCJb3WrQGO9E
+lOizNutfEk9NlGJliNKkdZO3SZP9Uw/pKHiyxH+vWfUJ3E1DbtTVzmH8DA==
+-----END CERTIFICATE REQUEST-----
diff --git a/scan/crypto/tls/generate_cert.go b/scan/crypto/tls/generate_cert.go
index 8eaa452ad..559cdc822 100644
--- a/scan/crypto/tls/generate_cert.go
+++ b/scan/crypto/tls/generate_cert.go
@@ -12,6 +12,7 @@ package main
 
 import (
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/elliptic"
 	"crypto/rand"
 	"crypto/rsa"
@@ -26,6 +27,8 @@ import (
 	"os"
 	"strings"
 	"time"
+
+	"github.com/cloudflare/cfssl/helpers/derhelpers"
 )
 
 var (
@@ -41,6 +44,8 @@ func publicKey(priv interface{}) interface{} {
 	switch k := priv.(type) {
 	case *rsa.PrivateKey:
 		return &k.PublicKey
+	case *ed25519.PrivateKey:
+		return &k.Public()
 	case *ecdsa.PrivateKey:
 		return &k.PublicKey
 	default:
@@ -52,6 +57,13 @@ func pemBlockForKey(priv interface{}) *pem.Block {
 	switch k := priv.(type) {
 	case *rsa.PrivateKey:
 		return &pem.Block{Type: "RSA PRIVATE KEY", Bytes: x509.MarshalPKCS1PrivateKey(k)}
+	case *ed25519.PrivateKey:
+		b, err := derhelpers.MarshalEd25519PrivateKey(priv)
+		if err != nil {
+			fmt.Fprintf(os.Stderr, "Unable to marshal ED25519 private key: %v", err)
+			os.Exit(2)
+		}
+		return &pem.Block{Type: "Ed25519 PRIVATE KEY", Bytes: b}
 	case *ecdsa.PrivateKey:
 		b, err := x509.MarshalECPrivateKey(k)
 		if err != nil {
@@ -76,6 +88,8 @@ func main() {
 	switch *ecdsaCurve {
 	case "":
 		priv, err = rsa.GenerateKey(rand.Reader, *rsaBits)
+	case "ED25519":
+		_, priv, err = ed25519.GenerateKey(rand.Reader)
 	case "P224":
 		priv, err = ecdsa.GenerateKey(elliptic.P224(), rand.Reader)
 	case "P256":
diff --git a/signer/local/local_test.go b/signer/local/local_test.go
index 041e25486..51cdcf54f 100644
--- a/signer/local/local_test.go
+++ b/signer/local/local_test.go
@@ -365,6 +365,12 @@ var csrTests = []csrTest{
 		keyLen:        2048,
 		errorCallback: nil,
 	},
+	{
+		file:          "testdata/ed25519.csr",
+		keyAlgo:       "ed25519",
+		keyLen:        256,
+		errorCallback: nil,
+	},
 }
 
 func TestSignCSRs(t *testing.T) {
diff --git a/signer/local/testdata/ed25519.csr b/signer/local/testdata/ed25519.csr
new file mode 100644
index 000000000..a4b49b262
--- /dev/null
+++ b/signer/local/testdata/ed25519.csr
@@ -0,0 +1,8 @@
+-----BEGIN CERTIFICATE REQUEST-----
+MIIBFzCBygIBADBqMQswCQYDVQQGEwJVUzETMBEGA1UECBMKQ2FsaWZvcm5pYTEW
+MBQGA1UEBxMNU2FuIEZyYW5jaXNjbzEUMBIGA1UEChMLZXhhbXBsZS5jb20xGDAW
+BgNVBAMTD3d3dy5leGFtcGxlLmNvbTAqMAUGAytlcAMhAIvEIdwMxpLmXW+ZKI+u
+hb4/H/1qaEOCSbWmWF95m1HzoC0wKwYJKoZIhvcNAQkOMR4wHDAaBgNVHREEEzAR
+gg93d3cuZXhhbXBsZS5jb20wBQYDK2VwA0EA/FCjbBOJT6z5wdBLgCJb3WrQGO9E
+lOizNutfEk9NlGJliNKkdZO3SZP9Uw/pKHiyxH+vWfUJ3E1DbtTVzmH8DA==
+-----END CERTIFICATE REQUEST-----
diff --git a/signer/signer.go b/signer/signer.go
index ea650bd6d..d5b1f96f0 100644
--- a/signer/signer.go
+++ b/signer/signer.go
@@ -4,6 +4,7 @@ package signer
 import (
 	"crypto"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/elliptic"
 	"crypto/rsa"
 	"crypto/sha1"
@@ -168,6 +169,8 @@ func DefaultSigAlgo(priv crypto.Signer) x509.SignatureAlgorithm {
 		default:
 			return x509.ECDSAWithSHA1
 		}
+	case ed25519.PublicKey:
+		return x509.PureEd25519
 	default:
 		return x509.UnknownSignatureAlgorithm
 	}
diff --git a/transport/kp/key_provider.go b/transport/kp/key_provider.go
index 7663bad56..dc1fd6a3c 100644
--- a/transport/kp/key_provider.go
+++ b/transport/kp/key_provider.go
@@ -15,6 +15,7 @@ package kp
 import (
 	"crypto"
 	"crypto/ecdsa"
+	"crypto/ed25519"
 	"crypto/elliptic"
 	"crypto/rand"
 	"crypto/rsa"
@@ -22,11 +23,13 @@ import (
 	"crypto/x509"
 	"encoding/pem"
 	"errors"
+	"io"
 	"os"
 	"strings"
 
 	"github.com/cloudflare/cfssl/csr"
 	"github.com/cloudflare/cfssl/helpers"
+	"github.com/cloudflare/cfssl/helpers/derhelpers"
 	"github.com/cloudflare/cfssl/transport/core"
 )
 
@@ -241,9 +244,26 @@ func (sp *StandardProvider) Generate(algo string, size int) (err error) {
 		}
 		sp.internal.keyPEM = pem.EncodeToMemory(p)
 
+		sp.internal.priv = priv
+	case "ed25519":
+		seed := make([]byte, ed25519.SeedSize)
+		if _, err := io.ReadFull(rand.Reader, seed); err != nil {
+			return err
+		}
+		priv := ed25519.NewKeyFromSeed(seed)
+
+		keyPEM, err := derhelpers.MarshalEd25519PrivateKey(priv)
+		if err != nil {
+			return err
+		}
+		p := &pem.Block{
+			Type:  "Ed25519 PRIVATE KEY",
+			Bytes: keyPEM,
+		}
+		sp.internal.keyPEM = pem.EncodeToMemory(p)
 		sp.internal.priv = priv
 	default:
-		return errors.New("transport: invalid key algorithm; only RSA and ECDSA are supported")
+		return errors.New("transport: invalid key algorithm; only RSA, Ed25519 and ECDSA are supported")
 	}
 
 	return nil
@@ -324,6 +344,11 @@ func (sp *StandardProvider) Load() (err error) {
 			err = errors.New("transport: PEM type " + p.Type + " is invalid for an ECDSA key")
 			return
 		}
+	case ed25519.PublicKey:
+		if p.Type != "Ed25519 PRIVATE KEY" {
+			err = errors.New("transport: PEM type" + p.Type + "is invalid for an Ed25519 key")
+			return
+		}
 	default:
 		err = errors.New("transport: invalid public key type")
 	}
diff --git a/transport/kp/key_provider_test.go b/transport/kp/key_provider_test.go
index fe3218817..0ec04fb63 100644
--- a/transport/kp/key_provider_test.go
+++ b/transport/kp/key_provider_test.go
@@ -82,8 +82,18 @@ func TestGenerate(t *testing.T) {
 		t.Fatal("key provider shouldn't have a key yet")
 	}
 
+	err = kp.Generate("rsa", 2048)
+	if err != nil {
+		t.Fatalf("key provider couldn't generate key: %v", err)
+	}
+
 	err = kp.Generate("ecdsa", 256)
 	if err != nil {
 		t.Fatalf("key provider couldn't generate key: %v", err)
 	}
+
+	err = kp.Generate("ed25519", 256) // ed25519 key size is ignored
+	if err != nil {
+		t.Fatalf("key provider couldn't generate key: %v", err)
+	}
 }
diff --git a/vendor/github.com/cloudflare/circl/LICENSE b/vendor/github.com/cloudflare/circl/LICENSE
new file mode 100644
index 000000000..67edaa90a
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/LICENSE
@@ -0,0 +1,57 @@
+Copyright (c) 2019 Cloudflare. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+   * Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+   * Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+   * Neither the name of Cloudflare nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+========================================================================
+
+Copyright (c) 2009 The Go Authors. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+   * Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+   * Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+   * Neither the name of Google Inc. nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/vendor/github.com/cloudflare/circl/internal/conv/conv.go b/vendor/github.com/cloudflare/circl/internal/conv/conv.go
new file mode 100644
index 000000000..b4a4f0b16
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/internal/conv/conv.go
@@ -0,0 +1,89 @@
+package conv
+
+import (
+	"fmt"
+	"math/big"
+	"strings"
+)
+
+// BytesLe2Hex returns an hexadecimal string of a number stored in a
+// little-endian order slice x.
+func BytesLe2Hex(x []byte) string {
+	b := &strings.Builder{}
+	b.Grow(2*len(x) + 2)
+	fmt.Fprint(b, "0x")
+	if len(x) == 0 {
+		fmt.Fprint(b, "00")
+	}
+	for i := len(x) - 1; i >= 0; i-- {
+		fmt.Fprintf(b, "%02x", x[i])
+	}
+	return b.String()
+}
+
+// BytesLe2BigInt converts a little-endian slice x into a big-endian
+// math/big.Int.
+func BytesLe2BigInt(x []byte) *big.Int {
+	n := len(x)
+	b := new(big.Int)
+	if len(x) > 0 {
+		y := make([]byte, n)
+		for i := 0; i < n; i++ {
+			y[n-1-i] = x[i]
+		}
+		b.SetBytes(y)
+	}
+	return b
+}
+
+// BigInt2BytesLe stores a positive big.Int number x into a little-endian slice z.
+// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros).
+// If x does not fit in the slice or is negative, z is not modified.
+func BigInt2BytesLe(z []byte, x *big.Int) {
+	xLen := (x.BitLen() + 7) >> 3
+	zLen := len(z)
+	if zLen >= xLen && x.Sign() >= 0 {
+		y := x.Bytes()
+		for i := 0; i < xLen; i++ {
+			z[i] = y[xLen-1-i]
+		}
+		for i := xLen; i < zLen; i++ {
+			z[i] = 0
+		}
+	}
+}
+
+// Uint64Le2BigInt converts a llitle-endian slice x into a big number.
+func Uint64Le2BigInt(x []uint64) *big.Int {
+	n := len(x)
+	b := new(big.Int)
+	var bi big.Int
+	for i := n - 1; i >= 0; i-- {
+		bi.SetUint64(x[i])
+		b.Lsh(b, 64)
+		b.Add(b, &bi)
+	}
+	return b
+}
+
+// BigInt2Uint64Le stores a positive big.Int number x into a little-endian slice z.
+// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros).
+// If x does not fit in the slice or is negative, z is not modified.
+func BigInt2Uint64Le(z []uint64, x *big.Int) {
+	xLen := (x.BitLen() + 63) >> 6 // number of 64-bit words
+	zLen := len(z)
+	if zLen >= xLen && x.Sign() > 0 {
+		var y, yi big.Int
+		y.Set(x)
+		two64 := big.NewInt(1)
+		two64.Lsh(two64, 64).Sub(two64, big.NewInt(1))
+		for i := 0; i < xLen; i++ {
+			yi.And(&y, two64)
+			z[i] = yi.Uint64()
+			y.Rsh(&y, 64)
+		}
+	}
+	for i := xLen; i < zLen; i++ {
+		z[i] = 0
+	}
+}
diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp.go
new file mode 100644
index 000000000..496287ec5
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp.go
@@ -0,0 +1,205 @@
+// Package fp25519 provides prime field arithmetic over GF(2^255-19).
+package fp25519
+
+import (
+	"errors"
+
+	"github.com/cloudflare/circl/internal/conv"
+)
+
+// Size in bytes of an element.
+const Size = 32
+
+// Elt is a prime field element.
+type Elt [Size]byte
+
+func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) }
+
+// p is the prime modulus 2^255-19.
+var p = Elt{
+	0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f,
+}
+
+// P returns the prime modulus 2^255-19.
+func P() Elt { return p }
+
+// ToBytes stores in b the little-endian byte representation of x.
+func ToBytes(b []byte, x *Elt) error {
+	if len(b) != Size {
+		return errors.New("wrong size")
+	}
+	Modp(x)
+	copy(b, x[:])
+	return nil
+}
+
+// IsZero returns true if x is equal to 0.
+func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} }
+
+// SetOne assigns x=1.
+func SetOne(x *Elt) { *x = Elt{}; x[0] = 1 }
+
+// Neg calculates z = -x.
+func Neg(z, x *Elt) { Sub(z, &p, x) }
+
+// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue, which is
+// indicated by returning isQR = true. Otherwise, when x/y is a quadratic
+// non-residue, z will have an undetermined value and isQR = false.
+func InvSqrt(z, x, y *Elt) (isQR bool) {
+	sqrtMinusOne := &Elt{
+		0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4,
+		0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f,
+		0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b,
+		0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b,
+	}
+	t0, t1, t2, t3 := &Elt{}, &Elt{}, &Elt{}, &Elt{}
+
+	Mul(t0, x, y)   // t0 = u*v
+	Sqr(t1, y)      // t1 = v^2
+	Mul(t2, t0, t1) // t2 = u*v^3
+	Sqr(t0, t1)     // t0 = v^4
+	Mul(t1, t0, t2) // t1 = u*v^7
+
+	var Tab [4]*Elt
+	Tab[0] = &Elt{}
+	Tab[1] = &Elt{}
+	Tab[2] = t3
+	Tab[3] = t1
+
+	*Tab[0] = *t1
+	Sqr(Tab[0], Tab[0])
+	Sqr(Tab[1], Tab[0])
+	Sqr(Tab[1], Tab[1])
+	Mul(Tab[1], Tab[1], Tab[3])
+	Mul(Tab[0], Tab[0], Tab[1])
+	Sqr(Tab[0], Tab[0])
+	Mul(Tab[0], Tab[0], Tab[1])
+	Sqr(Tab[1], Tab[0])
+	for i := 0; i < 4; i++ {
+		Sqr(Tab[1], Tab[1])
+	}
+	Mul(Tab[1], Tab[1], Tab[0])
+	Sqr(Tab[2], Tab[1])
+	for i := 0; i < 4; i++ {
+		Sqr(Tab[2], Tab[2])
+	}
+	Mul(Tab[2], Tab[2], Tab[0])
+	Sqr(Tab[1], Tab[2])
+	for i := 0; i < 14; i++ {
+		Sqr(Tab[1], Tab[1])
+	}
+	Mul(Tab[1], Tab[1], Tab[2])
+	Sqr(Tab[2], Tab[1])
+	for i := 0; i < 29; i++ {
+		Sqr(Tab[2], Tab[2])
+	}
+	Mul(Tab[2], Tab[2], Tab[1])
+	Sqr(Tab[1], Tab[2])
+	for i := 0; i < 59; i++ {
+		Sqr(Tab[1], Tab[1])
+	}
+	Mul(Tab[1], Tab[1], Tab[2])
+	for i := 0; i < 5; i++ {
+		Sqr(Tab[1], Tab[1])
+	}
+	Mul(Tab[1], Tab[1], Tab[0])
+	Sqr(Tab[2], Tab[1])
+	for i := 0; i < 124; i++ {
+		Sqr(Tab[2], Tab[2])
+	}
+	Mul(Tab[2], Tab[2], Tab[1])
+	Sqr(Tab[2], Tab[2])
+	Sqr(Tab[2], Tab[2])
+	Mul(Tab[2], Tab[2], Tab[3])
+
+	Mul(z, t3, t2) // z = xy^(p+3)/8 = xy^3*(xy^7)^(p-5)/8
+	// Checking whether y z^2 == x
+	Sqr(t0, z)     // t0 = z^2
+	Mul(t0, t0, y) // t0 = yz^2
+	Sub(t1, t0, x) // t1 = t0-u
+	Add(t2, t0, x) // t2 = t0+u
+	if IsZero(t1) {
+		return true
+	} else if IsZero(t2) {
+		Mul(z, z, sqrtMinusOne) // z = z*sqrt(-1)
+		return true
+	} else {
+		return false
+	}
+}
+
+// Inv calculates z = 1/x mod p.
+func Inv(z, x *Elt) {
+	x0, x1, x2 := &Elt{}, &Elt{}, &Elt{}
+	Sqr(x1, x)
+	Sqr(x0, x1)
+	Sqr(x0, x0)
+	Mul(x0, x0, x)
+	Mul(z, x0, x1)
+	Sqr(x1, z)
+	Mul(x0, x0, x1)
+	Sqr(x1, x0)
+	for i := 0; i < 4; i++ {
+		Sqr(x1, x1)
+	}
+	Mul(x0, x0, x1)
+	Sqr(x1, x0)
+	for i := 0; i < 9; i++ {
+		Sqr(x1, x1)
+	}
+	Mul(x1, x1, x0)
+	Sqr(x2, x1)
+	for i := 0; i < 19; i++ {
+		Sqr(x2, x2)
+	}
+	Mul(x2, x2, x1)
+	for i := 0; i < 10; i++ {
+		Sqr(x2, x2)
+	}
+	Mul(x2, x2, x0)
+	Sqr(x0, x2)
+	for i := 0; i < 49; i++ {
+		Sqr(x0, x0)
+	}
+	Mul(x0, x0, x2)
+	Sqr(x1, x0)
+	for i := 0; i < 99; i++ {
+		Sqr(x1, x1)
+	}
+	Mul(x1, x1, x0)
+	for i := 0; i < 50; i++ {
+		Sqr(x1, x1)
+	}
+	Mul(x1, x1, x2)
+	for i := 0; i < 5; i++ {
+		Sqr(x1, x1)
+	}
+	Mul(z, z, x1)
+}
+
+// Cmov assigns y to x if n is 1.
+func Cmov(x, y *Elt, n uint) { cmov(x, y, n) }
+
+// Cswap interchages x and y if n is 1.
+func Cswap(x, y *Elt, n uint) { cswap(x, y, n) }
+
+// Add calculates z = x+y mod p.
+func Add(z, x, y *Elt) { add(z, x, y) }
+
+// Sub calculates z = x-y mod p.
+func Sub(z, x, y *Elt) { sub(z, x, y) }
+
+// AddSub calculates (x,y) = (x+y mod p, x-y mod p).
+func AddSub(x, y *Elt) { addsub(x, y) }
+
+// Mul calculates z = x*y mod p.
+func Mul(z, x, y *Elt) { mul(z, x, y) }
+
+// Sqr calculates z = x^2 mod p.
+func Sqr(z, x *Elt) { sqr(z, x) }
+
+// Modp ensures that z is between [0,p-1].
