// Verify returns true iff sig is a valid signature of message by publicKey.
func Verify(publicKey *[PublicKeySize]byte, message []byte, sig *[SignatureSize]byte) bool {
if sig[63]&224 != 0 {
return false
}
var A edwards25519.ExtendedGroupElement
if !A.FromBytes(publicKey) {
return false
}
edwards25519.FeNeg(&A.X, &A.X)
edwards25519.FeNeg(&A.T, &A.T)
h := sha512.New()
h.Write(sig[:32])
h.Write(publicKey[:])
h.Write(message)
var digest [64]byte
h.Sum(digest[:0])
var hReduced [32]byte
edwards25519.ScReduce(&hReduced, &digest)
var R edwards25519.ProjectiveGroupElement
var b [32]byte
copy(b[:], sig[32:])
edwards25519.GeDoubleScalarMultVartime(&R, &hReduced, &A, &b)
var checkR [32]byte
R.ToBytes(&checkR)
return subtle.ConstantTimeCompare(sig[:32], checkR[:]) == 1
}
// GenerateKey generates a public/private key pair using randomness from rand.
func GenerateKey(rand io.Reader) (publicKey *[PublicKeySize]byte, privateKey *[PrivateKeySize]byte, err error) {
privateKey = new([64]byte)
publicKey = new([32]byte)
_, err = io.ReadFull(rand, privateKey[:32])
if err != nil {
return nil, nil, err
}
h := sha512.New()
h.Write(privateKey[:32])
digest := h.Sum(nil)
digest[0] &= 248
digest[31] &= 127
digest[31] |= 64
var A edwards25519.ExtendedGroupElement
var hBytes [32]byte
copy(hBytes[:], digest)
edwards25519.GeScalarMultBase(&A, &hBytes)
A.ToBytes(publicKey)
copy(privateKey[32:], publicKey[:])
return
}
// PublicKeyToCurve25519 converts an Ed25519 public key into the curve25519
// public key that would be generated from the same private key.
func PublicKeyToCurve25519(curve25519Public *[32]byte, publicKey *[32]byte) bool {
var A edwards25519.ExtendedGroupElement
if !A.FromBytes(publicKey) {
return false
}
// A.Z = 1 as a postcondition of FromBytes.
var x edwards25519.FieldElement
edwardsToMontgomeryX(&x, &A.Y)
edwards25519.FeToBytes(curve25519Public, &x)
return true
}
func TestUnmarshalMarshal(t *testing.T) {
pk, _, _ := GenerateKey(rand.Reader)
var A edwards25519.ExtendedGroupElement
ret := A.FromBytes(pk)
var pk2 [32]byte
A.ToBytes(&pk2)
if *pk != pk2 {
_ = ret
t.Errorf("FromBytes(%v)->ToBytes not idempotent:\n%x\nbytes:\n\t%x\n\t%x\ndelta: %x\n", ret, A, *pk, pk2, int(pk[31])-int(pk2[31]))
}
}
func TestUnmarshalMarshalNegative(t *testing.T) {
pk, _, _ := GenerateKey(rand.Reader)
var A edwards25519.ExtendedGroupElement
ret := A.FromBytes(pk)
var pk2 [32]byte
A.ToBytes(&pk2)
pk2[31] ^= 0x80
if *pk == pk2 {
t.Errorf("flipping sign did not change public key:\n%x\nbytes:\n\t%x\n\t%x\ndelta: %x\n", ret, A, *pk, pk2, int(pk[31])-int(pk2[31]))
}
}
func TestUnmarshalMarshal(t *testing.T) {
pub, _, _ := GenerateKey(rand.Reader)
var A edwards25519.ExtendedGroupElement
if !A.FromBytes(pub) {
t.Fatalf("ExtendedGroupElement.FromBytes failed")
}
var pub2 [32]byte
A.ToBytes(&pub2)
if *pub != pub2 {
t.Errorf("FromBytes(%v)->ToBytes does not round-trip, got %x\n", *pub, pub2)
}
}
// Rederive an Ed25519 public key from a private key.
