Implement https://sci-hub.do/10.1109/ICCKE.2013.6682844

Previous to this commit there was the implementation of "[An Efficient Blind Signature Scheme Based on the Elliptic Curve Discrete Logarithm Problem](http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf)" paper by by Morteza Nikooghadama & Ali Zakerolhosseini.

This commit adds the implementation of "[New Blind Signature Schemes Based on the (Elliptic Curve) Discrete Logarithm Problem](https://sci-hub.do/10.1109/ICCKE.2013.6682844)" paper by Hamid Mala & Nafiseh Nezhadansari.

README.md

@@ -1,6 +1,6 @@
 # go-blindsecp256k1 [![GoDoc](https://godoc.org/github.com/arnaucube/go-blindsecp256k1?status.svg)](https://godoc.org/github.com/arnaucube/go-blindsecp256k1) [![Go Report Card](https://goreportcard.com/badge/github.com/arnaucube/go-blindsecp256k1)](https://goreportcard.com/report/github.com/arnaucube/go-blindsecp256k1) [![Test](https://github.com/arnaucube/go-blindsecp256k1/workflows/Test/badge.svg)](https://github.com/arnaucube/go-blindsecp256k1/actions?query=workflow%3ATest)
 
-Blind signature over [secp256k1](https://en.bitcoin.it/wiki/Secp256k1), based on *"[An Efficient Blind Signature Scheme Based on the Elliptic Curve Discrete Logarithm Problem](http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf)"* paper.
+Blind signature over [secp256k1](https://en.bitcoin.it/wiki/Secp256k1), based on *"[New Blind Signature Schemes Based on the (Elliptic Curve) Discrete Logarithm Problem](https://sci-hub.do/10.1109/ICCKE.2013.6682844)"* paper by Hamid Mala & Nafiseh Nezhadansari.
 
 **WARNING**: this repo is experimental, do not use in production.
 

blindsecp256k1.go

@@ -1,5 +1,7 @@
 // Package blindsecp256k1 implements the Blind signature scheme explained at
-// http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf
+// "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
 //
@@ -13,6 +15,7 @@ import (
 	"math/big"
 
 	"github.com/btcsuite/btcd/btcec"
+	"github.com/ethereum/go-ethereum/crypto"
 )
 
 var (
@@ -127,7 +130,7 @@ func (signer *SignerPrivateData) PublicData() *SignerPublicData {
 // SignerPrivateData values
 func (signer *SignerPrivateData) BlindSign(mBlinded *big.Int) *big.Int {
 	// TODO add pending checks
-	// s' = d(m') + k
+	// s' = dm' + k
 	sBlind := new(big.Int).Add(
 		new(big.Int).Mul(signer.D.BigInt(), mBlinded),
 		signer.K)
@@ -139,9 +142,8 @@ func (signer *SignerPrivateData) BlindSign(mBlinded *big.Int) *big.Int {
 type UserSecretData struct {
 	A *big.Int
 	B *big.Int
-	C *big.Int
 
-	F *Point // public
+	F *Point // public (in the paper is R)
 }
 
 // Blind performs the blinding operation on m using SignerPublicData parameters
@@ -149,25 +151,21 @@ func Blind(m *big.Int, signer *SignerPublicData) (*big.Int, *UserSecretData) {
 	u := &UserSecretData{}
 	u.A = newRand()
 	u.B = newRand()
-	u.C = newRand()
-	binv := new(big.Int).ModInverse(u.B, N)
-
-	// F = b^-1 R + a b^-1 Q + c G
-	bR := signer.R.Mul(binv)
-	abinv := new(big.Int).Mul(u.A, binv)
-	abinv = new(big.Int).Mod(abinv, N)
-	abQ := signer.Q.Point().Mul(abinv)
-	cG := G.Mul(u.C)
-	u.F = bR.Add(abQ).Add(cG)
-	// TODO check F==O
-
-	r := new(big.Int).Mod(u.F.X, N)
-
-	// m' = br(m)+a
-	br := new(big.Int).Mul(u.B, r)
-	brm := new(big.Int).Mul(br, m)
-	mBlinded := new(big.Int).Add(brm, u.A)
-	mBlinded = new(big.Int).Mod(mBlinded, N)
+
+	// (R) F = aR' + bG
+	aR := signer.R.Mul(u.A)
+	bG := G.Mul(u.B)
+	u.F = aR.Add(bG)
+
+	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
 }
 
@@ -180,11 +178,9 @@ type Signature struct {
 // 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 = b^-1 s' + c
-	binv := new(big.Int).ModInverse(u.B, N)
-	bs := new(big.Int).Mul(binv, sBlind)
-	s := new(big.Int).Add(bs, u.C)
-	s = new(big.Int).Mod(s, N)
+	// s = a s' + b
+	as := new(big.Int).Mul(u.A, sBlind)
+	s := new(big.Int).Add(as, u.B)
 
 	return &Signature{
 		S: s,
@@ -197,15 +193,19 @@ func Verify(m *big.Int, signature *Signature, q *PublicKey) bool {
 	// TODO add pending checks
 	sG := G.Mul(signature.S) // sG
 