+func Modp(z *Elt) { modp(z) }
diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go
new file mode 100644
index 000000000..1c35c0079
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go
@@ -0,0 +1,44 @@
+// +build amd64,!purego
+
+package fp25519
+
+import (
+	"golang.org/x/sys/cpu"
+)
+
+var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX
+
+var _ = hasBmi2Adx
+
+func cmov(x, y *Elt, n uint)  { cmovAmd64(x, y, n) }
+func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) }
+func add(z, x, y *Elt)        { addAmd64(z, x, y) }
+func sub(z, x, y *Elt)        { subAmd64(z, x, y) }
+func addsub(x, y *Elt)        { addsubAmd64(x, y) }
+func mul(z, x, y *Elt)        { mulAmd64(z, x, y) }
+func sqr(z, x *Elt)           { sqrAmd64(z, x) }
+func modp(z *Elt)             { modpAmd64(z) }
+
+//go:noescape
+func cmovAmd64(x, y *Elt, n uint)
+
+//go:noescape
+func cswapAmd64(x, y *Elt, n uint)
+
+//go:noescape
+func addAmd64(z, x, y *Elt)
+
+//go:noescape
+func subAmd64(z, x, y *Elt)
+
+//go:noescape
+func addsubAmd64(x, y *Elt)
+
+//go:noescape
+func mulAmd64(z, x, y *Elt)
+
+//go:noescape
+func sqrAmd64(z, x *Elt)
+
+//go:noescape
+func modpAmd64(z *Elt)
diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h
new file mode 100644
index 000000000..7b25f16e4
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h
@@ -0,0 +1,350 @@
+// This code was imported from https://github.com/armfazh/rfc7748_precomputed
+
+// CHECK_BMI2ADX triggers bmi2adx if supported,
+// otherwise it fallbacks to legacy code.
+#define CHECK_BMI2ADX(label, legacy, bmi2adx) \
+    CMPB ·hasBmi2Adx(SB), $0  \
+    JE label                  \
+    bmi2adx                   \
+    RET                       \
+    label:                    \
+    legacy                    \
+    RET
+
+// cselect is a conditional move
+// if b=1: it copies y into x;
+// if b=0: x remains with the same value;
+// if b<> 0,1: undefined.
+// Uses: AX, DX, FLAGS
+// Instr: x86_64, cmov
+#define cselect(x,y,b) \
+    TESTQ b, b \
+    MOVQ  0+x, AX; MOVQ  0+y, DX; CMOVQNE DX, AX; MOVQ AX,  0+x; \
+    MOVQ  8+x, AX; MOVQ  8+y, DX; CMOVQNE DX, AX; MOVQ AX,  8+x; \
+    MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \
+    MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x;
+
+// cswap is a conditional swap
+// if b=1: x,y <- y,x;
+// if b=0: x,y remain with the same values;
+// if b<> 0,1: undefined.
+// Uses: AX, DX, R8, FLAGS
+// Instr: x86_64, cmov
+#define cswap(x,y,b) \
+    TESTQ b, b \
+    MOVQ  0+x, AX; MOVQ AX, R8; MOVQ  0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX,  0+x; MOVQ DX,  0+y; \
+    MOVQ  8+x, AX; MOVQ AX, R8; MOVQ  8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX,  8+x; MOVQ DX,  8+y; \
+    MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \
+    MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y;
+
+// additionLeg adds x and y and stores in z
+// Uses: AX, DX, R8-R11, FLAGS
+// Instr: x86_64, cmov
+#define additionLeg(z,x,y) \
+    MOVL $38, AX; \
+    MOVL  $0, DX; \
+    MOVQ  0+x,  R8;  ADDQ  0+y,  R8; \
+    MOVQ  8+x,  R9;  ADCQ  8+y,  R9; \
+    MOVQ 16+x, R10;  ADCQ 16+y, R10; \
+    MOVQ 24+x, R11;  ADCQ 24+y, R11; \
+    CMOVQCS AX, DX;    \
+    ADDQ DX,  R8; \
+    ADCQ $0,  R9;  MOVQ  R9,  8+z; \
+    ADCQ $0, R10;  MOVQ R10, 16+z; \
+    ADCQ $0, R11;  MOVQ R11, 24+z; \
+    MOVL $0,  DX; \
+    CMOVQCS AX, DX; \
+    ADDQ DX,  R8;  MOVQ  R8,  0+z;
+
+// additionAdx adds x and y and stores in z
+// Uses: AX, DX, R8-R11, FLAGS
+// Instr: x86_64, cmov, adx
+#define additionAdx(z,x,y) \
+    MOVL $38, AX; \
+    XORL  DX, DX; \
+    MOVQ  0+x,  R8;  ADCXQ  0+y,  R8; \
+    MOVQ  8+x,  R9;  ADCXQ  8+y,  R9; \
+    MOVQ 16+x, R10;  ADCXQ 16+y, R10; \
+    MOVQ 24+x, R11;  ADCXQ 24+y, R11; \
+    CMOVQCS AX, DX ; \
+    XORL  AX,  AX; \
+    ADCXQ DX,  R8; \
+    ADCXQ AX,  R9;  MOVQ  R9,  8+z; \
+    ADCXQ AX, R10;  MOVQ R10, 16+z; \
+    ADCXQ AX, R11;  MOVQ R11, 24+z; \
+    MOVL $38,  DX; \
+    CMOVQCS DX, AX; \
+    ADDQ  AX,  R8;  MOVQ  R8,  0+z;
+
+// subtraction subtracts y from x and stores in z
+// Uses: AX, DX, R8-R11, FLAGS
+// Instr: x86_64, cmov
+#define subtraction(z,x,y) \
+    MOVL   $38,  AX; \
+    MOVQ  0+x,  R8;  SUBQ  0+y,  R8; \
+    MOVQ  8+x,  R9;  SBBQ  8+y,  R9; \
+    MOVQ 16+x, R10;  SBBQ 16+y, R10; \
+    MOVQ 24+x, R11;  SBBQ 24+y, R11; \
+    MOVL $0, DX; \
+    CMOVQCS AX, DX; \
+    SUBQ  DX,  R8; \
+    SBBQ  $0,  R9;  MOVQ  R9,  8+z; \
+    SBBQ  $0, R10;  MOVQ R10, 16+z; \
+    SBBQ  $0, R11;  MOVQ R11, 24+z; \
+    MOVL  $0,  DX; \
+    CMOVQCS AX, DX; \
+    SUBQ  DX,  R8;  MOVQ  R8,  0+z;
+
+// integerMulAdx multiplies x and y and stores in z
+// Uses: AX, DX, R8-R15, FLAGS
+// Instr: x86_64, bmi2, adx
+#define integerMulAdx(z,x,y) \
+    MOVQ   0+y, DX;       XORL  AX,  AX; \
+    MULXQ  0+x, AX,  R8;  MOVQ  AX, 0+z; \
+    MULXQ  8+x, AX,  R9;  ADCXQ AX,  R8; \
+    MULXQ 16+x, AX, R10;  ADCXQ AX,  R9; \
+    MULXQ 24+x, AX, R11;  ADCXQ AX, R10; \
+    MOVL $0, AX;;;;;;;;;  ADCXQ AX, R11; \
+    MOVQ   8+y, DX;       XORL   AX,  AX; \
+    MULXQ  0+x, AX, R12;  ADCXQ  R8,  AX;  MOVQ  AX,  8+z; \
+    MULXQ  8+x, AX, R13;  ADCXQ  R9, R12;  ADOXQ AX, R12; \
+    MULXQ 16+x, AX, R14;  ADCXQ R10, R13;  ADOXQ AX, R13; \
+    MULXQ 24+x, AX, R15;  ADCXQ R11, R14;  ADOXQ AX, R14; \
+    MOVL $0, AX;;;;;;;;;  ADCXQ  AX, R15;  ADOXQ AX, R15; \
+    MOVQ  16+y, DX;       XORL   AX,  AX; \
+    MULXQ  0+x, AX,  R8;  ADCXQ R12,  AX;  MOVQ  AX, 16+z; \
+    MULXQ  8+x, AX,  R9;  ADCXQ R13,  R8;  ADOXQ AX,  R8; \
+    MULXQ 16+x, AX, R10;  ADCXQ R14,  R9;  ADOXQ AX,  R9; \
+    MULXQ 24+x, AX, R11;  ADCXQ R15, R10;  ADOXQ AX, R10; \
+    MOVL $0, AX;;;;;;;;;  ADCXQ  AX, R11;  ADOXQ AX, R11; \
+    MOVQ  24+y, DX;       XORL   AX,  AX; \
+    MULXQ  0+x, AX, R12;  ADCXQ  R8,  AX;  MOVQ  AX, 24+z; \
+    MULXQ  8+x, AX, R13;  ADCXQ  R9, R12;  ADOXQ AX, R12;  MOVQ R12, 32+z; \
+    MULXQ 16+x, AX, R14;  ADCXQ R10, R13;  ADOXQ AX, R13;  MOVQ R13, 40+z; \
+    MULXQ 24+x, AX, R15;  ADCXQ R11, R14;  ADOXQ AX, R14;  MOVQ R14, 48+z; \
+    MOVL $0, AX;;;;;;;;;  ADCXQ  AX, R15;  ADOXQ AX, R15;  MOVQ R15, 56+z;
+
+// integerMulLeg multiplies x and y and stores in z
+// Uses: AX, DX, R8-R15, FLAGS
+// Instr: x86_64
+#define integerMulLeg(z,x,y) \
+    MOVQ  0+y, R8; \
+    MOVQ  0+x, AX; MULQ R8; MOVQ AX, 0+z; MOVQ DX, R15; \
+    MOVQ  8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \
+    MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \
+    MOVQ 24+x, AX; MULQ R8; \
+    ADDQ R13, R15; \
+    ADCQ R14, R10;  MOVQ R10, 16+z; \
+    ADCQ  AX, R11;  MOVQ R11, 24+z; \
+    ADCQ  $0,  DX;  MOVQ  DX, 32+z; \
+    MOVQ  8+y, R8; \
+    MOVQ  0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX,  R9; \
+    MOVQ  8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \
+    MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \
+    MOVQ 24+x, AX; MULQ R8; \
+    ADDQ R12, R15; MOVQ R15,  8+z; \
+    ADCQ R13,  R9; \
+    ADCQ R14, R10; \
+    ADCQ  AX, R11; \
+    ADCQ  $0,  DX; \
+    ADCQ 16+z,  R9;  MOVQ  R9,  R15; \
+    ADCQ 24+z, R10;  MOVQ R10, 24+z; \
+    ADCQ 32+z, R11;  MOVQ R11, 32+z; \
+    ADCQ   $0,  DX;  MOVQ  DX, 40+z; \
+    MOVQ 16+y, R8; \
+    MOVQ  0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX,  R9; \
+    MOVQ  8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \
+    MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \
+    MOVQ 24+x, AX; MULQ R8; \
+    ADDQ R12, R15;  MOVQ R15, 16+z; \
+    ADCQ R13,  R9; \
+    ADCQ R14, R10; \
+    ADCQ  AX, R11; \
+    ADCQ  $0,  DX; \
+    ADCQ 24+z,  R9;  MOVQ  R9,  R15; \
+    ADCQ 32+z, R10;  MOVQ R10, 32+z; \
+    ADCQ 40+z, R11;  MOVQ R11, 40+z; \
+    ADCQ   $0,  DX;  MOVQ  DX, 48+z; \
+    MOVQ 24+y, R8; \
+    MOVQ  0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX,  R9; \
+    MOVQ  8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \
+    MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \
+    MOVQ 24+x, AX; MULQ R8; \
+    ADDQ R12, R15; MOVQ R15, 24+z; \
+    ADCQ R13,  R9; \
+    ADCQ R14, R10; \
+    ADCQ  AX, R11; \
+    ADCQ  $0,  DX; \
+    ADCQ 32+z,  R9;  MOVQ  R9, 32+z; \
+    ADCQ 40+z, R10;  MOVQ R10, 40+z; \
+    ADCQ 48+z, R11;  MOVQ R11, 48+z; \
+    ADCQ   $0,  DX;  MOVQ  DX, 56+z;
+
+// integerSqrLeg squares x and stores in z
+// Uses: AX, CX, DX, R8-R15, FLAGS
+// Instr: x86_64
+#define integerSqrLeg(z,x) \
+    MOVQ  0+x, R8; \
+    MOVQ  8+x, AX; MULQ R8; MOVQ AX,  R9; MOVQ DX, R10; /* A[0]*A[1] */ \
+    MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; /* A[0]*A[2] */ \
+    MOVQ 24+x, AX; MULQ R8; MOVQ AX, R15; MOVQ DX, R12; /* A[0]*A[3] */ \
+    MOVQ 24+x, R8; \
+    MOVQ  8+x, AX; MULQ R8; MOVQ AX,  CX; MOVQ DX, R13; /* A[3]*A[1] */ \
+    MOVQ 16+x, AX; MULQ R8; /* A[3]*A[2] */ \
+    \
+    ADDQ R14, R10;\
+    ADCQ R15, R11; MOVL $0, R15;\
+    ADCQ  CX, R12;\
+    ADCQ  AX, R13;\
+    ADCQ  $0,  DX; MOVQ DX, R14;\
+    MOVQ 8+x, AX; MULQ 16+x;\
+    \
+    ADDQ AX, R11;\
+    ADCQ DX, R12;\
+    ADCQ $0, R13;\
+    ADCQ $0, R14;\
+    ADCQ $0, R15;\
+    \
+    SHLQ $1, R14, R15; MOVQ R15, 56+z;\
+    SHLQ $1, R13, R14; MOVQ R14, 48+z;\
+    SHLQ $1, R12, R13; MOVQ R13, 40+z;\
+    SHLQ $1, R11, R12; MOVQ R12, 32+z;\
+    SHLQ $1, R10, R11; MOVQ R11, 24+z;\
+    SHLQ $1,  R9, R10; MOVQ R10, 16+z;\
+    SHLQ $1,  R9;      MOVQ  R9,  8+z;\
+    \
+    MOVQ  0+x,AX; MULQ AX; MOVQ AX, 0+z; MOVQ DX,  R9;\
+    MOVQ  8+x,AX; MULQ AX; MOVQ AX, R10; MOVQ DX, R11;\
+    MOVQ 16+x,AX; MULQ AX; MOVQ AX, R12; MOVQ DX, R13;\
+    MOVQ 24+x,AX; MULQ AX; MOVQ AX, R14; MOVQ DX, R15;\
+    \
+    ADDQ  8+z,  R9; MOVQ  R9,  8+z;\
+    ADCQ 16+z, R10; MOVQ R10, 16+z;\
+    ADCQ 24+z, R11; MOVQ R11, 24+z;\
+    ADCQ 32+z, R12; MOVQ R12, 32+z;\
+    ADCQ 40+z, R13; MOVQ R13, 40+z;\
+    ADCQ 48+z, R14; MOVQ R14, 48+z;\
+    ADCQ 56+z, R15; MOVQ R15, 56+z;
+
+// integerSqrAdx squares x and stores in z
+// Uses: AX, CX, DX, R8-R15, FLAGS
+// Instr: x86_64, bmi2, adx
+#define integerSqrAdx(z,x) \
+    MOVQ   0+x,  DX; /* A[0] */ \
+    MULXQ  8+x,  R8, R14; /* A[1]*A[0] */  XORL  R15, R15; \
+    MULXQ 16+x,  R9, R10; /* A[2]*A[0] */  ADCXQ R14,  R9; \
+    MULXQ 24+x,  AX,  CX; /* A[3]*A[0] */  ADCXQ  AX, R10; \
+    MOVQ  24+x,  DX; /* A[3] */ \
+    MULXQ  8+x, R11, R12; /* A[1]*A[3] */  ADCXQ  CX, R11; \
+    MULXQ 16+x,  AX, R13; /* A[2]*A[3] */  ADCXQ  AX, R12; \
+    MOVQ   8+x,  DX; /* A[1] */            ADCXQ R15, R13; \
+    MULXQ 16+x,  AX,  CX; /* A[2]*A[1] */  MOVL   $0, R14; \
+    ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;  ADCXQ R15, R14; \
+    XORL  R15, R15; \
+    ADOXQ  AX, R10;  ADCXQ  R8,  R8; \
+    ADOXQ  CX, R11;  ADCXQ  R9,  R9; \
+    ADOXQ R15, R12;  ADCXQ R10, R10; \
+    ADOXQ R15, R13;  ADCXQ R11, R11; \
+    ADOXQ R15, R14;  ADCXQ R12, R12; \
+    ;;;;;;;;;;;;;;;  ADCXQ R13, R13; \
+    ;;;;;;;;;;;;;;;  ADCXQ R14, R14; \
+    MOVQ  0+x, DX;  MULXQ DX, AX, CX; /* A[0]^2 */ \
+    ;;;;;;;;;;;;;;;  MOVQ  AX,  0+z; \
+    ADDQ CX,  R8;    MOVQ  R8,  8+z; \
+    MOVQ  8+x, DX;  MULXQ DX, AX, CX; /* A[1]^2 */ \
+    ADCQ AX,  R9;    MOVQ  R9, 16+z; \
+    ADCQ CX, R10;    MOVQ R10, 24+z; \
+    MOVQ 16+x, DX;  MULXQ DX, AX, CX; /* A[2]^2 */ \
+    ADCQ AX, R11;    MOVQ R11, 32+z; \
+    ADCQ CX, R12;    MOVQ R12, 40+z; \
+    MOVQ 24+x, DX;  MULXQ DX, AX, CX; /* A[3]^2 */ \
+    ADCQ AX, R13;    MOVQ R13, 48+z; \
+    ADCQ CX, R14;    MOVQ R14, 56+z;
+
+// reduceFromDouble finds z congruent to x modulo p such that 0<z<2^256
+// Uses: AX, DX, R8-R13, FLAGS
+// Instr: x86_64
+#define reduceFromDoubleLeg(z,x) \
+    /* 2*C = 38 = 2^256 */ \
+    MOVL $38, AX; MULQ 32+x; MOVQ AX,  R8; MOVQ DX,  R9; /* C*C[4] */ \
+    MOVL $38, AX; MULQ 40+x; MOVQ AX, R12; MOVQ DX, R10; /* C*C[5] */ \
+    MOVL $38, AX; MULQ 48+x; MOVQ AX, R13; MOVQ DX, R11; /* C*C[6] */ \
+    MOVL $38, AX; MULQ 56+x; /* C*C[7] */ \
+    ADDQ R12,  R9; \
+    ADCQ R13, R10; \
+    ADCQ  AX, R11; \
+    ADCQ  $0,  DX; \
+    ADDQ  0+x,  R8; \
+    ADCQ  8+x,  R9; \
+    ADCQ 16+x, R10; \
+    ADCQ 24+x, R11; \
+    ADCQ    $0, DX; \
+    MOVL $38, AX; \
+    IMULQ AX, DX; /* C*C[4], CF=0, OF=0 */ \
+    ADDQ DX,  R8; \
+    ADCQ $0,  R9; MOVQ  R9,  8+z; \
+    ADCQ $0, R10; MOVQ R10, 16+z; \
+    ADCQ $0, R11; MOVQ R11, 24+z; \
+    MOVL $0,  DX; \
+    CMOVQCS AX, DX; \
+    ADDQ DX,  R8; MOVQ  R8,  0+z;
+