func Ed25519RederivePublic(privateKey *[64]byte) (publicKey *[32]byte) {
h := sha512.New()
h.Write(privateKey[:32])
digest := h.Sum(nil)
digest[0] &= 248
digest[31] &= 127
digest[31] |= 64
var A edwards25519.ExtendedGroupElement
var hBytes [32]byte
copy(hBytes[:], digest)
edwards25519.GeScalarMultBase(&A, &hBytes)
publicKey = new([32]byte)
A.ToBytes(publicKey)
return
}
// MakePublicKey makes a publicKey from the first half of privateKey.
func MakePublicKey(privateKey *[PrivateKeySize]byte) (publicKey *[PublicKeySize]byte) {
publicKey = new([32]byte)
h := sha512.New()
h.Write(privateKey[:32])
digest := h.Sum(nil)
digest[0] &= 248
digest[31] &= 127
digest[31] |= 64
var A edwards25519.ExtendedGroupElement
var hBytes [32]byte
copy(hBytes[:], digest)
edwards25519.GeScalarMultBase(&A, &hBytes)
A.ToBytes(publicKey)
copy(privateKey[32:], publicKey[:])
return
}
// Sign signs the message with privateKey and returns a signature.
func Sign(privateKey *[PrivateKeySize]byte, message []byte) *[SignatureSize]byte {
h := sha512.New()
h.Write(privateKey[:32])
var digest1, messageDigest, hramDigest [64]byte
var expandedSecretKey [32]byte
h.Sum(digest1[:0])
copy(expandedSecretKey[:], digest1[:])
expandedSecretKey[0] &= 248
expandedSecretKey[31] &= 63
expandedSecretKey[31] |= 64
h.Reset()
h.Write(digest1[32:])
h.Write(message)
h.Sum(messageDigest[:0])
var messageDigestReduced [32]byte
edwards25519.ScReduce(&messageDigestReduced, &messageDigest)
var R edwards25519.ExtendedGroupElement
edwards25519.GeScalarMultBase(&R, &messageDigestReduced)
var encodedR [32]byte
R.ToBytes(&encodedR)
h.Reset()
h.Write(encodedR[:])
h.Write(privateKey[32:])
h.Write(message)
h.Sum(hramDigest[:0])
var hramDigestReduced [32]byte
edwards25519.ScReduce(&hramDigestReduced, &hramDigest)
var s [32]byte
edwards25519.ScMulAdd(&s, &hramDigestReduced, &expandedSecretKey, &messageDigestReduced)
signature := new([64]byte)
copy(signature[:], encodedR[:])
copy(signature[32:], s[:])
return signature
}
// Sign signs the message with privateKey and returns a signature.
func Sign(privateKey *[32]byte, message []byte, random [64]byte) *[64]byte {
// Calculate Ed25519 public key from Curve25519 private key
var A edwards25519.ExtendedGroupElement
var publicKey [32]byte
edwards25519.GeScalarMultBase(&A, privateKey)
A.ToBytes(&publicKey)
// Calculate r
diversifier := [32]byte{
0xFE, 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, 0xFF}
var r [64]byte
h := sha512.New()
h.Write(diversifier[:])
h.Write(privateKey[:])
h.Write(message)
h.Write(random[:])
h.Sum(r[:0])
// Calculate R
var rReduced [32]byte
edwards25519.ScReduce(&rReduced, &r)
var R edwards25519.ExtendedGroupElement
edwards25519.GeScalarMultBase(&R, &rReduced)
var encodedR [32]byte
R.ToBytes(&encodedR)
// Calculate S = r + SHA2-512(R || A_ed || msg) * a (mod L)
var hramDigest [64]byte
h.Reset()
h.Write(encodedR[:])
h.Write(publicKey[:])
h.Write(message)
h.Sum(hramDigest[:0])
var hramDigestReduced [32]byte
edwards25519.ScReduce(&hramDigestReduced, &hramDigest)
var s [32]byte
edwards25519.ScMulAdd(&s, &hramDigestReduced, privateKey, &rReduced)
signature := new([64]byte)
copy(signature[:], encodedR[:])
copy(signature[32:], s[:])
signature[63] |= publicKey[31] & 0x80
return signature
}