// SignThreshold signs a message 'hash' using the given private scalar priv in
// a threshold group signature. It uses RFC6979 to generate a deterministic nonce.
// Considered experimental.
// As opposed to the threshold signing function for secp256k1, this function
// takes the entirety of the public nonce point (all points added) instead of
// the public nonce point with n-1 keys added.
// r = K_Sum
// s = r + hash512(k || A || M) * a
func SignThreshold(curve *TwistedEdwardsCurve, priv *PrivateKey,
groupPub *PublicKey, hash []byte, privNonce *PrivateKey,
pubNonceSum *PublicKey) (r, s *big.Int, err error) {
if priv == nil || hash == nil || privNonce == nil || pubNonceSum == nil {
return nil, nil, fmt.Errorf("nil input")
}
privateScalar := copyBytes(priv.Serialize())
reverse(privateScalar) // BE --> LE
// Threshold variant scheme:
// R = K_Sum
// Where K_Sum is the sum of the public keys corresponding to
// the private nonce scalars of each group signature member.
// That is, R = k1G + ... + knG.
encodedGroupR := BigIntPointToEncodedBytes(pubNonceSum.GetX(),
pubNonceSum.GetY())
// h = hash512(k || A || M)
var hramDigest [64]byte
h := sha512.New()
h.Reset()
h.Write(encodedGroupR[:])
h.Write(groupPub.Serialize()[:])
h.Write(hash)
h.Sum(hramDigest[:0])
var hramDigestReduced [32]byte
edwards25519.ScReduce(&hramDigestReduced, &hramDigest)
// s = r + h * a
var localS [32]byte
privNonceLE := copyBytes(privNonce.Serialize())
reverse(privNonceLE) // BE --> LE
edwards25519.ScMulAdd(&localS, &hramDigestReduced, privateScalar,
privNonceLE)
signature := new([64]byte)
copy(signature[:], encodedGroupR[:])
copy(signature[32:], localS[:])
sigEd, err := ParseSignature(curve, signature[:])
if err != nil {
return nil, nil, err
}
return sigEd.GetR(), sigEd.GetS(), nil
}
// 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
}
// 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
}