+// reduceFromDoubleAdx finds z congruent to x modulo p such that 0<z<2^256
+// Uses: AX, DX, R8-R13, FLAGS
+// Instr: x86_64, bmi2, adx
+#define reduceFromDoubleAdx(z,x) \
+    MOVL    $38,  DX; /* 2*C = 38 = 2^256 */ \
+    MULXQ 32+x,  R8, R10; /* C*C[4] */  XORL AX, AX;     ADOXQ  0+x,  R8; \
+    MULXQ 40+x,  R9, R11; /* C*C[5] */  ADCXQ R10,  R9;  ADOXQ  8+x,  R9; \
+    MULXQ 48+x, R10, R13; /* C*C[6] */  ADCXQ R11, R10;  ADOXQ 16+x, R10; \
+    MULXQ 56+x, R11, R12; /* C*C[7] */  ADCXQ R13, R11;  ADOXQ 24+x, R11; \
+    ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;  ADCXQ  AX, R12;  ADOXQ   AX, R12; \
+    IMULQ  DX, R12; /* C*C[4], CF=0, OF=0 */ \
+    ADCXQ R12, R8; \
+    ADCXQ AX,  R9; MOVQ  R9,  8+z; \
+    ADCXQ AX, R10; MOVQ R10, 16+z; \
+    ADCXQ AX, R11; MOVQ R11, 24+z; \
+    MOVL  $0, R12; \
+    CMOVQCS DX, R12; \
+    ADDQ R12,  R8; MOVQ  R8,  0+z;
+
+// addSub calculates two operations: x,y = x+y,x-y
+// Uses: AX, DX, R8-R15, FLAGS
+#define addSub(x,y) \
+    MOVL $38, AX; \
+    XORL  DX, DX; \
+    MOVQ  0+x,  R8;  MOVQ  R8, R12;  ADDQ  0+y,  R8; \
+    MOVQ  8+x,  R9;  MOVQ  R9, R13;  ADCQ  8+y,  R9; \
+    MOVQ 16+x, R10;  MOVQ R10, R14;  ADCQ 16+y, R10; \
+    MOVQ 24+x, R11;  MOVQ R11, R15;  ADCQ 24+y, R11; \
+    CMOVQCS AX, DX; \
+    XORL AX,  AX; \
+    ADDQ DX,  R8; \
+    ADCQ $0,  R9; \
+    ADCQ $0, R10; \
+    ADCQ $0, R11; \
+    MOVL $38, DX; \
+    CMOVQCS DX, AX; \
+    ADDQ  AX, R8; \
+    MOVL $38, AX; \
+    SUBQ  0+y, R12; \
+    SBBQ  8+y, R13; \
+    SBBQ 16+y, R14; \
+    SBBQ 24+y, R15; \
+    MOVL $0, DX; \
+    CMOVQCS AX, DX; \
+    SUBQ DX, R12; \
+    SBBQ $0, R13; \
+    SBBQ $0, R14; \
+    SBBQ $0, R15; \
+    MOVL $0,  DX; \
+    CMOVQCS AX, DX; \
+    SUBQ DX, R12; \
+    MOVQ  R8,  0+x; \
+    MOVQ  R9,  8+x; \
+    MOVQ R10, 16+x; \
+    MOVQ R11, 24+x; \
+    MOVQ R12,  0+y; \
+    MOVQ R13,  8+y; \
+    MOVQ R14, 16+y; \
+    MOVQ R15, 24+y;
diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.s b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.s
new file mode 100644
index 000000000..5c4aeddec
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.s
@@ -0,0 +1,111 @@
+// +build amd64
+
+#include "textflag.h"
+#include "fp_amd64.h"
+
+// func cmovAmd64(x, y *Elt, n uint)
+TEXT ·cmovAmd64(SB),NOSPLIT,$0-24
+    MOVQ x+0(FP), DI
+    MOVQ y+8(FP), SI
+    MOVQ n+16(FP), BX
+    cselect(0(DI),0(SI),BX)
+    RET
+
+// func cswapAmd64(x, y *Elt, n uint)
+TEXT ·cswapAmd64(SB),NOSPLIT,$0-24
+    MOVQ x+0(FP), DI
+    MOVQ y+8(FP), SI
+    MOVQ n+16(FP), BX
+    cswap(0(DI),0(SI),BX)
+    RET
+
+// func subAmd64(z, x, y *Elt)
+TEXT ·subAmd64(SB),NOSPLIT,$0-24
+    MOVQ z+0(FP), DI
+    MOVQ x+8(FP), SI
+    MOVQ y+16(FP), BX
+    subtraction(0(DI),0(SI),0(BX))
+    RET
+
+// func addsubAmd64(x, y *Elt)
+TEXT ·addsubAmd64(SB),NOSPLIT,$0-16
+    MOVQ x+0(FP), DI
+    MOVQ y+8(FP), SI
+    addSub(0(DI),0(SI))
+    RET
+
+#define addLegacy \
+    additionLeg(0(DI),0(SI),0(BX))
+#define addBmi2Adx \
+    additionAdx(0(DI),0(SI),0(BX))
+
+#define mulLegacy \
+    integerMulLeg(0(SP),0(SI),0(BX)) \
+    reduceFromDoubleLeg(0(DI),0(SP))
+#define mulBmi2Adx \
+    integerMulAdx(0(SP),0(SI),0(BX)) \
+    reduceFromDoubleAdx(0(DI),0(SP))
+
+#define sqrLegacy \
+    integerSqrLeg(0(SP),0(SI)) \
+    reduceFromDoubleLeg(0(DI),0(SP))
+#define sqrBmi2Adx \
+    integerSqrAdx(0(SP),0(SI)) \
+    reduceFromDoubleAdx(0(DI),0(SP))
+
+// func addAmd64(z, x, y *Elt)
+TEXT ·addAmd64(SB),NOSPLIT,$0-24
+    MOVQ z+0(FP), DI
+    MOVQ x+8(FP), SI
+    MOVQ y+16(FP), BX
+    CHECK_BMI2ADX(LADD, addLegacy, addBmi2Adx)
+
+// func mulAmd64(z, x, y *Elt)
+TEXT ·mulAmd64(SB),NOSPLIT,$64-24
+    MOVQ z+0(FP), DI
+    MOVQ x+8(FP), SI
+    MOVQ y+16(FP), BX
+    CHECK_BMI2ADX(LMUL, mulLegacy, mulBmi2Adx)
+
+// func sqrAmd64(z, x *Elt)
+TEXT ·sqrAmd64(SB),NOSPLIT,$64-16
+    MOVQ z+0(FP), DI
+    MOVQ x+8(FP), SI
+    CHECK_BMI2ADX(LSQR, sqrLegacy, sqrBmi2Adx)
+
+// func modpAmd64(z *Elt)
+TEXT ·modpAmd64(SB),NOSPLIT,$0-8
+    MOVQ z+0(FP), DI
+
+    MOVQ   (DI),  R8
+    MOVQ  8(DI),  R9
+    MOVQ 16(DI), R10
+    MOVQ 24(DI), R11
+
+    MOVL $19, AX
+    MOVL $38, CX
+
+    BTRQ $63, R11 // PUT BIT 255 IN CARRY FLAG AND CLEAR
+    CMOVLCC AX, CX // C[255] ? 38 : 19
+
+    // ADD EITHER 19 OR 38 TO C
+    ADDQ CX,  R8
+    ADCQ $0,  R9
+    ADCQ $0, R10
+    ADCQ $0, R11
+
+    // TEST FOR BIT 255 AGAIN; ONLY TRIGGERED ON OVERFLOW MODULO 2^255-19
+    MOVL     $0,  CX
+    CMOVLPL  AX,  CX // C[255] ? 0 : 19
+    BTRQ    $63, R11 // CLEAR BIT 255
+
+    // SUBTRACT 19 IF NECESSARY
+    SUBQ CX,  R8
+    MOVQ  R8,   (DI)
+    SBBQ $0,  R9
+    MOVQ  R9,  8(DI)
+    SBBQ $0, R10
+    MOVQ R10, 16(DI)
+    SBBQ $0, R11
+    MOVQ R11, 24(DI)
+    RET
diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_generic.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_generic.go
new file mode 100644
index 000000000..c10b4dac3
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_generic.go
@@ -0,0 +1,248 @@
+package fp25519
+
+import (
+	"math/bits"
+	"unsafe"
+)
+
+type elt64 [4]uint64
+
+func cmovGeneric(x, y *Elt, n uint) {
+	xx, yy := (*elt64)(unsafe.Pointer(x)), (*elt64)(unsafe.Pointer(y))
+	m := -uint64(n & 0x1)
+	xx[0] = (xx[0] &^ m) | (yy[0] & m)
+	xx[1] = (xx[1] &^ m) | (yy[1] & m)
+	xx[2] = (xx[2] &^ m) | (yy[2] & m)
+	xx[3] = (xx[3] &^ m) | (yy[3] & m)
+}
+
+func cswapGeneric(x, y *Elt, n uint) {
+	xx, yy := (*elt64)(unsafe.Pointer(x)), (*elt64)(unsafe.Pointer(y))
+	m := -uint64(n & 0x1)
+	t0 := m & (xx[0] ^ yy[0])
+	t1 := m & (xx[1] ^ yy[1])
+	t2 := m & (xx[2] ^ yy[2])
+	t3 := m & (xx[3] ^ yy[3])
+	xx[0] ^= t0
+	xx[1] ^= t1
+	xx[2] ^= t2
+	xx[3] ^= t3
+	yy[0] ^= t0
+	yy[1] ^= t1
+	yy[2] ^= t2
+	yy[3] ^= t3
+}
+
+func addGeneric(z, x, y *Elt) {
+	zz := (*elt64)(unsafe.Pointer(z))
+	xx := (*elt64)(unsafe.Pointer(x))
+	yy := (*elt64)(unsafe.Pointer(y))
+
+	z0, c0 := bits.Add64(xx[0], yy[0], 0)
+	z1, c1 := bits.Add64(xx[1], yy[1], c0)
+	z2, c2 := bits.Add64(xx[2], yy[2], c1)
+	z3, c3 := bits.Add64(xx[3], yy[3], c2)
+
+	z0, c0 = bits.Add64(z0, (-c3)&38, 0)
+	zz[1], c1 = bits.Add64(z1, 0, c0)
+	zz[2], c2 = bits.Add64(z2, 0, c1)
+	zz[3], c3 = bits.Add64(z3, 0, c2)
+	zz[0], _ = bits.Add64(z0, (-c3)&38, 0)
+}
+
+func subGeneric(z, x, y *Elt) {
+	zz := (*elt64)(unsafe.Pointer(z))
+	xx := (*elt64)(unsafe.Pointer(x))
+	yy := (*elt64)(unsafe.Pointer(y))
+
+	z0, c0 := bits.Sub64(xx[0], yy[0], 0)
+	z1, c1 := bits.Sub64(xx[1], yy[1], c0)
+	z2, c2 := bits.Sub64(xx[2], yy[2], c1)
+	z3, c3 := bits.Sub64(xx[3], yy[3], c2)
+
+	z0, c0 = bits.Sub64(z0, (-c3)&38, 0)
+	zz[1], c1 = bits.Sub64(z1, 0, c0)
+	zz[2], c2 = bits.Sub64(z2, 0, c1)
+	zz[3], c3 = bits.Sub64(z3, 0, c2)
+	zz[0], _ = bits.Sub64(z0, (-c3)&38, 0)
+}
+
+func addsubGeneric(x, y *Elt) {
+	z := &Elt{}
+	addGeneric(z, x, y)
+	subGeneric(y, x, y)
+	*x = *z
+}
+
+func mulGeneric(z, x, y *Elt) {
+	zz := (*elt64)(unsafe.Pointer(z))
+	xx := (*elt64)(unsafe.Pointer(x))
+	yy := (*elt64)(unsafe.Pointer(y))
+
+	x0, x1, x2, x3 := xx[0], xx[1], xx[2], xx[3]
+	yi := yy[0]
+	h0, l0 := bits.Mul64(x0, yi)
+	h1, l1 := bits.Mul64(x1, yi)
+	h2, l2 := bits.Mul64(x2, yi)
+	h3, l3 := bits.Mul64(x3, yi)
+
+	zz[0] = l0
+	a0, c0 := bits.Add64(h0, l1, 0)
+	a1, c1 := bits.Add64(h1, l2, c0)
+	a2, c2 := bits.Add64(h2, l3, c1)
+	a3, _ := bits.Add64(h3, 0, c2)
+
+	yi = yy[1]
+	h0, l0 = bits.Mul64(x0, yi)
+	h1, l1 = bits.Mul64(x1, yi)
+	h2, l2 = bits.Mul64(x2, yi)
+	h3, l3 = bits.Mul64(x3, yi)
+
+	zz[1], c0 = bits.Add64(a0, l0, 0)
+	h0, c1 = bits.Add64(h0, l1, c0)
+	h1, c2 = bits.Add64(h1, l2, c1)
+	h2, c3 := bits.Add64(h2, l3, c2)
+	h3, _ = bits.Add64(h3, 0, c3)
+
+	a0, c0 = bits.Add64(a1, h0, 0)
+	a1, c1 = bits.Add64(a2, h1, c0)
+	a2, c2 = bits.Add64(a3, h2, c1)
+	a3, _ = bits.Add64(0, h3, c2)
+
+	yi = yy[2]
+	h0, l0 = bits.Mul64(x0, yi)
+	h1, l1 = bits.Mul64(x1, yi)
+	h2, l2 = bits.Mul64(x2, yi)
+	h3, l3 = bits.Mul64(x3, yi)
+
+	zz[2], c0 = bits.Add64(a0, l0, 0)
+	h0, c1 = bits.Add64(h0, l1, c0)
+	h1, c2 = bits.Add64(h1, l2, c1)
+	h2, c3 = bits.Add64(h2, l3, c2)
+	h3, _ = bits.Add64(h3, 0, c3)
+
+	a0, c0 = bits.Add64(a1, h0, 0)
+	a1, c1 = bits.Add64(a2, h1, c0)
+	a2, c2 = bits.Add64(a3, h2, c1)
+	a3, _ = bits.Add64(0, h3, c2)
+
+	yi = yy[3]
+	h0, l0 = bits.Mul64(x0, yi)
+	h1, l1 = bits.Mul64(x1, yi)
+	h2, l2 = bits.Mul64(x2, yi)
+	h3, l3 = bits.Mul64(x3, yi)
+
+	zz[3], c0 = bits.Add64(a0, l0, 0)
+	h0, c1 = bits.Add64(h0, l1, c0)
+	h1, c2 = bits.Add64(h1, l2, c1)
+	h2, c3 = bits.Add64(h2, l3, c2)
+	h3, _ = bits.Add64(h3, 0, c3)
+
+	b4, c0 := bits.Add64(a1, h0, 0)
+	b5, c1 := bits.Add64(a2, h1, c0)
+	b6, c2 := bits.Add64(a3, h2, c1)
+	b7, _ := bits.Add64(0, h3, c2)
+
+	red64(zz, &elt64{b4, b5, b6, b7})
+}
+
+func sqrGeneric(z, x *Elt) {
+	zz := (*elt64)(unsafe.Pointer(z))
+	xx := (*elt64)(unsafe.Pointer(x))
+
+	x0, x1, x2, x3 := xx[0], xx[1], xx[2], xx[3]
+	h0, a0 := bits.Mul64(x0, x1)
+	h1, l1 := bits.Mul64(x0, x2)
+	h2, l2 := bits.Mul64(x0, x3)
+	h3, l3 := bits.Mul64(x3, x1)
+	h4, l4 := bits.Mul64(x3, x2)
+	h, l := bits.Mul64(x1, x2)
+
+	a1, c0 := bits.Add64(l1, h0, 0)
+	a2, c1 := bits.Add64(l2, h1, c0)
+	a3, c2 := bits.Add64(l3, h2, c1)
+	a4, c3 := bits.Add64(l4, h3, c2)
+	a5, _ := bits.Add64(h4, 0, c3)
+
+	a2, c0 = bits.Add64(a2, l, 0)
+	a3, c1 = bits.Add64(a3, h, c0)
+	a4, c2 = bits.Add64(a4, 0, c1)
+	a5, c3 = bits.Add64(a5, 0, c2)
+	a6, _ := bits.Add64(0, 0, c3)
+
+	a0, c0 = bits.Add64(a0, a0, 0)
+	a1, c1 = bits.Add64(a1, a1, c0)
+	a2, c2 = bits.Add64(a2, a2, c1)
+	a3, c3 = bits.Add64(a3, a3, c2)
+	a4, c4 := bits.Add64(a4, a4, c3)
+	a5, c5 := bits.Add64(a5, a5, c4)
+	a6, _ = bits.Add64(a6, a6, c5)
+
+	b1, b0 := bits.Mul64(x0, x0)
+	b3, b2 := bits.Mul64(x1, x1)
+	b5, b4 := bits.Mul64(x2, x2)
+	b7, b6 := bits.Mul64(x3, x3)
+
+	b1, c0 = bits.Add64(b1, a0, 0)
+	b2, c1 = bits.Add64(b2, a1, c0)
+	b3, c2 = bits.Add64(b3, a2, c1)
+	b4, c3 = bits.Add64(b4, a3, c2)
+	b5, c4 = bits.Add64(b5, a4, c3)
+	b6, c5 = bits.Add64(b6, a5, c4)
+	b7, _ = bits.Add64(b7, a6, c5)
+	zz[0] = b0
+	zz[1] = b1
+	zz[2] = b2
+	zz[3] = b3
+	red64(zz, &elt64{b4, b5, b6, b7})
+}
+
+func modpGeneric(x *Elt) {
+	xx := (*elt64)(unsafe.Pointer(x))
+	x3 := xx[3]
+	// CX = C[255] ? 38 : 19
+	cx := uint64(19) << (x3 >> 63)
+	// PUT BIT 255 IN CARRY FLAG AND CLEAR
+	x3 &^= 1 << 63
+
+	x0, c0 := bits.Add64(xx[0], cx, 0)
+	x1, c1 := bits.Add64(xx[1], 0, c0)
+	x2, c2 := bits.Add64(xx[2], 0, c1)
+	x3, _ = bits.Add64(x3, 0, c2)
+
+	// TEST FOR BIT 255 AGAIN; ONLY TRIGGERED ON OVERFLOW MODULO 2^255-19
+	// cx = C[255] ? 0 : 19
+	cx = uint64(19) &^ (-(x3 >> 63))
+	// CLEAR BIT 255
+	x3 &^= 1 << 63
+
+	xx[0], c0 = bits.Sub64(x0, cx, 0)
+	xx[1], c1 = bits.Sub64(x1, 0, c0)
+	xx[2], c2 = bits.Sub64(x2, 0, c1)
+	xx[3], _ = bits.Sub64(x3, 0, c2)
+}
+
+func red64(z, h *elt64) {
+	h0, l0 := bits.Mul64(h[0], 38)
+	h1, l1 := bits.Mul64(h[1], 38)
+	h2, l2 := bits.Mul64(h[2], 38)
+	h3, l3 := bits.Mul64(h[3], 38)
+
+	l1, c0 := bits.Add64(h0, l1, 0)
+	l2, c1 := bits.Add64(h1, l2, c0)
+	l3, c2 := bits.Add64(h2, l3, c1)
+	l4, _ := bits.Add64(h3, 0, c2)
+
+	l0, c0 = bits.Add64(l0, z[0], 0)
+	l1, c1 = bits.Add64(l1, z[1], c0)
+	l2, c2 = bits.Add64(l2, z[2], c1)
+	l3, c3 := bits.Add64(l3, z[3], c2)
+	l4, _ = bits.Add64(l4, 0, c3)
+
+	_, l4 = bits.Mul64(l4, 38)
+	l0, c0 = bits.Add64(l0, l4, 0)
+	z[1], c1 = bits.Add64(l1, 0, c0)
+	z[2], c2 = bits.Add64(l2, 0, c1)
+	z[3], c3 = bits.Add64(l3, 0, c2)
+	z[0], _ = bits.Add64(l0, (-c3)&38, 0)
+}
diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go
new file mode 100644
index 000000000..08a07b667
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go
@@ -0,0 +1,12 @@
+// +build !amd64 purego
+
+package fp25519
+
+func cmov(x, y *Elt, n uint)  { cmovGeneric(x, y, n) }
+func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) }
+func add(z, x, y *Elt)        { addGeneric(z, x, y) }
+func sub(z, x, y *Elt)        { subGeneric(z, x, y) }
+func addsub(x, y *Elt)        { addsubGeneric(x, y) }
+func mul(z, x, y *Elt)        { mulGeneric(z, x, y) }
+func sqr(z, x *Elt)           { sqrGeneric(z, x) }
+func modp(z *Elt)             { modpGeneric(z) }
diff --git a/vendor/github.com/cloudflare/circl/math/wnaf.go b/vendor/github.com/cloudflare/circl/math/wnaf.go
new file mode 100644
index 000000000..df7a9c9ba
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/math/wnaf.go
@@ -0,0 +1,84 @@
+// Package math provides some utility functions for big integers.
