// EncodedBytesToBigIntPoint converts a 32 byte representation of a point
// on the elliptical curve into a big integer point. It returns an error
// if the point does not fall on the curve.
func (curve *TwistedEdwardsCurve) EncodedBytesToBigIntPoint(s *[32]byte) (*big.Int,
*big.Int, error) {
sCopy := new([32]byte)
for i := 0; i < fieldIntSize; i++ {
sCopy[i] = s[i]
}
xIsNegBytes := sCopy[31]>>7 == 1
p := new(edwards25519.ExtendedGroupElement)
if p.FromBytes(sCopy) == false {
return nil, nil, fmt.Errorf("point not on curve")
}
// Normalize the X and Y coordinates in affine space.
x, y, isNegative := curve.extendedToBigAffine(&p.X, &p.Y, &p.Z)
// We got the wrong sign; flip the bit and recalculate.
if xIsNegBytes != isNegative {
x.Sub(curve.P, x)
}
// This should hopefully never happen, since the
// library itself should never let us create a bad
// point.
if !curve.IsOnCurve(x, y) {
return nil, nil, fmt.Errorf("point not on curve")
}
return x, y, nil
}
// 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) {
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)
}
}
// 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
}
// Add adds two points represented by pairs of big integers on the elliptical
// curve.
func (curve *TwistedEdwardsCurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) {
// Convert to extended from affine.
a := BigIntPointToEncodedBytes(x1, y1)
aEGE := new(edwards25519.ExtendedGroupElement)
aEGE.FromBytes(a)
b := BigIntPointToEncodedBytes(x2, y2)
bEGE := new(edwards25519.ExtendedGroupElement)
bEGE.FromBytes(b)
// Cache b for use in group element addition.
bCached := new(cachedGroupElement)
toCached(bCached, bEGE)
p := aEGE
q := bCached
// geAdd(r*CompletedGroupElement, p*ExtendedGroupElement,
// q*CachedGroupElement)
// r is the result.
r := new(edwards25519.CompletedGroupElement)
var t0 edwards25519.FieldElement
edwards25519.FeAdd(&r.X, &p.Y, &p.X)
edwards25519.FeSub(&r.Y, &p.Y, &p.X)
edwards25519.FeMul(&r.Z, &r.X, &q.yPlusX)
edwards25519.FeMul(&r.Y, &r.Y, &q.yMinusX)
edwards25519.FeMul(&r.T, &q.T2d, &p.T)
edwards25519.FeMul(&r.X, &p.Z, &q.Z)
edwards25519.FeAdd(&t0, &r.X, &r.X)
edwards25519.FeSub(&r.X, &r.Z, &r.Y)
edwards25519.FeAdd(&r.Y, &r.Z, &r.Y)
edwards25519.FeAdd(&r.Z, &t0, &r.T)
edwards25519.FeSub(&r.T, &t0, &r.T)
rEGE := new(edwards25519.ExtendedGroupElement)
r.ToExtended(rEGE)
s := new([32]byte)
rEGE.ToBytes(s)
x, y, _ = curve.EncodedBytesToBigIntPoint(s)
return
}
// Double adds the same pair of big integer coordinates to itself on the
// elliptical curve.
func (curve *TwistedEdwardsCurve) Double(x1, y1 *big.Int) (x, y *big.Int) {
// Convert to extended projective coordinates.
a := BigIntPointToEncodedBytes(x1, y1)
aEGE := new(edwards25519.ExtendedGroupElement)
aEGE.FromBytes(a)
r := new(edwards25519.CompletedGroupElement)
aEGE.Double(r)
rEGE := new(edwards25519.ExtendedGroupElement)
r.ToExtended(rEGE)
s := new([32]byte)
rEGE.ToBytes(s)
x, y, _ = curve.EncodedBytesToBigIntPoint(s)
return
}
// SignFromScalar signs a message 'hash' using the given private scalar priv.
// It uses RFC6979 to generate a deterministic nonce. Considered experimental.
// r = kG, where k is the RFC6979 nonce
// s = r + hash512(k || A || M) * a
func SignFromScalar(curve *TwistedEdwardsCurve, priv *PrivateKey,
nonce []byte, hash []byte) (r, s *big.Int, err error) {
publicKey := new([PubKeyBytesLen]byte)
var A edwards25519.ExtendedGroupElement
privateScalar := copyBytes(priv.Serialize())
reverse(privateScalar) // BE --> LE
edwards25519.GeScalarMultBase(&A, privateScalar)
A.ToBytes(publicKey)
// For signing from a scalar, r = nonce.
nonceLE := copyBytes(nonce)
reverse(nonceLE)
var R edwards25519.ExtendedGroupElement
edwards25519.GeScalarMultBase(&R, nonceLE)
var encodedR [32]byte
R.ToBytes(&encodedR)
// h = hash512(k || A || M)
h := sha512.New()
h.Reset()
h.Write(encodedR[:])
h.Write(publicKey[:])
h.Write(hash)
// s = r + h * a
var hramDigest [64]byte
h.Sum(hramDigest[:0])
var hramDigestReduced [32]byte
edwards25519.ScReduce(&hramDigestReduced, &hramDigest)
var localS [32]byte
edwards25519.ScMulAdd(&localS, &hramDigestReduced, privateScalar,
nonceLE)
signature := new([64]byte)
copy(signature[:], encodedR[:])
copy(signature[32:], localS[:])
sigEd, err := ParseSignature(curve, signature[:])
if err != nil {
return nil, nil, err
}
return sigEd.GetR(), sigEd.GetS(), nil
}
// ScalarMult returns k*(Bx,By) where k is a number in big-endian form. This
// uses the repeated doubling method, which is variable time.
// TODO use a constant time method to prevent side channel attacks.
func (curve *TwistedEdwardsCurve) ScalarMult(x1, y1 *big.Int,
k []byte) (x, y *big.Int) {
// Convert the scalar to a big int.
s := new(big.Int).SetBytes(k)
// Get a new group element to do cached doubling
// calculations in.
dEGE := new(edwards25519.ExtendedGroupElement)
dEGE.Zero()
// Use the doubling method for the multiplication.
// p := given point
// q := point(zero)
// for each bit in the scalar, descending:
// double(q)
// if bit == 1:
// add(q, p)
// return q
//
// Note that the addition is skipped for zero bits,
// making this variable time and thus vulnerable to
// side channel attack vectors.
for i := s.BitLen() - 1; i >= 0; i-- {
dCGE := new(edwards25519.CompletedGroupElement)
dEGE.Double(dCGE)
dCGE.ToExtended(dEGE)
if s.Bit(i) == 1 {
ss := new([32]byte)
dEGE.ToBytes(ss)
var err error
xi, yi, err := curve.EncodedBytesToBigIntPoint(ss)
if err != nil {
return nil, nil
}
xAdd, yAdd := curve.Add(xi, yi, x1, y1)
dTempBytes := BigIntPointToEncodedBytes(xAdd, yAdd)
dEGE.FromBytes(dTempBytes)
}
}
finalBytes := new([32]byte)
dEGE.ToBytes(finalBytes)
var err error
x, y, err = curve.EncodedBytesToBigIntPoint(finalBytes)
if err != nil {
return nil, nil
}
return
}