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// Package blindsecp256k1 implements the Blind signature scheme explained at
// "New Blind Signature Schemes Based on the (Elliptic Curve) Discrete
// Logarithm Problem", by Hamid Mala & Nafiseh Nezhadansari
// https://sci-hub.do/10.1109/ICCKE.2013.6682844
//
// LICENSE can be found at https://github.com/arnaucube/go-blindsecp256k1/blob/master/LICENSE
//
package blindsecp256k1
// WARNING: WIP code
import (
"bytes"
"crypto/rand"
"math/big"
"github.com/btcsuite/btcd/btcec"
"github.com/ethereum/go-ethereum/crypto"
)
var (
// G represents the base point of secp256k1
G *Point = &Point{
X: btcec.S256().Gx,
Y: btcec.S256().Gy,
}
// N represents the order of G of secp256k1
N *big.Int = btcec.S256().N
)
// Point represents a point on the secp256k1 curve
type Point struct {
X *big.Int
Y *big.Int
}
// Add performs the Point addition
func (p *Point) Add(q *Point) *Point {
x, y := btcec.S256().Add(p.X, p.Y, q.X, q.Y)
return &Point{
X: x,
Y: y,
}
}
// Mul performs the Point scalar multiplication
func (p *Point) Mul(scalar *big.Int) *Point {
x, y := btcec.S256().ScalarMult(p.X, p.Y, scalar.Bytes())
return &Point{
X: x,
Y: y,
}
}
// WIP
func newRand() *big.Int {
var b [32]byte
_, err := rand.Read(b[:])
if err != nil {
panic(err)
}
bi := new(big.Int).SetBytes(b[:])
return new(big.Int).Mod(bi, N)
}
// PrivateKey represents the signer's private key
type PrivateKey big.Int
// PublicKey represents the signer's public key
type PublicKey Point
// NewPrivateKey returns a new random private key
func NewPrivateKey() *PrivateKey {
k := newRand()
sk := PrivateKey(*k)
return &sk
}
// BigInt returns a *big.Int representation of the PrivateKey
func (sk *PrivateKey) BigInt() *big.Int {
return (*big.Int)(sk)
}
// Public returns the PublicKey from the PrivateKey
func (sk *PrivateKey) Public() *PublicKey {
Q := G.Mul(sk.BigInt())
pk := PublicKey(*Q)
return &pk
}
// Point returns a *Point representation of the PublicKey
func (pk *PublicKey) Point() *Point {
return (*Point)(pk)
}
// NewRequestParameters returns a new random k (secret) & R (public) parameters
func NewRequestParameters() (*big.Int, *Point) {
k := newRand()
return k, G.Mul(k) // R = kG
}
// BlindSign performs the blind signature on the given mBlinded using the
// PrivateKey and the secret k values
func (sk *PrivateKey) BlindSign(mBlinded *big.Int, k *big.Int) *big.Int {
// TODO add pending checks
// s' = dm' + k
sBlind := new(big.Int).Add(
new(big.Int).Mul(sk.BigInt(), mBlinded),
k)
return sBlind
}
// UserSecretData contains the secret values from the User (a, b, c) and the
// public F
type UserSecretData struct {
A *big.Int
B *big.Int
F *Point // public (in the paper is R)
}
// Blind performs the blinding operation on m using signerR parameter
func Blind(m *big.Int, signerR *Point) (*big.Int, *UserSecretData) {
u := &UserSecretData{}
u.A = newRand()
u.B = newRand()
// (R) F = aR' + bG
aR := signerR.Mul(u.A)
bG := G.Mul(u.B)
u.F = aR.Add(bG)
// TODO check that F != O (point at infinity)
rx := new(big.Int).Mod(u.F.X, N)
// m' = a^-1 rx h(m)
ainv := new(big.Int).ModInverse(u.A, N)
ainvrx := new(big.Int).Mul(ainv, rx)
hBytes := crypto.Keccak256(m.Bytes())
h := new(big.Int).SetBytes(hBytes)
mBlinded := new(big.Int).Mul(ainvrx, h)
return mBlinded, u
}
// Signature contains the signature values S & F
type Signature struct {
S *big.Int
F *Point
}
// Unblind performs the unblinding operation of the blinded signature for the
// given message m and the UserSecretData
func Unblind(sBlind, m *big.Int, u *UserSecretData) *Signature {
// s = a s' + b
as := new(big.Int).Mul(u.A, sBlind)
s := new(big.Int).Add(as, u.B)
return &Signature{
S: s,
F: u.F,
}
}
// Verify checks the signature of the message m for the given PublicKey
func Verify(m *big.Int, s *Signature, q *PublicKey) bool {
// TODO add pending checks
sG := G.Mul(s.S) // sG
hBytes := crypto.Keccak256(m.Bytes())
h := new(big.Int).SetBytes(hBytes)
rx := new(big.Int).Mod(s.F.X, N)
rxh := new(big.Int).Mul(rx, h)
// rxhG := G.Mul(rxh) // originally the paper uses G
rxhG := q.Point().Mul(rxh)
right := s.F.Add(rxhG)
// check sG == R + rx h(m) G (where R in this code is F)
if bytes.Equal(sG.X.Bytes(), right.X.Bytes()) &&
bytes.Equal(sG.Y.Bytes(), right.Y.Bytes()) {
return true
}
return false
}