+package math
+
+import "math/big"
+
+// SignedDigit obtains the signed-digit recoding of n and returns a list L of
+// digits such that n = sum( L[i]*2^(i*(w-1)) ), and each L[i] is an odd number
+// in the set {±1, ±3, ..., ±2^(w-1)-1}. The third parameter ensures that the
+// output has ceil(l/(w-1)) digits.
+//
+// Restrictions:
+//  - n is odd and n > 0.
+//  - 1 < w < 32.
+//  - l >= bit length of n.
+//
+// References:
+//  - Alg.6 in "Exponent Recoding and Regular Exponentiation Algorithms"
+//    by Joye-Tunstall. http://doi.org/10.1007/978-3-642-02384-2_21
+//  - Alg.6 in "Selecting Elliptic Curves for Cryptography: An Efficiency and
+//    Security Analysis" by Bos et al. http://doi.org/10.1007/s13389-015-0097-y
+func SignedDigit(n *big.Int, w, l uint) []int32 {
+	if n.Sign() <= 0 || n.Bit(0) == 0 {
+		panic("n must be non-zero, odd, and positive")
+	}
+	if w <= 1 || w >= 32 {
+		panic("Verify that 1 < w < 32")
+	}
+	if uint(n.BitLen()) > l {
+		panic("n is too big to fit in l digits")
+	}
+	lenN := (l + (w - 1) - 1) / (w - 1) // ceil(l/(w-1))
+	L := make([]int32, lenN+1)
+	var k, v big.Int
+	k.Set(n)
+
+	var i uint
+	for i = 0; i < lenN; i++ {
+		words := k.Bits()
+		value := int32(words[0] & ((1 << w) - 1))
+		value -= int32(1) << (w - 1)
+		L[i] = value
+		v.SetInt64(int64(value))
+		k.Sub(&k, &v)
+		k.Rsh(&k, w-1)
+	}
+	L[i] = int32(k.Int64())
+	return L
+}
+
+// OmegaNAF obtains the window-w Non-Adjacent Form of a positive number n and
+// 1 < w < 32. The returned slice L holds n = sum( L[i]*2^i ).
+//
+// Reference:
+//  - Alg.9 "Efficient arithmetic on Koblitz curves" by Solinas.
+//    http://doi.org/10.1023/A:1008306223194
+func OmegaNAF(n *big.Int, w uint) (L []int32) {
+	if n.Sign() < 0 {
+		panic("n must be positive")
+	}
+	if w <= 1 || w >= 32 {
+		panic("Verify that 1 < w < 32")
+	}
+
+	L = make([]int32, n.BitLen()+1)
+	var k, v big.Int
+	k.Set(n)
+
+	i := 0
+	for ; k.Sign() > 0; i++ {
+		value := int32(0)
+		if k.Bit(0) == 1 {
+			words := k.Bits()
+			value = int32(words[0] & ((1 << w) - 1))
+			if value >= (int32(1) << (w - 1)) {
+				value -= int32(1) << w
+			}
+			v.SetInt64(int64(value))
+			k.Sub(&k, &v)
+		}
+		L[i] = value
+		k.Rsh(&k, 1)
+	}
+	return L[:i]
+}
diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/ed25519.go b/vendor/github.com/cloudflare/circl/sign/ed25519/ed25519.go
new file mode 100644
index 000000000..b94b09bf1
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/sign/ed25519/ed25519.go
@@ -0,0 +1,178 @@
+// Package ed25519 implements Ed25519 signature scheme as described in RFC-8032.
+//
+// References:
+//  - RFC8032 https://rfc-editor.org/rfc/rfc8032.txt
+//  - Ed25519 https://ed25519.cr.yp.to/
+//  - High-speed high-security signatures. https://doi.org/10.1007/s13389-012-0027-1
+package ed25519
+
+import (
+	"bytes"
+	"crypto"
+	cryptoRand "crypto/rand"
+	"crypto/sha512"
+	"errors"
+	"io"
+)
+
+const (
+	// PublicKeySize is the length in bytes of Ed25519 public keys.
+	PublicKeySize = 32
+	// PrivateKeySize is the length in bytes of Ed25519 private keys.
+	PrivateKeySize = 32
+	// SignatureSize is the length in bytes of signatures.
+	SignatureSize = 64
+)
+const (
+	paramB = 256 / 8 // Size of keys in bytes.
+)
+
+// PublicKey represents a public key of Ed25519.
+type PublicKey []byte
+
+// PrivateKey represents a private key of Ed25519.
+type PrivateKey []byte
+
+// KeyPair implements crypto.Signer (golang.org/pkg/crypto/#Signer) interface.
+type KeyPair struct {
+	private [PrivateKeySize]byte
+	public  [PublicKeySize]byte
+}
+
+// GetPrivate returns a copy of the private key.
+func (kp *KeyPair) GetPrivate() PrivateKey { z := kp.private; return z[:] }
+
+// GetPublic returns a copy of the public key.
+func (kp *KeyPair) GetPublic() PublicKey { z := kp.public; return z[:] }
+
+// Seed returns the private key seed.
+func (kp *KeyPair) Seed() []byte { return kp.GetPrivate() }
+
+// Public returns a crypto.PublicKey.
+func (kp *KeyPair) Public() crypto.PublicKey { return kp.GetPublic() }
+
+// Sign creates a signature of a message given a key pair.
+// Ed25519 performs two passes over messages to be signed and therefore cannot
+// handle pre-hashed messages.
+// The opts.HashFunc() must return zero to indicate the message hasn't been
+// hashed. This can be achieved by passing crypto.Hash(0) as the value for opts.
+func (kp *KeyPair) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) ([]byte, error) {
+	if opts.HashFunc() != crypto.Hash(0) {
+		return nil, errors.New("ed25519: cannot sign hashed message")
+	}
+	return kp.SignPure(message)
+}
+
+// GenerateKey produces public and private keys using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (*KeyPair, error) {
+	if rand == nil {
+		rand = cryptoRand.Reader
+	}
+	seed := make(PrivateKey, PrivateKeySize)
+	if _, err := io.ReadFull(rand, seed); err != nil {
+		return nil, err
+	}
+	return NewKeyFromSeed(seed), nil
+}
+
+// NewKeyFromSeed generates a pair of Ed25519 keys given a private key.
+func NewKeyFromSeed(seed PrivateKey) *KeyPair {
+	if len(seed) != PrivateKeySize {
+		panic("ed25519: bad private key length")
+	}
+	var P pointR1
+	k := sha512.Sum512(seed)
+	clamp(k[:])
+	reduceModOrder(k[:paramB], false)
+	P.fixedMult(k[:paramB])
+
+	pair := &KeyPair{}
+	copy(pair.private[:], seed)
+	_ = P.ToBytes(pair.public[:])
+	return pair
+}
+
+// SignPure creates a signature of a message.
+func (kp *KeyPair) SignPure(message []byte) ([]byte, error) {
+	// 1.  Hash the 32-byte private key using SHA-512.
+	H := sha512.New()
+	_, _ = H.Write(kp.private[:])
+	h := H.Sum(nil)
+	clamp(h[:])
+	prefix, s := h[paramB:], h[:paramB]
+
+	// 2.  Compute SHA-512(dom2(F, C) || prefix || PH(M))
+	H.Reset()
+	_, _ = H.Write(prefix)
+	_, _ = H.Write(message)
+	r := H.Sum(nil)
+	reduceModOrder(r[:], true)
+
+	// 3.  Compute the point [r]B.
+	var P pointR1
+	P.fixedMult(r[:paramB])
+	R := (&[paramB]byte{})[:]
+	err := P.ToBytes(R)
+
+	// 4.  Compute SHA512(dom2(F, C) || R || A || PH(M)).
+	H.Reset()
+	_, _ = H.Write(R)
+	_, _ = H.Write(kp.public[:])
+	_, _ = H.Write(message)
+	hRAM := H.Sum(nil)
+
+	reduceModOrder(hRAM[:], true)
+	// 5.  Compute S = (r + k * s) mod order.
+	S := (&[paramB]byte{})[:]
+	calculateS(S, r[:paramB], hRAM[:paramB], s)
+
+	// 6.  The signature is the concatenation of R and S.
+	var signature [SignatureSize]byte
+	copy(signature[:paramB], R[:])
+	copy(signature[paramB:], S[:])
+	return signature[:], err
+}
+
+// Verify returns true if the signature is valid. Failure cases are invalid
+// signature, or when the public key cannot be decoded.
+func Verify(public PublicKey, message, signature []byte) bool {
+	if len(public) != PublicKeySize ||
+		len(signature) != SignatureSize ||
+		!isLessThanOrder(signature[paramB:]) {
+		return false
+	}
+	var P pointR1
+	if ok := P.FromBytes(public); !ok {
+		return false
+	}
+
+	R := signature[:paramB]
+	H := sha512.New()
+	_, _ = H.Write(R)
+	_, _ = H.Write(public)
+	_, _ = H.Write(message)
+	hRAM := H.Sum(nil)
+	reduceModOrder(hRAM[:], true)
+
+	var Q pointR1
+	encR := (&[paramB]byte{})[:]
+	P.neg()
+	Q.doubleMult(&P, signature[paramB:], hRAM[:paramB])
+	_ = Q.ToBytes(encR)
+	return bytes.Equal(R, encR)
+}
+
+func clamp(k []byte) {
+	k[0] &= 248
+	k[paramB-1] = (k[paramB-1] & 127) | 64
+}
+
+// isLessThanOrder returns true if 0 <= x < order.
+func isLessThanOrder(x []byte) bool {
+	i := len(order) - 1
+	for i > 0 && x[i] == order[i] {
+		i--
+	}
+	return x[i] < order[i]
+}
diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/modular.go b/vendor/github.com/cloudflare/circl/sign/ed25519/modular.go
new file mode 100644
index 000000000..10efafdca
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/sign/ed25519/modular.go
@@ -0,0 +1,175 @@
+package ed25519
+
+import (
+	"encoding/binary"
+	"math/bits"
+)
+
+var order = [paramB]byte{
+	0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
+	0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
+	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10,
+}
+
+// isLessThan returns true if 0 <= x < y, and assumes that slices have the same length.
+func isLessThan(x, y []byte) bool {
+	i := len(x) - 1
+	for i > 0 && x[i] == y[i] {
+		i--
+	}
+	return x[i] < y[i]
+}
+
+// reduceModOrder calculates k = k mod order of the curve.
+func reduceModOrder(k []byte, is512Bit bool) {
+	var X [((2 * paramB) * 8) / 64]uint64
+	numWords := len(k) >> 3
+	for i := 0; i < numWords; i++ {
+		X[i] = binary.LittleEndian.Uint64(k[i*8 : (i+1)*8])
+	}
+	red512(&X, is512Bit)
+	for i := 0; i < numWords; i++ {
+		binary.LittleEndian.PutUint64(k[i*8:(i+1)*8], X[i])
+	}
+}
+
+// red512 calculates x = x mod Order of the curve.
+func red512(x *[8]uint64, full bool) {
+	// Implementation of Algs.(14.47)+(14.52) of Handbook of Applied
+	// Cryptography, by A. Menezes, P. van Oorschot, and S. Vanstone.
+	const (
+		ell0   = uint64(0x5812631a5cf5d3ed)
+		ell1   = uint64(0x14def9dea2f79cd6)
+		ell160 = uint64(0x812631a5cf5d3ed0)
+		ell161 = uint64(0x4def9dea2f79cd65)
+		ell162 = uint64(0x0000000000000001)
+	)
+
+	var c0, c1, c2, c3 uint64
+	r0, r1, r2, r3, r4 := x[0], x[1], x[2], x[3], uint64(0)
+
+	if full {
+		q0, q1, q2, q3 := x[4], x[5], x[6], x[7]
+
+		for i := 0; i < 3; i++ {
+			h0, s0 := bits.Mul64(q0, ell160)
+			h1, s1 := bits.Mul64(q1, ell160)
+			h2, s2 := bits.Mul64(q2, ell160)
+			h3, s3 := bits.Mul64(q3, ell160)
+
+			s1, c0 = bits.Add64(h0, s1, 0)
+			s2, c1 = bits.Add64(h1, s2, c0)
+			s3, c2 = bits.Add64(h2, s3, c1)
+			s4, _ := bits.Add64(h3, 0, c2)
+
+			h0, l0 := bits.Mul64(q0, ell161)
+			h1, l1 := bits.Mul64(q1, ell161)
+			h2, l2 := bits.Mul64(q2, ell161)
+			h3, l3 := bits.Mul64(q3, ell161)
+
+			l1, c0 = bits.Add64(h0, l1, 0)
+			l2, c1 = bits.Add64(h1, l2, c0)
+			l3, c2 = bits.Add64(h2, l3, c1)
+			l4, _ := bits.Add64(h3, 0, c2)
+
+			s1, c0 = bits.Add64(s1, l0, 0)
+			s2, c1 = bits.Add64(s2, l1, c0)
+			s3, c2 = bits.Add64(s3, l2, c1)
+			s4, c3 = bits.Add64(s4, l3, c2)
+			s5, s6 := bits.Add64(l4, 0, c3)
+
+			s2, c0 = bits.Add64(s2, q0, 0)
+			s3, c1 = bits.Add64(s3, q1, c0)
+			s4, c2 = bits.Add64(s4, q2, c1)
+			s5, c3 = bits.Add64(s5, q3, c2)
+			s6, s7 := bits.Add64(s6, 0, c3)
+
+			q := q0 | q1 | q2 | q3
+			m := -((q | -q) >> 63) // if q=0 then m=0...0 else m=1..1
+			s0 &= m
+			s1 &= m
+			s2 &= m
+			s3 &= m
+			q0, q1, q2, q3 = s4, s5, s6, s7
+
+			if (i+1)%2 == 0 {
+				r0, c0 = bits.Add64(r0, s0, 0)
+				r1, c1 = bits.Add64(r1, s1, c0)
+				r2, c2 = bits.Add64(r2, s2, c1)
+				r3, c3 = bits.Add64(r3, s3, c2)
+				r4, _ = bits.Add64(r4, 0, c3)
+			} else {
+				r0, c0 = bits.Sub64(r0, s0, 0)
+				r1, c1 = bits.Sub64(r1, s1, c0)
+				r2, c2 = bits.Sub64(r2, s2, c1)
+				r3, c3 = bits.Sub64(r3, s3, c2)
+				r4, _ = bits.Sub64(r4, 0, c3)
+			}
+		}
+
+		m := -(r4 >> 63)
+		r0, c0 = bits.Add64(r0, m&ell160, 0)
+		r1, c1 = bits.Add64(r1, m&ell161, c0)
+		r2, c2 = bits.Add64(r2, m&ell162, c1)
+		r3, c3 = bits.Add64(r3, 0, c2)
+		r4, _ = bits.Add64(r4, m&1, c3)
+		x[4], x[5], x[6], x[7] = 0, 0, 0, 0
+	}
+
+	q0 := (r4 << 4) | (r3 >> 60)
+	r3 &= (uint64(1) << 60) - 1
+
+	h0, s0 := bits.Mul64(ell0, q0)
+	h1, s1 := bits.Mul64(ell1, q0)
+	s1, c0 = bits.Add64(h0, s1, 0)
+	s2, _ := bits.Add64(h1, 0, c0)
+
+	r0, c0 = bits.Sub64(r0, s0, 0)
+	r1, c1 = bits.Sub64(r1, s1, c0)
+	r2, c2 = bits.Sub64(r2, s2, c1)
+	r3, _ = bits.Sub64(r3, 0, c2)
+
+	x[0], x[1], x[2], x[3] = r0, r1, r2, r3
+}
+
+// calculateS performs s = r+k*a mod Order of the curve.
+func calculateS(s, r, k, a []byte) {
+	K := [4]uint64{
+		binary.LittleEndian.Uint64(k[0*8 : 1*8]),
+		binary.LittleEndian.Uint64(k[1*8 : 2*8]),
+		binary.LittleEndian.Uint64(k[2*8 : 3*8]),
+		binary.LittleEndian.Uint64(k[3*8 : 4*8]),
+	}
+	S := [8]uint64{
+		binary.LittleEndian.Uint64(r[0*8 : 1*8]),
+		binary.LittleEndian.Uint64(r[1*8 : 2*8]),
+		binary.LittleEndian.Uint64(r[2*8 : 3*8]),
+		binary.LittleEndian.Uint64(r[3*8 : 4*8]),
+	}
+	var c3 uint64
+	for i := range K {
+		ai := binary.LittleEndian.Uint64(a[i*8 : (i+1)*8])
+
+		h0, l0 := bits.Mul64(K[0], ai)
+		h1, l1 := bits.Mul64(K[1], ai)
+		h2, l2 := bits.Mul64(K[2], ai)
+		h3, l3 := bits.Mul64(K[3], ai)
+
+		l1, c0 := bits.Add64(h0, l1, 0)
+		l2, c1 := bits.Add64(h1, l2, c0)
+		l3, c2 := bits.Add64(h2, l3, c1)
+		l4, _ := bits.Add64(h3, 0, c2)
+
+		S[i+0], c0 = bits.Add64(S[i+0], l0, 0)
+		S[i+1], c1 = bits.Add64(S[i+1], l1, c0)
+		S[i+2], c2 = bits.Add64(S[i+2], l2, c1)
+		S[i+3], c3 = bits.Add64(S[i+3], l3, c2)
+		S[i+4], _ = bits.Add64(S[i+4], l4, c3)
+	}
+	red512(&S, true)
+	binary.LittleEndian.PutUint64(s[0*8:1*8], S[0])
+	binary.LittleEndian.PutUint64(s[1*8:2*8], S[1])
+	binary.LittleEndian.PutUint64(s[2*8:3*8], S[2])
+	binary.LittleEndian.PutUint64(s[3*8:4*8], S[3])
+}
diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/mult.go b/vendor/github.com/cloudflare/circl/sign/ed25519/mult.go
new file mode 100644
index 000000000..ddcd71a39
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/sign/ed25519/mult.go
@@ -0,0 +1,179 @@
+package ed25519
+
+import (
+	"crypto/subtle"
+	"encoding/binary"
+	"math/bits"
+
+	"github.com/cloudflare/circl/internal/conv"
+	"github.com/cloudflare/circl/math"
+	fp "github.com/cloudflare/circl/math/fp25519"
+)
+
+var paramD = fp.Elt{
+	0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75,
+	0xab, 0xd8, 0x41, 0x41, 0x4d, 0x0a, 0x70, 0x00,
+	0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, 0xc7, 0x8c,
+	0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52,
+}
+
+// mLSBRecoding parameters.
+const (
+	fxT        = 257
+	fxV        = 2
+	fxW        = 3
+	fx2w1      = 1 << (uint(fxW) - 1)
+	numWords64 = (paramB * 8 / 64)
+)
+
+// mLSBRecoding is the odd-only modified LSB-set.
+//
+// Reference:
+//  "Efficient and secure algorithms for GLV-based scalar multiplication and
+//   their implementation on GLV–GLS curves" by (Faz-Hernandez et al.)
+//   http://doi.org/10.1007/s13389-014-0085-7.
+func mLSBRecoding(L []int8, k []byte) {
+	const ee = (fxT + fxW*fxV - 1) / (fxW * fxV)
+	const dd = ee * fxV
+	const ll = dd * fxW
+	if len(L) == (ll + 1) {
+		var m [numWords64 + 1]uint64
+		for i := 0; i < numWords64; i++ {
+			m[i] = binary.LittleEndian.Uint64(k[8*i : 8*i+8])
+		}
+		condAddOrderN(&m)
+		L[dd-1] = 1
+		for i := 0; i < dd-1; i++ {
+			kip1 := (m[(i+1)/64] >> (uint(i+1) % 64)) & 0x1
+			L[i] = int8(kip1<<1) - 1
+		}
+		{ // right-shift by d
+			right := uint(dd % 64)
+			left := uint(64) - right
+			lim := ((numWords64+1)*64 - dd) / 64
+			j := dd / 64
+			for i := 0; i < lim; i++ {
+				m[i] = (m[i+j] >> right) | (m[i+j+1] << left)
+			}
+			m[lim] = m[lim+j] >> right
+		}
+		for i := dd; i < ll; i++ {
+			L[i] = L[i%dd] * int8(m[0]&0x1)
+			div2subY(m[:], int64(L[i]>>1), numWords64)
+		}
+		L[ll] = int8(m[0])
+	}
+}
+
+// absolute returns always a positive value.
+func absolute(x int32) int32 {
+	mask := x >> 31
+	return (x + mask) ^ mask
+}
+
+// condAddOrderN updates x = x+order if x is even, otherwise x remains unchanged.
+func condAddOrderN(x *[numWords64 + 1]uint64) {
+	isOdd := (x[0] & 0x1) - 1
+	c := uint64(0)
+	for i := 0; i < numWords64; i++ {
+		orderWord := binary.LittleEndian.Uint64(order[8*i : 8*i+8])
+		o := isOdd & orderWord
+		x0, c0 := bits.Add64(x[i], o, c)
+		x[i] = x0
+		c = c0
+	}
+	x[numWords64], _ = bits.Add64(x[numWords64], 0, c)
+}
+
+// div2subY update x = (x/2) - y.
+func div2subY(x []uint64, y int64, l int) {
+	s := uint64(y >> 63)
+	for i := 0; i < l-1; i++ {
+		x[i] = (x[i] >> 1) | (x[i+1] << 63)
+	}
+	x[l-1] = (x[l-1] >> 1)
+
+	b := uint64(0)
+	x0, b0 := bits.Sub64(x[0], uint64(y), b)
+	x[0] = x0
+	b = b0
+	for i := 1; i < l-1; i++ {
+		x0, b0 := bits.Sub64(x[i], s, b)
+		x[i] = x0
+		b = b0
+	}
+	x[l-1], _ = bits.Sub64(x[l-1], s, b)
+}
+
+func (P *pointR1) fixedMult(scalar []byte) {
+	if len(scalar) != paramB {
+		panic("wrong scalar size")
+	}
+	const ee = (fxT + fxW*fxV - 1) / (fxW * fxV)
+	const dd = ee * fxV
+	const ll = dd * fxW
+
+	L := make([]int8, ll+1)
+	mLSBRecoding(L[:], scalar)
+	S := &pointR3{}
+	P.SetIdentity()
+	for ii := ee - 1; ii >= 0; ii-- {
+		P.double()
+		for j := 0; j < fxV; j++ {
+			dig := L[fxW*dd-j*ee+ii-ee]
+			for i := (fxW-1)*dd - j*ee + ii - ee; i >= (2*dd - j*ee + ii - ee); i = i - dd {
+				dig = 2*dig + L[i]
+			}
+			idx := absolute(int32(dig))
+			sig := L[dd-j*ee+ii-ee]
+			Tabj := &tabSign[fxV-j-1]
+			for k := 0; k < fx2w1; k++ {
+				S.cmov(&Tabj[k], subtle.ConstantTimeEq(int32(k), idx))
+			}
+			S.cneg(subtle.ConstantTimeEq(int32(sig), -1))
+			P.mixAdd(S)
+		}
+	}
+}
+
+const (
+	omegaFix = 7
+	omegaVar = 5
+)
+
+// doubleMult returns P=mG+nQ.
+func (P *pointR1) doubleMult(Q *pointR1, m, n []byte) {
+	nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m), omegaFix)
+	nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n), omegaVar)
+
+	if len(nafFix) > len(nafVar) {
+		nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...)
+	} else if len(nafFix) < len(nafVar) {
+		nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...)
+	}
+
+	var TabQ [1 << (omegaVar - 2)]pointR2
+	Q.oddMultiples(TabQ[:])
+	P.SetIdentity()
+	for i := len(nafFix) - 1; i >= 0; i-- {
+		P.double()
+		// Generator point
+		if nafFix[i] != 0 {
+			idxM := absolute(nafFix[i]) >> 1
+			R := tabVerif[idxM]
+			if nafFix[i] < 0 {
+				R.neg()
+			}
+			P.mixAdd(&R)
+		}
+		// Variable input point
+		if nafVar[i] != 0 {
+			idxN := absolute(nafVar[i]) >> 1
+			S := TabQ[idxN]
+			if nafVar[i] < 0 {
+				S.neg()
+			}
+			P.add(&S)
+		}
+	}
+}
diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/point.go b/vendor/github.com/cloudflare/circl/sign/ed25519/point.go
new file mode 100644
index 000000000..73505a6fd
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/sign/ed25519/point.go
@@ -0,0 +1,193 @@
+package ed25519
+
+import fp "github.com/cloudflare/circl/math/fp25519"
+
+type pointR1 struct{ x, y, z, ta, tb fp.Elt }
+type pointR2 struct {
+	pointR3
+	z2 fp.Elt
+}
+type pointR3 struct{ addYX, subYX, dt2 fp.Elt }
+
+func (P *pointR1) neg() {
+	fp.Neg(&P.x, &P.x)
+	fp.Neg(&P.ta, &P.ta)
+}
+
+func (P *pointR1) SetIdentity() {
+	P.x = fp.Elt{}
+	fp.SetOne(&P.y)
+	fp.SetOne(&P.z)
+	P.ta = fp.Elt{}
+	P.tb = fp.Elt{}
+}
+
+func (P *pointR1) toAffine() {
+	fp.Inv(&P.z, &P.z)
+	fp.Mul(&P.x, &P.x, &P.z)
+	fp.Mul(&P.y, &P.y, &P.z)
+	fp.Modp(&P.x)
+	fp.Modp(&P.y)
+	fp.SetOne(&P.z)
+	P.ta = P.x
+	P.tb = P.y
+}
+
+func (P *pointR1) ToBytes(k []byte) error {
+	P.toAffine()
+	var x [fp.Size]byte
+	err := fp.ToBytes(k[:fp.Size], &P.y)
+	if err != nil {
+		return err
+	}
+	err = fp.ToBytes(x[:], &P.x)
+	if err != nil {
+		return err
+	}
+	b := x[0] & 1
+	k[paramB-1] = k[paramB-1] | (b << 7)
+	return nil
+}
+
+func (P *pointR1) FromBytes(k []byte) bool {
+	if len(k) != paramB {
+		panic("wrong size")
+	}
+	signX := k[paramB-1] >> 7
+	copy(P.y[:], k[:fp.Size])
+	P.y[fp.Size-1] &= 0x7F
+	p := fp.P()
+	if !isLessThan(P.y[:], p[:]) {
+		return false
+	}
+
+	one, u, v := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}
+	fp.SetOne(one)
+	fp.Sqr(u, &P.y)                // u = y^2
+	fp.Mul(v, u, &paramD)          // v = dy^2
+	fp.Sub(u, u, one)              // u = y^2-1
+	fp.Add(v, v, one)              // v = dy^2+1
+	isQR := fp.InvSqrt(&P.x, u, v) // x = sqrt(u/v)
+	if !isQR {
+		return false
+	}
+	fp.Modp(&P.x) // x = x mod p
+	if fp.IsZero(&P.x) && signX == 1 {
+		return false
+	}
+	if signX != (P.x[0] & 1) {
+		fp.Neg(&P.x, &P.x)
+	}
+	P.ta = P.x
+	P.tb = P.y
+	fp.SetOne(&P.z)
+	return true
+}
+
+// double calculates 2P for curves with A=-1.
+func (P *pointR1) double() {
+	Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb
+	a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb
+	fp.Add(e, Px, Py) // x+y
+	fp.Sqr(a, Px)     // A = x^2
+	fp.Sqr(b, Py)     // B = y^2
+	fp.Sqr(c, Pz)     // z^2
+	fp.Add(c, c, c)   // C = 2*z^2
+	fp.Add(h, a, b)   // H = A+B
+	fp.Sqr(e, e)      // (x+y)^2
+	fp.Sub(e, e, h)   // E = (x+y)^2-A-B
+	fp.Sub(g, b, a)   // G = B-A
+	fp.Sub(f, c, g)   // F = C-G
+	fp.Mul(Pz, f, g)  // Z = F * G
+	fp.Mul(Px, e, f)  // X = E * F
+	fp.Mul(Py, g, h)  // Y = G * H, T = E * H
+}
+
+func (P *pointR1) mixAdd(Q *pointR3) {
+	fp.Add(&P.z, &P.z, &P.z) // D = 2*z1
+	P.coreAddition(Q)
+}
+
+func (P *pointR1) add(Q *pointR2) {
+	fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2
+	P.coreAddition(&Q.pointR3)
+}
+
+// coreAddition calculates P=P+Q for curves with A=-1.
+func (P *pointR1) coreAddition(Q *pointR3) {
+	Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb
+	addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2
+	a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb
+	fp.Mul(c, Pta, Ptb)  // t1 = ta*tb
+	fp.Sub(h, Py, Px)    // y1-x1
+	fp.Add(b, Py, Px)    // y1+x1
+	fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2)
+	fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2)
+	fp.Mul(c, c, dt2)    // C = 2*D*t1*t2
+	fp.Sub(e, b, a)      // E = B-A
+	fp.Add(h, b, a)      // H = B+A
+	fp.Sub(f, d, c)      // F = D-C
+	fp.Add(g, d, c)      // G = D+C
+	fp.Mul(Pz, f, g)     // Z = F * G
+	fp.Mul(Px, e, f)     // X = E * F
+	fp.Mul(Py, g, h)     // Y = G * H, T = E * H
+}
+
+func (P *pointR1) oddMultiples(T []pointR2) {
+	var R pointR2
+	n := len(T)
+	T[0].fromR1(P)
+	_2P := *P
+	_2P.double()
+	R.fromR1(&_2P)
+	for i := 1; i < n; i++ {
+		P.add(&R)
+		T[i].fromR1(P)
+	}
+}
+
+func (P *pointR1) isEqual(Q *pointR1) bool {
+	l, r := &fp.Elt{}, &fp.Elt{}
+	fp.Mul(l, &P.x, &Q.z)
+	fp.Mul(r, &Q.x, &P.z)
+	fp.Sub(l, l, r)
+	b := fp.IsZero(l)
+	fp.Mul(l, &P.y, &Q.z)
+	fp.Mul(r, &Q.y, &P.z)
+	fp.Sub(l, l, r)
+	b = b && fp.IsZero(l)
+	fp.Mul(l, &P.ta, &P.tb)
+	fp.Mul(l, l, &Q.z)
+	fp.Mul(r, &Q.ta, &Q.tb)
+	fp.Mul(r, r, &P.z)
+	fp.Sub(l, l, r)
+	b = b && fp.IsZero(l)
+	return b
+}
+
+func (P *pointR3) neg() {
+	P.addYX, P.subYX = P.subYX, P.addYX
+	fp.Neg(&P.dt2, &P.dt2)
+}
+
+func (P *pointR2) fromR1(Q *pointR1) {
+	fp.Add(&P.addYX, &Q.y, &Q.x)
+	fp.Sub(&P.subYX, &Q.y, &Q.x)
+	fp.Mul(&P.dt2, &Q.ta, &Q.tb)
+	fp.Mul(&P.dt2, &P.dt2, &paramD)
+	fp.Add(&P.dt2, &P.dt2, &P.dt2)
+	fp.Add(&P.z2, &Q.z, &Q.z)
+}
+
+func (P *pointR3) cneg(b int) {
+	t := &fp.Elt{}
+	fp.Cswap(&P.addYX, &P.subYX, uint(b))
+	fp.Neg(t, &P.dt2)
+	fp.Cmov(&P.dt2, t, uint(b))
+}
+
+func (P *pointR3) cmov(Q *pointR3, b int) {
+	fp.Cmov(&P.addYX, &Q.addYX, uint(b))
+	fp.Cmov(&P.subYX, &Q.subYX, uint(b))
+	fp.Cmov(&P.dt2, &Q.dt2, uint(b))
+}
diff --git a/vendor/github.com/cloudflare/circl/sign/ed25519/tables.go b/vendor/github.com/cloudflare/circl/sign/ed25519/tables.go
new file mode 100644
index 000000000..8763b426f
--- /dev/null
+++ b/vendor/github.com/cloudflare/circl/sign/ed25519/tables.go
@@ -0,0 +1,213 @@
+package ed25519
+
+import fp "github.com/cloudflare/circl/math/fp25519"
+
+var tabSign = [fxV][fx2w1]pointR3{
+	{
+		pointR3{
+			addYX: fp.Elt{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0x0e, 0x8c, 0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48, 0x0b, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x07},
+			subYX: fp.Elt{0x3e, 0x91, 0x40, 0xd7, 0x05, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40, 0xd1, 0x05, 0x9f, 0x39, 0xfd, 0x09, 0x8a, 0x8f, 0x68, 0x34, 0x84, 0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44},
+			dt2:   fp.Elt{0x68, 0xaa, 0x7a, 0x87, 0x05, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa, 0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d, 0x1b, 0x5a, 0xa8, 0x65, 0x0c, 0x9f, 0x68, 0x7b, 0x11, 0x6f},
+		},
+		{
+			addYX: fp.Elt{0x7c, 0xb0, 0x9e, 0xe6, 0xc5, 0xbf, 0xfa, 0x13, 0x8e, 0x0d, 0x22, 0xde, 0xc8, 0xd1, 0xce, 0x52, 0x02, 0xd5, 0x62, 0x31, 0x71, 0x0e, 0x8e, 0x9d, 0xb0, 0xd6, 0x00, 0xa5, 0x5a, 0x0e, 0xce, 0x72},
+			subYX: fp.Elt{0x1a, 0x8e, 0x5c, 0xdc, 0xa4, 0xb3, 0x6c, 0x51, 0x18, 0xa0, 0x09, 0x80, 0x9a, 0x46, 0x33, 0xd5, 0xe0, 0x3c, 0x4d, 0x3b, 0xfc, 0x49, 0xa2, 0x43, 0x29, 0xe1, 0x29, 0xa9, 0x93, 0xea, 0x7c, 0x35},
+			dt2:   fp.Elt{0x08, 0x46, 0x6f, 0x68, 0x7f, 0x0b, 0x7c, 0x9e, 0xad, 0xba, 0x07, 0x61, 0x74, 0x83, 0x2f, 0xfc, 0x26, 0xd6, 0x09, 0xb9, 0x00, 0x34, 0x36, 0x4f, 0x01, 0xf3, 0x48, 0xdb, 0x43, 0xba, 0x04, 0x44},
+		},
+		{
+			addYX: fp.Elt{0x4c, 0xda, 0x0d, 0x13, 0x66, 0xfd, 0x82, 0x84, 0x9f, 0x75, 0x5b, 0xa2, 0x17, 0xfe, 0x34, 0xbf, 0x1f, 0xcb, 0xba, 0x90, 0x55, 0x80, 0x83, 0xfd, 0x63, 0xb9, 0x18, 0xf8, 0x5b, 0x5d, 0x94, 0x1e},
+			subYX: fp.Elt{0xb9, 0xdb, 0x6c, 0x04, 0x88, 0x22, 0xd8, 0x79, 0x83, 0x2f, 0x8d, 0x65, 0x6b, 0xd2, 0xab, 0x1b, 0xdd, 0x65, 0xe5, 0x93, 0x63, 0xf8, 0xa2, 0xd8, 0x3c, 0xf1, 0x4b, 0xc5, 0x99, 0xd1, 0xf2, 0x12},
+			dt2:   fp.Elt{0x05, 0x4c, 0xb8, 0x3b, 0xfe, 0xf5, 0x9f, 0x2e, 0xd1, 0xb2, 0xb8, 0xff, 0xfe, 0x6d, 0xd9, 0x37, 0xe0, 0xae, 0xb4, 0x5a, 0x51, 0x80, 0x7e, 0x9b, 0x1d, 0xd1, 0x8d, 0x8c, 0x56, 0xb1, 0x84, 0x35},
+		},
+		{
+			addYX: fp.Elt{0x39, 0x71, 0x43, 0x34, 0xe3, 0x42, 0x45, 0xa1, 0xf2, 0x68, 0x71, 0xa7, 0xe8, 0x23, 0xfd, 0x9f, 0x86, 0x48, 0xff, 0xe5, 0x96, 0x74, 0xcf, 0x05, 0x49, 0xe2, 0xb3, 0x6c, 0x17, 0x77, 0x2f, 0x6d},
+			subYX: fp.Elt{0x73, 0x3f, 0xc1, 0xc7, 0x6a, 0x66, 0xa1, 0x20, 0xdd, 0x11, 0xfb, 0x7a, 0x6e, 0xa8, 0x51, 0xb8, 0x3f, 0x9d, 0xa2, 0x97, 0x84, 0xb5, 0xc7, 0x90, 0x7c, 0xab, 0x48, 0xd6, 0x84, 0xa3, 0xd5, 0x1a},
+			dt2:   fp.Elt{0x63, 0x27, 0x3c, 0x49, 0x4b, 0xfc, 0x22, 0xf2, 0x0b, 0x50, 0xc2, 0x0f, 0xb4, 0x1f, 0x31, 0x0c, 0x2f, 0x53, 0xab, 0xaa, 0x75, 0x6f, 0xe0, 0x69, 0x39, 0x56, 0xe0, 0x3b, 0xb7, 0xa8, 0xbf, 0x45},
+		},
+	},
+	{
+		{
+			addYX: fp.Elt{0x00, 0x45, 0xd9, 0x0d, 0x58, 0x03, 0xfc, 0x29, 0x93, 0xec, 0xbb, 0x6f, 0xa4, 0x7a, 0xd2, 0xec, 0xf8, 0xa7, 0xe2, 0xc2, 0x5f, 0x15, 0x0a, 0x13, 0xd5, 0xa1, 0x06, 0xb7, 0x1a, 0x15, 0x6b, 0x41},
+			subYX: fp.Elt{0x85, 0x8c, 0xb2, 0x17, 0xd6, 0x3b, 0x0a, 0xd3, 0xea, 0x3b, 0x77, 0x39, 0xb7, 0x77, 0xd3, 0xc5, 0xbf, 0x5c, 0x6a, 0x1e, 0x8c, 0xe7, 0xc6, 0xc6, 0xc4, 0xb7, 0x2a, 0x8b, 0xf7, 0xb8, 0x61, 0x0d},
+			dt2:   fp.Elt{0xb0, 0x36, 0xc1, 0xe9, 0xef, 0xd7, 0xa8, 0x56, 0x20, 0x4b, 0xe4, 0x58, 0xcd, 0xe5, 0x07, 0xbd, 0xab, 0xe0, 0x57, 0x1b, 0xda, 0x2f, 0xe6, 0xaf, 0xd2, 0xe8, 0x77, 0x42, 0xf7, 0x2a, 0x1a, 0x19},
+		},
+		{
+			addYX: fp.Elt{0x6a, 0x6d, 0x6d, 0xd1, 0xfa, 0xf5, 0x03, 0x30, 0xbd, 0x6d, 0xc2, 0xc8, 0xf5, 0x38, 0x80, 0x4f, 0xb2, 0xbe, 0xa1, 0x76, 0x50, 0x1a, 0x73, 0xf2, 0x78, 0x2b, 0x8e, 0x3a, 0x1e, 0x34, 0x47, 0x7b},
+			subYX: fp.Elt{0xc3, 0x2c, 0x36, 0xdc, 0xc5, 0x45, 0xbc, 0xef, 0x1b, 0x64, 0xd6, 0x65, 0x28, 0xe9, 0xda, 0x84, 0x13, 0xbe, 0x27, 0x8e, 0x3f, 0x98, 0x2a, 0x37, 0xee, 0x78, 0x97, 0xd6, 0xc0, 0x6f, 0xb4, 0x53},
+			dt2:   fp.Elt{0x58, 0x5d, 0xa7, 0xa3, 0x68, 0xbb, 0x20, 0x30, 0x2e, 0x03, 0xe9, 0xb1, 0xd4, 0x90, 0x72, 0xe3, 0x71, 0xb2, 0x36, 0x3e, 0x73, 0xa0, 0x2e, 0x3d, 0xd1, 0x85, 0x33, 0x62, 0x4e, 0xa7, 0x7b, 0x31},
+		},
+		{
+			addYX: fp.Elt{0xbf, 0xc4, 0x38, 0x53, 0xfb, 0x68, 0xa9, 0x77, 0xce, 0x55, 0xf9, 0x05, 0xcb, 0xeb, 0xfb, 0x8c, 0x46, 0xc2, 0x32, 0x7c, 0xf0, 0xdb, 0xd7, 0x2c, 0x62, 0x8e, 0xdd, 0x54, 0x75, 0xcf, 0x3f, 0x33},
+			subYX: fp.Elt{0x49, 0x50, 0x1f, 0x4e, 0x6e, 0x55, 0x55, 0xde, 0x8c, 0x4e, 0x77, 0x96, 0x38, 0x3b, 0xfe, 0xb6, 0x43, 0x3c, 0x86, 0x69, 0xc2, 0x72, 0x66, 0x1f, 0x6b, 0xf9, 0x87, 0xbc, 0x4f, 0x37, 0x3e, 0x3c},
+			dt2:   fp.Elt{0xd2, 0x2f, 0x06, 0x6b, 0x08, 0x07, 0x69, 0x77, 0xc0, 0x94, 0xcc, 0xae, 0x43, 0x00, 0x59, 0x6e, 0xa3, 0x63, 0xa8, 0xdd, 0xfa, 0x24, 0x18, 0xd0, 0x35, 0xc7, 0x78, 0xf7, 0x0d, 0xd4, 0x5a, 0x1e},
+		},
+		{
+			addYX: fp.Elt{0x45, 0xc1, 0x17, 0x51, 0xf8, 0xed, 0x7e, 0xc7, 0xa9, 0x1a, 0x11, 0x6e, 0x2d, 0xef, 0x0b, 0xd5, 0x3f, 0x98, 0xb0, 0xa3, 0x9d, 0x65, 0xf1, 0xcd, 0x53, 0x4a, 0x8a, 0x18, 0x70, 0x0a, 0x7f, 0x23},
+			subYX: fp.Elt{0xdd, 0xef, 0xbe, 0x3a, 0x31, 0xe0, 0xbc, 0xbe, 0x6d, 0x5d, 0x79, 0x87, 0xd6, 0xbe, 0x68, 0xe3, 0x59, 0x76, 0x8c, 0x86, 0x0e, 0x7a, 0x92, 0x13, 0x14, 0x8f, 0x67, 0xb3, 0xcb, 0x1a, 0x76, 0x76},
+			dt2:   fp.Elt{0x56, 0x7a, 0x1c, 0x9d, 0xca, 0x96, 0xf9, 0xf9, 0x03, 0x21, 0xd4, 0xe8, 0xb3, 0xd5, 0xe9, 0x52, 0xc8, 0x54, 0x1e, 0x1b, 0x13, 0xb6, 0xfd, 0x47, 0x7d, 0x02, 0x32, 0x33, 0x27, 0xe2, 0x1f, 0x19},
+		},
+	},
+}
+
+var tabVerif = [1 << (omegaFix - 2)]pointR3{
+	{ /* 1P */
+		addYX: fp.Elt{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0x0e, 0x8c, 0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48, 0x0b, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x07},
+		subYX: fp.Elt{0x3e, 0x91, 0x40, 0xd7, 0x05, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40, 0xd1, 0x05, 0x9f, 0x39, 0xfd, 0x09, 0x8a, 0x8f, 0x68, 0x34, 0x84, 0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44},
+		dt2:   fp.Elt{0x68, 0xaa, 0x7a, 0x87, 0x05, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa, 0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d, 0x1b, 0x5a, 0xa8, 0x65, 0x0c, 0x9f, 0x68, 0x7b, 0x11, 0x6f},
+	},
+	{ /* 3P */
+		addYX: fp.Elt{0x30, 0x97, 0xee, 0x4c, 0xa8, 0xb0, 0x25, 0xaf, 0x8a, 0x4b, 0x86, 0xe8, 0x30, 0x84, 0x5a, 0x02, 0x32, 0x67, 0x01, 0x9f, 0x02, 0x50, 0x1b, 0xc1, 0xf4, 0xf8, 0x80, 0x9a, 0x1b, 0x4e, 0x16, 0x7a},
+		subYX: fp.Elt{0x65, 0xd2, 0xfc, 0xa4, 0xe8, 0x1f, 0x61, 0x56, 0x7d, 0xba, 0xc1, 0xe5, 0xfd, 0x53, 0xd3, 0x3b, 0xbd, 0xd6, 0x4b, 0x21, 0x1a, 0xf3, 0x31, 0x81, 0x62, 0xda, 0x5b, 0x55, 0x87, 0x15, 0xb9, 0x2a},
+		dt2:   fp.Elt{0x89, 0xd8, 0xd0, 0x0d, 0x3f, 0x93, 0xae, 0x14, 0x62, 0xda, 0x35, 0x1c, 0x22, 0x23, 0x94, 0x58, 0x4c, 0xdb, 0xf2, 0x8c, 0x45, 0xe5, 0x70, 0xd1, 0xc6, 0xb4, 0xb9, 0x12, 0xaf, 0x26, 0x28, 0x5a},
+	},
+	{ /* 5P */
+		addYX: fp.Elt{0x33, 0xbb, 0xa5, 0x08, 0x44, 0xbc, 0x12, 0xa2, 0x02, 0xed, 0x5e, 0xc7, 0xc3, 0x48, 0x50, 0x8d, 0x44, 0xec, 0xbf, 0x5a, 0x0c, 0xeb, 0x1b, 0xdd, 0xeb, 0x06, 0xe2, 0x46, 0xf1, 0xcc, 0x45, 0x29},
+		subYX: fp.Elt{0xba, 0xd6, 0x47, 0xa4, 0xc3, 0x82, 0x91, 0x7f, 0xb7, 0x29, 0x27, 0x4b, 0xd1, 0x14, 0x00, 0xd5, 0x87, 0xa0, 0x64, 0xb8, 0x1c, 0xf1, 0x3c, 0xe3, 0xf3, 0x55, 0x1b, 0xeb, 0x73, 0x7e, 0x4a, 0x15},
+		dt2:   fp.Elt{0x85, 0x82, 0x2a, 0x81, 0xf1, 0xdb, 0xbb, 0xbc, 0xfc, 0xd1, 0xbd, 0xd0, 0x07, 0x08, 0x0e, 0x27, 0x2d, 0xa7, 0xbd, 0x1b, 0x0b, 0x67, 0x1b, 0xb4, 0x9a, 0xb6, 0x3b, 0x6b, 0x69, 0xbe, 0xaa, 0x43},
+	},
+	{ /* 7P */
+		addYX: fp.Elt{0xbf, 0xa3, 0x4e, 0x94, 0xd0, 0x5c, 0x1a, 0x6b, 0xd2, 0xc0, 0x9d, 0xb3, 0x3a, 0x35, 0x70, 0x74, 0x49, 0x2e, 0x54, 0x28, 0x82, 0x52, 0xb2, 0x71, 0x7e, 0x92, 0x3c, 0x28, 0x69, 0xea, 0x1b, 0x46},
+		subYX: fp.Elt{0xb1, 0x21, 0x32, 0xaa, 0x9a, 0x2c, 0x6f, 0xba, 0xa7, 0x23, 0xba, 0x3b, 0x53, 0x21, 0xa0, 0x6c, 0x3a, 0x2c, 0x19, 0x92, 0x4f, 0x76, 0xea, 0x9d, 0xe0, 0x17, 0x53, 0x2e, 0x5d, 0xdd, 0x6e, 0x1d},
+		dt2:   fp.Elt{0xa2, 0xb3, 0xb8, 0x01, 0xc8, 0x6d, 0x83, 0xf1, 0x9a, 0xa4, 0x3e, 0x05, 0x47, 0x5f, 0x03, 0xb3, 0xf3, 0xad, 0x77, 0x58, 0xba, 0x41, 0x9c, 0x52, 0xa7, 0x90, 0x0f, 0x6a, 0x1c, 0xbb, 0x9f, 0x7a},
+	},
+	{ /* 9P */
+		addYX: fp.Elt{0x2f, 0x63, 0xa8, 0xa6, 0x8a, 0x67, 0x2e, 0x9b, 0xc5, 0x46, 0xbc, 0x51, 0x6f, 0x9e, 0x50, 0xa6, 0xb5, 0xf5, 0x86, 0xc6, 0xc9, 0x33, 0xb2, 0xce, 0x59, 0x7f, 0xdd, 0x8a, 0x33, 0xed, 0xb9, 0x34},
+		subYX: fp.Elt{0x64, 0x80, 0x9d, 0x03, 0x7e, 0x21, 0x6e, 0xf3, 0x9b, 0x41, 0x20, 0xf5, 0xb6, 0x81, 0xa0, 0x98, 0x44, 0xb0, 0x5e, 0xe7, 0x08, 0xc6, 0xcb, 0x96, 0x8f, 0x9c, 0xdc, 0xfa, 0x51, 0x5a, 0xc0, 0x49},
+		dt2:   fp.Elt{0x1b, 0xaf, 0x45, 0x90, 0xbf, 0xe8, 0xb4, 0x06, 0x2f, 0xd2, 0x19, 0xa7, 0xe8, 0x83, 0xff, 0xe2, 0x16, 0xcf, 0xd4, 0x93, 0x29, 0xfc, 0xf6, 0xaa, 0x06, 0x8b, 0x00, 0x1b, 0x02, 0x72, 0xc1, 0x73},
+	},
+	{ /* 11P */
+		addYX: fp.Elt{0xde, 0x2a, 0x80, 0x8a, 0x84, 0x00, 0xbf, 0x2f, 0x27, 0x2e, 0x30, 0x02, 0xcf, 0xfe, 0xd9, 0xe5, 0x06, 0x34, 0x70, 0x17, 0x71, 0x84, 0x3e, 0x11, 0xaf, 0x8f, 0x6d, 0x54, 0xe2, 0xaa, 0x75, 0x42},
+		subYX: fp.Elt{0x48, 0x43, 0x86, 0x49, 0x02, 0x5b, 0x5f, 0x31, 0x81, 0x83, 0x08, 0x77, 0x69, 0xb3, 0xd6, 0x3e, 0x95, 0xeb, 0x8d, 0x6a, 0x55, 0x75, 0xa0, 0xa3, 0x7f, 0xc7, 0xd5, 0x29, 0x80, 0x59, 0xab, 0x18},
+		dt2:   fp.Elt{0xe9, 0x89, 0x60, 0xfd, 0xc5, 0x2c, 0x2b, 0xd8, 0xa4, 0xe4, 0x82, 0x32, 0xa1, 0xb4, 0x1e, 0x03, 0x22, 0x86, 0x1a, 0xb5, 0x99, 0x11, 0x31, 0x44, 0x48, 0xf9, 0x3d, 0xb5, 0x22, 0x55, 0xc6, 0x3d},
+	},
+	{ /* 13P */
+		addYX: fp.Elt{0x6d, 0x7f, 0x00, 0xa2, 0x22, 0xc2, 0x70, 0xbf, 0xdb, 0xde, 0xbc, 0xb5, 0x9a, 0xb3, 0x84, 0xbf, 0x07, 0xba, 0x07, 0xfb, 0x12, 0x0e, 0x7a, 0x53, 0x41, 0xf2, 0x46, 0xc3, 0xee, 0xd7, 0x4f, 0x23},
+		subYX: fp.Elt{0x93, 0xbf, 0x7f, 0x32, 0x3b, 0x01, 0x6f, 0x50, 0x6b, 0x6f, 0x77, 0x9b, 0xc9, 0xeb, 0xfc, 0xae, 0x68, 0x59, 0xad, 0xaa, 0x32, 0xb2, 0x12, 0x9d, 0xa7, 0x24, 0x60, 0x17, 0x2d, 0x88, 0x67, 0x02},
+		dt2:   fp.Elt{0x78, 0xa3, 0x2e, 0x73, 0x19, 0xa1, 0x60, 0x53, 0x71, 0xd4, 0x8d, 0xdf, 0xb1, 0xe6, 0x37, 0x24, 0x33, 0xe5, 0xa7, 0x91, 0xf8, 0x37, 0xef, 0xa2, 0x63, 0x78, 0x09, 0xaa, 0xfd, 0xa6, 0x7b, 0x49},
+	},
+	{ /* 15P */
+		addYX: fp.Elt{0xa0, 0xea, 0xcf, 0x13, 0x03, 0xcc, 0xce, 0x24, 0x6d, 0x24, 0x9c, 0x18, 0x8d, 0xc2, 0x48, 0x86, 0xd0, 0xd4, 0xf2, 0xc1, 0xfa, 0xbd, 0xbd, 0x2d, 0x2b, 0xe7, 0x2d, 0xf1, 0x17, 0x29, 0xe2, 0x61},
+		subYX: fp.Elt{0x0b, 0xcf, 0x8c, 0x46, 0x86, 0xcd, 0x0b, 0x04, 0xd6, 0x10, 0x99, 0x2a, 0xa4, 0x9b, 0x82, 0xd3, 0x92, 0x51, 0xb2, 0x07, 0x08, 0x30, 0x08, 0x75, 0xbf, 0x5e, 0xd0, 0x18, 0x42, 0xcd, 0xb5, 0x43},
+		dt2:   fp.Elt{0x16, 0xb5, 0xd0, 0x9b, 0x2f, 0x76, 0x9a, 0x5d, 0xee, 0xde, 0x3f, 0x37, 0x4e, 0xaf, 0x38, 0xeb, 0x70, 0x42, 0xd6, 0x93, 0x7d, 0x5a, 0x2e, 0x03, 0x42, 0xd8, 0xe4, 0x0a, 0x21, 0x61, 0x1d, 0x51},
+	},
+	{ /* 17P */
+		addYX: fp.Elt{0x81, 0x9d, 0x0e, 0x95, 0xef, 0x76, 0xc6, 0x92, 0x4f, 0x04, 0xd7, 0xc0, 0xcd, 0x20, 0x46, 0xa5, 0x48, 0x12, 0x8f, 0x6f, 0x64, 0x36, 0x9b, 0xaa, 0xe3, 0x55, 0xb8, 0xdd, 0x24, 0x59, 0x32, 0x6d},
+		subYX: fp.Elt{0x87, 0xde, 0x20, 0x44, 0x48, 0x86, 0x13, 0x08, 0xb4, 0xed, 0x92, 0xb5, 0x16, 0xf0, 0x1c, 0x8a, 0x25, 0x2d, 0x94, 0x29, 0x27, 0x4e, 0xfa, 0x39, 0x10, 0x28, 0x48, 0xe2, 0x6f, 0xfe, 0xa7, 0x71},
+		dt2:   fp.Elt{0x54, 0xc8, 0xc8, 0xa5, 0xb8, 0x82, 0x71, 0x6c, 0x03, 0x2a, 0x5f, 0xfe, 0x79, 0x14, 0xfd, 0x33, 0x0c, 0x8d, 0x77, 0x83, 0x18, 0x59, 0xcf, 0x72, 0xa9, 0xea, 0x9e, 0x55, 0xb6, 0xc4, 0x46, 0x47},
+	},
+	{ /* 19P */
+		addYX: fp.Elt{0x2b, 0x9a, 0xc6, 0x6d, 0x3c, 0x7b, 0x77, 0xd3, 0x17, 0xf6, 0x89, 0x6f, 0x27, 0xb2, 0xfa, 0xde, 0xb5, 0x16, 0x3a, 0xb5, 0xf7, 0x1c, 0x65, 0x45, 0xb7, 0x9f, 0xfe, 0x34, 0xde, 0x51, 0x9a, 0x5c},
+		subYX: fp.Elt{0x47, 0x11, 0x74, 0x64, 0xc8, 0x46, 0x85, 0x34, 0x49, 0xc8, 0xfc, 0x0e, 0xdd, 0xae, 0x35, 0x7d, 0x32, 0xa3, 0x72, 0x06, 0x76, 0x9a, 0x93, 0xff, 0xd6, 0xe6, 0xb5, 0x7d, 0x49, 0x63, 0x96, 0x21},
+		dt2:   fp.Elt{0x67, 0x0e, 0xf1, 0x79, 0xcf, 0xf1, 0x10, 0xf5, 0x5b, 0x51, 0x58, 0xe6, 0xa1, 0xda, 0xdd, 0xff, 0x77, 0x22, 0x14, 0x10, 0x17, 0xa7, 0xc3, 0x09, 0xbb, 0x23, 0x82, 0x60, 0x3c, 0x50, 0x04, 0x48},
+	},
+	{ /* 21P */
+		addYX: fp.Elt{0xc7, 0x7f, 0xa3, 0x2c, 0xd0, 0x9e, 0x24, 0xc4, 0xab, 0xac, 0x15, 0xa6, 0xe3, 0xa0, 0x59, 0xa0, 0x23, 0x0e, 0x6e, 0xc9, 0xd7, 0x6e, 0xa9, 0x88, 0x6d, 0x69, 0x50, 0x16, 0xa5, 0x98, 0x33, 0x55},
+		subYX: fp.Elt{0x75, 0xd1, 0x36, 0x3a, 0xd2, 0x21, 0x68, 0x3b, 0x32, 0x9e, 0x9b, 0xe9, 0xa7, 0x0a, 0xb4, 0xbb, 0x47, 0x8a, 0x83, 0x20, 0xe4, 0x5c, 0x9e, 0x5d, 0x5e, 0x4c, 0xde, 0x58, 0x88, 0x09, 0x1e, 0x77},
+		dt2:   fp.Elt{0xdf, 0x1e, 0x45, 0x78, 0xd2, 0xf5, 0x12, 0x9a, 0xcb, 0x9c, 0x89, 0x85, 0x79, 0x5d, 0xda, 0x3a, 0x08, 0x95, 0xa5, 0x9f, 0x2d, 0x4a, 0x7f, 0x47, 0x11, 0xa6, 0xf5, 0x8f, 0xd6, 0xd1, 0x5e, 0x5a},
+	},
+	{ /* 23P */
+		addYX: fp.Elt{0x83, 0x0e, 0x15, 0xfe, 0x2a, 0x12, 0x95, 0x11, 0xd8, 0x35, 0x4b, 0x7e, 0x25, 0x9a, 0x20, 0xcf, 0x20, 0x1e, 0x71, 0x1e, 0x29, 0xf8, 0x87, 0x73, 0xf0, 0x92, 0xbf, 0xd8, 0x97, 0xb8, 0xac, 0x44},
+		subYX: fp.Elt{0x59, 0x73, 0x52, 0x58, 0xc5, 0xe0, 0xe5, 0xba, 0x7e, 0x9d, 0xdb, 0xca, 0x19, 0x5c, 0x2e, 0x39, 0xe9, 0xab, 0x1c, 0xda, 0x1e, 0x3c, 0x65, 0x28, 0x44, 0xdc, 0xef, 0x5f, 0x13, 0x60, 0x9b, 0x01},
+		dt2:   fp.Elt{0x83, 0x4b, 0x13, 0x5e, 0x14, 0x68, 0x60, 0x1e, 0x16, 0x4c, 0x30, 0x24, 0x4f, 0xe6, 0xf5, 0xc4, 0xd7, 0x3e, 0x1a, 0xfc, 0xa8, 0x88, 0x6e, 0x50, 0x92, 0x2f, 0xad, 0xe6, 0xfd, 0x49, 0x0c, 0x15},
+	},
+	{ /* 25P */
+		addYX: fp.Elt{0x38, 0x11, 0x47, 0x09, 0x95, 0xf2, 0x7b, 0x8e, 0x51, 0xa6, 0x75, 0x4f, 0x39, 0xef, 0x6f, 0x5d, 0xad, 0x08, 0xa7, 0x25, 0xc4, 0x79, 0xaf, 0x10, 0x22, 0x99, 0xb9, 0x5b, 0x07, 0x5a, 0x2b, 0x6b},
+		subYX: fp.Elt{0x68, 0xa8, 0xdc, 0x9c, 0x3c, 0x86, 0x49, 0xb8, 0xd0, 0x4a, 0x71, 0xb8, 0xdb, 0x44, 0x3f, 0xc8, 0x8d, 0x16, 0x36, 0x0c, 0x56, 0xe3, 0x3e, 0xfe, 0xc1, 0xfb, 0x05, 0x1e, 0x79, 0xd7, 0xa6, 0x78},
+		dt2:   fp.Elt{0x76, 0xb9, 0xa0, 0x47, 0x4b, 0x70, 0xbf, 0x58, 0xd5, 0x48, 0x17, 0x74, 0x55, 0xb3, 0x01, 0xa6, 0x90, 0xf5, 0x42, 0xd5, 0xb1, 0x1f, 0x2b, 0xaa, 0x00, 0x5d, 0xd5, 0x4a, 0xfc, 0x7f, 0x5c, 0x72},
+	},
+	{ /* 27P */
+		addYX: fp.Elt{0xb2, 0x99, 0xcf, 0xd1, 0x15, 0x67, 0x42, 0xe4, 0x34, 0x0d, 0xa2, 0x02, 0x11, 0xd5, 0x52, 0x73, 0x9f, 0x10, 0x12, 0x8b, 0x7b, 0x15, 0xd1, 0x23, 0xa3, 0xf3, 0xb1, 0x7c, 0x27, 0xc9, 0x4c, 0x79},
+		subYX: fp.Elt{0xc0, 0x98, 0xd0, 0x1c, 0xf7, 0x2b, 0x80, 0x91, 0x66, 0x63, 0x5e, 0xed, 0xa4, 0x6c, 0x41, 0xfe, 0x4c, 0x99, 0x02, 0x49, 0x71, 0x5d, 0x58, 0xdf, 0xe7, 0xfa, 0x55, 0xf8, 0x25, 0x46, 0xd5, 0x4c},
+		dt2:   fp.Elt{0x53, 0x50, 0xac, 0xc2, 0x26, 0xc4, 0xf6, 0x4a, 0x58, 0x72, 0xf6, 0x32, 0xad, 0xed, 0x9a, 0xbc, 0x21, 0x10, 0x31, 0x0a, 0xf1, 0x32, 0xd0, 0x2a, 0x85, 0x8e, 0xcc, 0x6f, 0x7b, 0x35, 0x08, 0x70},
+	},
+	{ /* 29P */
+		addYX: fp.Elt{0x01, 0x3f, 0x77, 0x38, 0x27, 0x67, 0x88, 0x0b, 0xfb, 0xcc, 0xfb, 0x95, 0xfa, 0xc8, 0xcc, 0xb8, 0xb6, 0x29, 0xad, 0xb9, 0xa3, 0xd5, 0x2d, 0x8d, 0x6a, 0x0f, 0xad, 0x51, 0x98, 0x7e, 0xef, 0x06},
+		subYX: fp.Elt{0x34, 0x4a, 0x58, 0x82, 0xbb, 0x9f, 0x1b, 0xd0, 0x2b, 0x79, 0xb4, 0xd2, 0x63, 0x64, 0xab, 0x47, 0x02, 0x62, 0x53, 0x48, 0x9c, 0x63, 0x31, 0xb6, 0x28, 0xd4, 0xd6, 0x69, 0x36, 0x2a, 0xa9, 0x13},
+		dt2:   fp.Elt{0xe5, 0x7d, 0x57, 0xc0, 0x1c, 0x77, 0x93, 0xca, 0x5c, 0xdc, 0x35, 0x50, 0x1e, 0xe4, 0x40, 0x75, 0x71, 0xe0, 0x02, 0xd8, 0x01, 0x0f, 0x68, 0x24, 0x6a, 0xf8, 0x2a, 0x8a, 0xdf, 0x6d, 0x29, 0x3c},
+	},
+	{ /* 31P */
+		addYX: fp.Elt{0x13, 0xa7, 0x14, 0xd9, 0xf9, 0x15, 0xad, 0xae, 0x12, 0xf9, 0x8f, 0x8c, 0xf9, 0x7b, 0x2f, 0xa9, 0x30, 0xd7, 0x53, 0x9f, 0x17, 0x23, 0xf8, 0xaf, 0xba, 0x77, 0x0c, 0x49, 0x93, 0xd3, 0x99, 0x7a},
+		subYX: fp.Elt{0x41, 0x25, 0x1f, 0xbb, 0x2e, 0x4d, 0xeb, 0xfc, 0x1f, 0xb9, 0xad, 0x40, 0xc7, 0x10, 0x95, 0xb8, 0x05, 0xad, 0xa1, 0xd0, 0x7d, 0xa3, 0x71, 0xfc, 0x7b, 0x71, 0x47, 0x07, 0x70, 0x2c, 0x89, 0x0a},
+		dt2:   fp.Elt{0xe8, 0xa3, 0xbd, 0x36, 0x24, 0xed, 0x52, 0x8f, 0x94, 0x07, 0xe8, 0x57, 0x41, 0xc8, 0xa8, 0x77, 0xe0, 0x9c, 0x2f, 0x26, 0x63, 0x65, 0xa9, 0xa5, 0xd2, 0xf7, 0x02, 0x83, 0xd2, 0x62, 0x67, 0x28},
+	},
+	{ /* 33P */
+		addYX: fp.Elt{0x25, 0x5b, 0xe3, 0x3c, 0x09, 0x36, 0x78, 0x4e, 0x97, 0xaa, 0x6b, 0xb2, 0x1d, 0x18, 0xe1, 0x82, 0x3f, 0xb8, 0xc7, 0xcb, 0xd3, 0x92, 0xc1, 0x0c, 0x3a, 0x9d, 0x9d, 0x6a, 0x04, 0xda, 0xf1, 0x32},
+		subYX: fp.Elt{0xbd, 0xf5, 0x2e, 0xce, 0x2b, 0x8e, 0x55, 0x7c, 0x63, 0xbc, 0x47, 0x67, 0xb4, 0x6c, 0x98, 0xe4, 0xb8, 0x89, 0xbb, 0x3b, 0x9f, 0x17, 0x4a, 0x15, 0x7a, 0x76, 0xf1, 0xd6, 0xa3, 0xf2, 0x86, 0x76},
+		dt2:   fp.Elt{0x6a, 0x7c, 0x59, 0x6d, 0xa6, 0x12, 0x8d, 0xaa, 0x2b, 0x85, 0xd3, 0x04, 0x03, 0x93, 0x11, 0x8f, 0x22, 0xb0, 0x09, 0xc2, 0x73, 0xdc, 0x91, 0x3f, 0xa6, 0x28, 0xad, 0xa9, 0xf8, 0x05, 0x13, 0x56},
+	},
+	{ /* 35P */
+		addYX: fp.Elt{0xd1, 0xae, 0x92, 0xec, 0x8d, 0x97, 0x0c, 0x10, 0xe5, 0x73, 0x6d, 0x4d, 0x43, 0xd5, 0x43, 0xca, 0x48, 0xba, 0x47, 0xd8, 0x22, 0x1b, 0x13, 0x83, 0x2c, 0x4d, 0x5d, 0xe3, 0x53, 0xec, 0xaa},
+		subYX: fp.Elt{0xd5, 0xc0, 0xb0, 0xe7, 0x28, 0xcc, 0x22, 0x67, 0x53, 0x5c, 0x07, 0xdb, 0xbb, 0xe9, 0x9d, 0x70, 0x61, 0x0a, 0x01, 0xd7, 0xa7, 0x8d, 0xf6, 0xca, 0x6c, 0xcc, 0x57, 0x2c, 0xef, 0x1a, 0x0a, 0x03},
+		dt2:   fp.Elt{0xaa, 0xd2, 0x3a, 0x00, 0x73, 0xf7, 0xb1, 0x7b, 0x08, 0x66, 0x21, 0x2b, 0x80, 0x29, 0x3f, 0x0b, 0x3e, 0xd2, 0x0e, 0x52, 0x86, 0xdc, 0x21, 0x78, 0x80, 0x54, 0x06, 0x24, 0x1c, 0x9c, 0xbe, 0x20},
+	},
+	{ /* 37P */
+		addYX: fp.Elt{0xa6, 0x73, 0x96, 0x24, 0xd8, 0x87, 0x53, 0xe1, 0x93, 0xe4, 0x46, 0xf5, 0x2d, 0xbc, 0x43, 0x59, 0xb5, 0x63, 0x6f, 0xc3, 0x81, 0x9a, 0x7f, 0x1c, 0xde, 0xc1, 0x0a, 0x1f, 0x36, 0xb3, 0x0a, 0x75},
+		subYX: fp.Elt{0x60, 0x5e, 0x02, 0xe2, 0x4a, 0xe4, 0xe0, 0x20, 0x38, 0xb9, 0xdc, 0xcb, 0x2f, 0x3b, 0x3b, 0xb0, 0x1c, 0x0d, 0x5a, 0xf9, 0x9c, 0x63, 0x5d, 0x10, 0x11, 0xe3, 0x67, 0x50, 0x54, 0x4c, 0x76, 0x69},
+		dt2:   fp.Elt{0x37, 0x10, 0xf8, 0xa2, 0x83, 0x32, 0x8a, 0x1e, 0xf1, 0xcb, 0x7f, 0xbd, 0x23, 0xda, 0x2e, 0x6f, 0x63, 0x25, 0x2e, 0xac, 0x5b, 0xd1, 0x2f, 0xb7, 0x40, 0x50, 0x07, 0xb7, 0x3f, 0x6b, 0xf9, 0x54},
+	},
+	{ /* 39P */
+		addYX: fp.Elt{0x79, 0x92, 0x66, 0x29, 0x04, 0xf2, 0xad, 0x0f, 0x4a, 0x72, 0x7d, 0x7d, 0x04, 0xa2, 0xdd, 0x3a, 0xf1, 0x60, 0x57, 0x8c, 0x82, 0x94, 0x3d, 0x6f, 0x9e, 0x53, 0xb7, 0x2b, 0xc5, 0xe9, 0x7f, 0x3d},
+		subYX: fp.Elt{0xcd, 0x1e, 0xb1, 0x16, 0xc6, 0xaf, 0x7d, 0x17, 0x79, 0x64, 0x57, 0xfa, 0x9c, 0x4b, 0x76, 0x89, 0x85, 0xe7, 0xec, 0xe6, 0x10, 0xa1, 0xa8, 0xb7, 0xf0, 0xdb, 0x85, 0xbe, 0x9f, 0x83, 0xe6, 0x78},
+		dt2:   fp.Elt{0x6b, 0x85, 0xb8, 0x37, 0xf7, 0x2d, 0x33, 0x70, 0x8a, 0x17, 0x1a, 0x04, 0x43, 0x5d, 0xd0, 0x75, 0x22, 0x9e, 0xe5, 0xa0, 0x4a, 0xf7, 0x0f, 0x32, 0x42, 0x82, 0x08, 0x50, 0xf3, 0x68, 0xf2, 0x70},
+	},
+	{ /* 41P */
+		addYX: fp.Elt{0x47, 0x5f, 0x80, 0xb1, 0x83, 0x45, 0x86, 0x66, 0x19, 0x7c, 0xdd, 0x60, 0xd1, 0xc5, 0x35, 0xf5, 0x06, 0xb0, 0x4c, 0x1e, 0xb7, 0x4e, 0x87, 0xe9, 0xd9, 0x89, 0xd8, 0xfa, 0x5c, 0x34, 0x0d, 0x7c},
+		subYX: fp.Elt{0x55, 0xf3, 0xdc, 0x70, 0x20, 0x11, 0x24, 0x23, 0x17, 0xe1, 0xfc, 0xe7, 0x7e, 0xc9, 0x0c, 0x38, 0x98, 0xb6, 0x52, 0x35, 0xed, 0xde, 0x1d, 0xb3, 0xb9, 0xc4, 0xb8, 0x39, 0xc0, 0x56, 0x4e, 0x40},
+		dt2:   fp.Elt{0x8a, 0x33, 0x78, 0x8c, 0x4b, 0x1f, 0x1f, 0x59, 0xe1, 0xb5, 0xe0, 0x67, 0xb1, 0x6a, 0x36, 0xa0, 0x44, 0x3d, 0x5f, 0xb4, 0x52, 0x41, 0xbc, 0x5c, 0x77, 0xc7, 0xae, 0x2a, 0x76, 0x54, 0xd7, 0x20},
+	},
+	{ /* 43P */
+		addYX: fp.Elt{0x58, 0xb7, 0x3b, 0xc7, 0x6f, 0xc3, 0x8f, 0x5e, 0x9a, 0xbb, 0x3c, 0x36, 0xa5, 0x43, 0xe5, 0xac, 0x22, 0xc9, 0x3b, 0x90, 0x7d, 0x4a, 0x93, 0xa9, 0x62, 0xec, 0xce, 0xf3, 0x46, 0x1e, 0x8f, 0x2b},
+		subYX: fp.Elt{0x43, 0xf5, 0xb9, 0x35, 0xb1, 0xfe, 0x74, 0x9d, 0x6c, 0x95, 0x8c, 0xde, 0xf1, 0x7d, 0xb3, 0x84, 0xa9, 0x8b, 0x13, 0x57, 0x07, 0x2b, 0x32, 0xe9, 0xe1, 0x4c, 0x0b, 0x79, 0xa8, 0xad, 0xb8, 0x38},
+		dt2:   fp.Elt{0x5d, 0xf9, 0x51, 0xdf, 0x9c, 0x4a, 0xc0, 0xb5, 0xac, 0xde, 0x1f, 0xcb, 0xae, 0x52, 0x39, 0x2b, 0xda, 0x66, 0x8b, 0x32, 0x8b, 0x6d, 0x10, 0x1d, 0x53, 0x19, 0xba, 0xce, 0x32, 0xeb, 0x9a, 0x04},
+	},
+	{ /* 45P */
+		addYX: fp.Elt{0x31, 0x79, 0xfc, 0x75, 0x0b, 0x7d, 0x50, 0xaa, 0xd3, 0x25, 0x67, 0x7a, 0x4b, 0x92, 0xef, 0x0f, 0x30, 0x39, 0x6b, 0x39, 0x2b, 0x54, 0x82, 0x1d, 0xfc, 0x74, 0xf6, 0x30, 0x75, 0xe1, 0x5e, 0x79},
+		subYX: fp.Elt{0x7e, 0xfe, 0xdc, 0x63, 0x3c, 0x7d, 0x76, 0xd7, 0x40, 0x6e, 0x85, 0x97, 0x48, 0x59, 0x9c, 0x20, 0x13, 0x7c, 0x4f, 0xe1, 0x61, 0x68, 0x67, 0xb6, 0xfc, 0x25, 0xd6, 0xc8, 0xe0, 0x65, 0xc6, 0x51},
+		dt2:   fp.Elt{0x81, 0xbd, 0xec, 0x52, 0x0a, 0x5b, 0x4a, 0x25, 0xe7, 0xaf, 0x34, 0xe0, 0x6e, 0x1f, 0x41, 0x5d, 0x31, 0x4a, 0xee, 0xca, 0x0d, 0x4d, 0xa2, 0xe6, 0x77, 0x44, 0xc5, 0x9d, 0xf4, 0x9b, 0xd1, 0x6c},
+	},
+	{ /* 47P */
+		addYX: fp.Elt{0x86, 0xc3, 0xaf, 0x65, 0x21, 0x61, 0xfe, 0x1f, 0x10, 0x1b, 0xd5, 0xb8, 0x88, 0x2a, 0x2a, 0x08, 0xaa, 0x0b, 0x99, 0x20, 0x7e, 0x62, 0xf6, 0x76, 0xe7, 0x43, 0x9e, 0x42, 0xa7, 0xb3, 0x01, 0x5e},
+		subYX: fp.Elt{0xa3, 0x9c, 0x17, 0x52, 0x90, 0x61, 0x87, 0x7e, 0x85, 0x9f, 0x2c, 0x0b, 0x06, 0x0a, 0x1d, 0x57, 0x1e, 0x71, 0x99, 0x84, 0xa8, 0xba, 0xa2, 0x80, 0x38, 0xe6, 0xb2, 0x40, 0xdb, 0xf3, 0x20, 0x75},
+		dt2:   fp.Elt{0xa1, 0x57, 0x93, 0xd3, 0xe3, 0x0b, 0xb5, 0x3d, 0xa5, 0x94, 0x9e, 0x59, 0xdd, 0x6c, 0x7b, 0x96, 0x6e, 0x1e, 0x31, 0xdf, 0x64, 0x9a, 0x30, 0x1a, 0x86, 0xc9, 0xf3, 0xce, 0x9c, 0x2c, 0x09, 0x71},
+	},
+	{ /* 49P */
+		addYX: fp.Elt{0xcf, 0x1d, 0x05, 0x74, 0xac, 0xd8, 0x6b, 0x85, 0x1e, 0xaa, 0xb7, 0x55, 0x08, 0xa4, 0xf6, 0x03, 0xeb, 0x3c, 0x74, 0xc9, 0xcb, 0xe7, 0x4a, 0x3a, 0xde, 0xab, 0x37, 0x71, 0xbb, 0xa5, 0x73, 0x41},
+		subYX: fp.Elt{0x8c, 0x91, 0x64, 0x03, 0x3f, 0x52, 0xd8, 0x53, 0x1c, 0x6b, 0xab, 0x3f, 0xf4, 0x04, 0xb4, 0xa2, 0xa4, 0xe5, 0x81, 0x66, 0x9e, 0x4a, 0x0b, 0x08, 0xa7, 0x7b, 0x25, 0xd0, 0x03, 0x5b, 0xa1, 0x0e},
+		dt2:   fp.Elt{0x8a, 0x21, 0xf9, 0xf0, 0x31, 0x6e, 0xc5, 0x17, 0x08, 0x47, 0xfc, 0x1a, 0x2b, 0x6e, 0x69, 0x5a, 0x76, 0xf1, 0xb2, 0xf4, 0x68, 0x16, 0x93, 0xf7, 0x67, 0x3a, 0x4e, 0x4a, 0x61, 0x65, 0xc5, 0x5f},
+	},
+	{ /* 51P */
+		addYX: fp.Elt{0x8e, 0x98, 0x90, 0x77, 0xe6, 0xe1, 0x92, 0x48, 0x22, 0xd7, 0x5c, 0x1c, 0x0f, 0x95, 0xd5, 0x01, 0xed, 0x3e, 0x92, 0xe5, 0x9a, 0x81, 0xb0, 0xe3, 0x1b, 0x65, 0x46, 0x9d, 0x40, 0xc7, 0x14, 0x32},
+		subYX: fp.Elt{0xe5, 0x7a, 0x6d, 0xc4, 0x0d, 0x57, 0x6e, 0x13, 0x8f, 0xdc, 0xf8, 0x54, 0xcc, 0xaa, 0xd0, 0x0f, 0x86, 0xad, 0x0d, 0x31, 0x03, 0x9f, 0x54, 0x59, 0xa1, 0x4a, 0x45, 0x4c, 0x41, 0x1c, 0x71, 0x62},
+		dt2:   fp.Elt{0x70, 0x17, 0x65, 0x06, 0x74, 0x82, 0x29, 0x13, 0x36, 0x94, 0x27, 0x8a, 0x66, 0xa0, 0xa4, 0x3b, 0x3c, 0x22, 0x5d, 0x18, 0xec, 0xb8, 0xb6, 0xd9, 0x3c, 0x83, 0xcb, 0x3e, 0x07, 0x94, 0xea, 0x5b},
+	},
+	{ /* 53P */
+		addYX: fp.Elt{0xf8, 0xd2, 0x43, 0xf3, 0x63, 0xce, 0x70, 0xb4, 0xf1, 0xe8, 0x43, 0x05, 0x8f, 0xba, 0x67, 0x00, 0x6f, 0x7b, 0x11, 0xa2, 0xa1, 0x51, 0xda, 0x35, 0x2f, 0xbd, 0xf1, 0x44, 0x59, 0x78, 0xd0, 0x4a},
+		subYX: fp.Elt{0xe4, 0x9b, 0xc8, 0x12, 0x09, 0xbf, 0x1d, 0x64, 0x9c, 0x57, 0x6e, 0x7d, 0x31, 0x8b, 0xf3, 0xac, 0x65, 0xb0, 0x97, 0xf6, 0x02, 0x9e, 0xfe, 0xab, 0xec, 0x1e, 0xf6, 0x48, 0xc1, 0xd5, 0xac, 0x3a},
+		dt2:   fp.Elt{0x01, 0x83, 0x31, 0xc3, 0x34, 0x3b, 0x8e, 0x85, 0x26, 0x68, 0x31, 0x07, 0x47, 0xc0, 0x99, 0xdc, 0x8c, 0xa8, 0x9d, 0xd3, 0x2e, 0x5b, 0x08, 0x34, 0x3d, 0x85, 0x02, 0xd9, 0xb1, 0x0c, 0xff, 0x3a},
+	},
+	{ /* 55P */
+		addYX: fp.Elt{0x05, 0x35, 0xc5, 0xf4, 0x0b, 0x43, 0x26, 0x92, 0x83, 0x22, 0x1f, 0x26, 0x13, 0x9c, 0xe4, 0x68, 0xc6, 0x27, 0xd3, 0x8f, 0x78, 0x33, 0xef, 0x09, 0x7f, 0x9e, 0xd9, 0x2b, 0x73, 0x9f, 0xcf, 0x2c},
+		subYX: fp.Elt{0x5e, 0x40, 0x20, 0x3a, 0xeb, 0xc7, 0xc5, 0x87, 0xc9, 0x56, 0xad, 0xed, 0xef, 0x11, 0xe3, 0x8e, 0xf9, 0xd5, 0x29, 0xad, 0x48, 0x2e, 0x25, 0x29, 0x1d, 0x25, 0xcd, 0xf4, 0x86, 0x7e, 0x0e, 0x11},
+		dt2:   fp.Elt{0xe4, 0xf5, 0x03, 0xd6, 0x9e, 0xd8, 0xc0, 0x57, 0x0c, 0x20, 0xb0, 0xf0, 0x28, 0x86, 0x88, 0x12, 0xb7, 0x3b, 0x2e, 0xa0, 0x09, 0x27, 0x17, 0x53, 0x37, 0x3a, 0x69, 0xb9, 0xe0, 0x57, 0xc5, 0x05},
+	},
+	{ /* 57P */
+		addYX: fp.Elt{0xb0, 0x0e, 0xc2, 0x89, 0xb0, 0xbb, 0x76, 0xf7, 0x5c, 0xd8, 0x0f, 0xfa, 0xf6, 0x5b, 0xf8, 0x61, 0xfb, 0x21, 0x44, 0x63, 0x4e, 0x3f, 0xb9, 0xb6, 0x05, 0x12, 0x86, 0x41, 0x08, 0xef, 0x9f, 0x28},
+		subYX: fp.Elt{0x6f, 0x7e, 0xc9, 0x1f, 0x31, 0xce, 0xf9, 0xd8, 0xae, 0xfd, 0xf9, 0x11, 0x30, 0x26, 0x3f, 0x7a, 0xdd, 0x25, 0xed, 0x8b, 0xa0, 0x7e, 0x5b, 0xe1, 0x5a, 0x87, 0xe9, 0x8f, 0x17, 0x4c, 0x15, 0x6e},
+		dt2:   fp.Elt{0xbf, 0x9a, 0xd6, 0xfe, 0x36, 0x63, 0x61, 0xcf, 0x4f, 0xc9, 0x35, 0x83, 0xe7, 0xe4, 0x16, 0x9b, 0xe7, 0x7f, 0x3a, 0x75, 0x65, 0x97, 0x78, 0x13, 0x19, 0xa3, 0x5c, 0xa9, 0x42, 0xf6, 0xfb, 0x6a},
+	},
+	{ /* 59P */
+		addYX: fp.Elt{0xcc, 0xa8, 0x13, 0xf9, 0x70, 0x50, 0xe5, 0x5d, 0x61, 0xf5, 0x0c, 0x2b, 0x7b, 0x16, 0x1d, 0x7d, 0x89, 0xd4, 0xea, 0x90, 0xb6, 0x56, 0x29, 0xda, 0xd9, 0x1e, 0x80, 0xdb, 0xce, 0x93, 0xc0, 0x12},
+		subYX: fp.Elt{0xc1, 0xd2, 0xf5, 0x62, 0x0c, 0xde, 0xa8, 0x7d, 0x9a, 0x7b, 0x0e, 0xb0, 0xa4, 0x3d, 0xfc, 0x98, 0xe0, 0x70, 0xad, 0x0d, 0xda, 0x6a, 0xeb, 0x7d, 0xc4, 0x38, 0x50, 0xb9, 0x51, 0xb8, 0xb4, 0x0d},
+		dt2:   fp.Elt{0x0f, 0x19, 0xb8, 0x08, 0x93, 0x7f, 0x14, 0xfc, 0x10, 0xe3, 0x1a, 0xa1, 0xa0, 0x9d, 0x96, 0x06, 0xfd, 0xd7, 0xc7, 0xda, 0x72, 0x55, 0xe7, 0xce, 0xe6, 0x5c, 0x63, 0xc6, 0x99, 0x87, 0xaa, 0x33},
+	},
+	{ /* 61P */
+		addYX: fp.Elt{0xb1, 0x6c, 0x15, 0xfc, 0x88, 0xf5, 0x48, 0x83, 0x27, 0x6d, 0x0a, 0x1a, 0x9b, 0xba, 0xa2, 0x6d, 0xb6, 0x5a, 0xca, 0x87, 0x5c, 0x2d, 0x26, 0xe2, 0xa6, 0x89, 0xd5, 0xc8, 0xc1, 0xd0, 0x2c, 0x21},
+		subYX: fp.Elt{0xf2, 0x5c, 0x08, 0xbd, 0x1e, 0xf5, 0x0f, 0xaf, 0x1f, 0x3f, 0xd3, 0x67, 0x89, 0x1a, 0xf5, 0x78, 0x3c, 0x03, 0x60, 0x50, 0xe1, 0xbf, 0xc2, 0x6e, 0x86, 0x1a, 0xe2, 0xe8, 0x29, 0x6f, 0x3c, 0x23},
+		dt2:   fp.Elt{0x81, 0xc7, 0x18, 0x7f, 0x10, 0xd5, 0xf4, 0xd2, 0x28, 0x9d, 0x7e, 0x52, 0xf2, 0xcd, 0x2e, 0x12, 0x41, 0x33, 0x3d, 0x3d, 0x2a, 0x86, 0x0a, 0xa7, 0xe3, 0x4c, 0x91, 0x11, 0x89, 0x77, 0xb7, 0x1d},
+	},
+	{ /* 63P */
+		addYX: fp.Elt{0xb6, 0x1a, 0x70, 0xdd, 0x69, 0x47, 0x39, 0xb3, 0xa5, 0x8d, 0xcf, 0x19, 0xd4, 0xde, 0xb8, 0xe2, 0x52, 0xc8, 0x2a, 0xfd, 0x61, 0x41, 0xdf, 0x15, 0xbe, 0x24, 0x7d, 0x01, 0x8a, 0xca, 0xe2, 0x7a},
+		subYX: fp.Elt{0x6f, 0xc2, 0x6b, 0x7c, 0x39, 0x52, 0xf3, 0xdd, 0x13, 0x01, 0xd5, 0x53, 0xcc, 0xe2, 0x97, 0x7a, 0x30, 0xa3, 0x79, 0xbf, 0x3a, 0xf4, 0x74, 0x7c, 0xfc, 0xad, 0xe2, 0x26, 0xad, 0x97, 0xad, 0x31},
+		dt2:   fp.Elt{0x62, 0xb9, 0x20, 0x09, 0xed, 0x17, 0xe8, 0xb7, 0x9d, 0xda, 0x19, 0x3f, 0xcc, 0x18, 0x85, 0x1e, 0x64, 0x0a, 0x56, 0x25, 0x4f, 0xc1, 0x91, 0xe4, 0x83, 0x2c, 0x62, 0xa6, 0x53, 0xfc, 0xd1, 0x1e},
+	},
+}
diff --git a/vendor/golang.org/x/sys/AUTHORS b/vendor/golang.org/x/sys/AUTHORS
new file mode 100644
index 000000000..15167cd74
--- /dev/null
+++ b/vendor/golang.org/x/sys/AUTHORS
@@ -0,0 +1,3 @@
+# This source code refers to The Go Authors for copyright purposes.
+# The master list of authors is in the main Go distribution,
+# visible at http://tip.golang.org/AUTHORS.
diff --git a/vendor/golang.org/x/sys/CONTRIBUTORS b/vendor/golang.org/x/sys/CONTRIBUTORS
new file mode 100644
index 000000000..1c4577e96
--- /dev/null
+++ b/vendor/golang.org/x/sys/CONTRIBUTORS
@@ -0,0 +1,3 @@
+# This source code was written by the Go contributors.
+# The master list of contributors is in the main Go distribution,
+# visible at http://tip.golang.org/CONTRIBUTORS.
diff --git a/vendor/golang.org/x/sys/cpu/cpu_aix_ppc64.go b/vendor/golang.org/x/sys/cpu/cpu_aix_ppc64.go
new file mode 100644
index 000000000..be6027224
--- /dev/null
+++ b/vendor/golang.org/x/sys/cpu/cpu_aix_ppc64.go
@@ -0,0 +1,34 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build aix,ppc64
+
+package cpu
+
+const cacheLineSize = 128
+
+const (
+	// getsystemcfg constants
+	_SC_IMPL     = 2
+	_IMPL_POWER8 = 0x10000
+	_IMPL_POWER9 = 0x20000
+)
+
+func init() {
+	impl := getsystemcfg(_SC_IMPL)
+	if impl&_IMPL_POWER8 != 0 {
+		PPC64.IsPOWER8 = true
+	}
+	if impl&_IMPL_POWER9 != 0 {
+		PPC64.IsPOWER9 = true
+	}
+
+	Initialized = true
+}
+
+func getsystemcfg(label int) (n uint64) {
+	r0, _ := callgetsystemcfg(label)
+	n = uint64(r0)
+	return
+}
diff --git a/vendor/golang.org/x/sys/cpu/cpu_gccgo.c b/vendor/golang.org/x/sys/cpu/cpu_gccgo.c
new file mode 100644
index 000000000..e363c7d13
--- /dev/null
+++ b/vendor/golang.org/x/sys/cpu/cpu_gccgo.c
@@ -0,0 +1,43 @@
+// Copyright 2018 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build 386 amd64 amd64p32
+// +build gccgo
+
+#include <cpuid.h>
+#include <stdint.h>
+
+// Need to wrap __get_cpuid_count because it's declared as static.
+int
+gccgoGetCpuidCount(uint32_t leaf, uint32_t subleaf,
+                   uint32_t *eax, uint32_t *ebx,
+                   uint32_t *ecx, uint32_t *edx)
+{
+	return __get_cpuid_count(leaf, subleaf, eax, ebx, ecx, edx);
+}
+
+// xgetbv reads the contents of an XCR (Extended Control Register)
+// specified in the ECX register into registers EDX:EAX.
+// Currently, the only supported value for XCR is 0.
+//
+// TODO: Replace with a better alternative:
+//
+//     #include <xsaveintrin.h>
+//
+//     #pragma GCC target("xsave")
+//
+//     void gccgoXgetbv(uint32_t *eax, uint32_t *edx) {
+//       unsigned long long x = _xgetbv(0);
+//       *eax = x & 0xffffffff;
+//       *edx = (x >> 32) & 0xffffffff;
+//     }
+//
+// Note that _xgetbv is defined starting with GCC 8.
+void
+gccgoXgetbv(uint32_t *eax, uint32_t *edx)
+{
+	__asm("  xorl %%ecx, %%ecx\n"
+	      "  xgetbv"
+	    : "=a"(*eax), "=d"(*edx));
+}
diff --git a/vendor/golang.org/x/sys/cpu/cpu_gccgo.go b/vendor/golang.org/x/sys/cpu/cpu_gccgo.go
new file mode 100644
index 000000000..ba49b91bd
--- /dev/null
+++ b/vendor/golang.org/x/sys/cpu/cpu_gccgo.go
@@ -0,0 +1,26 @@
+// Copyright 2018 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build 386 amd64 amd64p32
+// +build gccgo
+
+package cpu
+
+//extern gccgoGetCpuidCount
+func gccgoGetCpuidCount(eaxArg, ecxArg uint32, eax, ebx, ecx, edx *uint32)
+
+func cpuid(eaxArg, ecxArg uint32) (eax, ebx, ecx, edx uint32) {
+	var a, b, c, d uint32
+	gccgoGetCpuidCount(eaxArg, ecxArg, &a, &b, &c, &d)
+	return a, b, c, d
+}
+
+//extern gccgoXgetbv
+func gccgoXgetbv(eax, edx *uint32)
+
+func xgetbv() (eax, edx uint32) {
+	var a, d uint32
+	gccgoXgetbv(&a, &d)
+	return a, d
+}