-	r := new(big.Int).Mod(signature.F.X, N) // r = Fx mod N
-	rm := new(big.Int).Mul(r, m)
-	rm = new(big.Int).Mod(rm, N)
-	rmQ := q.Point().Mul(rm)
-	rmQF := rmQ.Add(signature.F) // rmQ + F
+	hBytes := crypto.Keccak256(m.Bytes())
+	h := new(big.Int).SetBytes(hBytes)
+
+	rx := new(big.Int).Mod(signature.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 := signature.F.Add(rxhG)
 
-	// check sG == rmQ + F
-	if bytes.Equal(sG.X.Bytes(), rmQF.X.Bytes()) &&
-		bytes.Equal(sG.Y.Bytes(), rmQF.Y.Bytes()) {
+	// 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

go.mod

@@ -4,5 +4,6 @@ go 1.14
 
 require (
 	github.com/btcsuite/btcd v0.0.0-20171128150713-2e60448ffcc6
+	github.com/ethereum/go-ethereum v1.9.25
 	github.com/stretchr/testify v1.6.1
 )

go.sum

@@ -1,12 +1,206 @@
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 gopkg.in/yaml.v3 v3.0.0-20200313102051-9f266ea9e77c h1:dUUwHk2QECo/6vqA44rthZ8ie2QXMNeKRTHCNY2nXvo=
 gopkg.in/yaml.v3 v3.0.0-20200313102051-9f266ea9e77c/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM=
+gotest.tools v2.2.0+incompatible/go.mod h1:DsYFclhRJ6vuDpmuTbkuFWG+y2sxOXAzmJt81HFBacw=

v0/README.md

@@ -0,0 +1,5 @@
+# go-blindsecp256k1/v0
+
+The directory `v0` implements the blind signature over [secp256k1](https://en.bitcoin.it/wiki/Secp256k1), based on *"[An Efficient Blind Signature Scheme Based on the Elliptic Curve Discrete Logarithm Problem](http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf)"* paper by by Morteza Nikooghadama & Ali Zakerolhosseini.
+
+The implementation of *"[New Blind Signature Schemes Based on the (Elliptic Curve) Discrete Logarithm Problem](https://sci-hub.do/10.1109/ICCKE.2013.6682844)"* paper by Hamid Mala & Nafiseh Nezhadansari, can be found at the root directory of this repository: https://github.com/arnaucube/go-blindsecp256k1

v0/blindsecp256k1v0.go

@@ -0,0 +1,214 @@
+// Package blindsecp256k1v0 implements the Blind signature scheme explained at
+// "An Efficient Blind Signature Scheme Based on the Elliptic Curve Discrete
+// Logarithm Problem", by Morteza Nikooghadama & Ali Zakerolhosseini
+// http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf
+//
+// LICENSE can be found at https://github.com/arnaucube/go-blindsecp256k1/blob/master/LICENSE
+//
+package blindsecp256k1v0
+
+// WARNING: WIP code
+
+import (
+	"bytes"
+	"crypto/rand"
+	"math/big"
+
+	"github.com/btcsuite/btcd/btcec"
+)
+
+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)
+}
+
+// SignerPrivateData contains the secret values from the Signer
+type SignerPrivateData struct {
+	D *PrivateKey
+	K *big.Int
+}
+
+// SignerPublicData contains the public values from the Signer (generated from
+// its SignerPrivateData)
+type SignerPublicData struct {
+	// Q is the Signer Public Key
+	Q *PublicKey // = skG
+	R *Point     // = kG
+}
+
+// NewSigner returns a new SignerPrivateData with random D & K
+func NewSigner() *SignerPrivateData {
+	sk := NewPrivateKey()
+	k := newRand()
+	return &SignerPrivateData{
+		D: sk,
+		K: k,
+	}
+}
+
+// PublicData returns the SignerPublicData from the SignerPrivateData
+func (signer *SignerPrivateData) PublicData() *SignerPublicData {
+	return &SignerPublicData{
+		Q: signer.D.Public(), // Q = dG
+		R: G.Mul(signer.K),   // R = kG
+	}
+}
+
+// BlindSign performs the blind signature on the given mBlinded using
+// SignerPrivateData values
+func (signer *SignerPrivateData) BlindSign(mBlinded *big.Int) *big.Int {
+	// TODO add pending checks
+	// s' = d(m') + k
+	sBlind := new(big.Int).Add(
+		new(big.Int).Mul(signer.D.BigInt(), mBlinded),
+		signer.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
+	C *big.Int
+
+	F *Point // public
+}
+
+// Blind performs the blinding operation on m using SignerPublicData parameters
+func Blind(m *big.Int, signer *SignerPublicData) (*big.Int, *UserSecretData) {
+	u := &UserSecretData{}
+	u.A = newRand()
+	u.B = newRand()
+	u.C = newRand()
+	binv := new(big.Int).ModInverse(u.B, N)
+
+	// F = b^-1 R + a b^-1 Q + c G
+	bR := signer.R.Mul(binv)
+	abinv := new(big.Int).Mul(u.A, binv)
+	abinv = new(big.Int).Mod(abinv, N)
+	abQ := signer.Q.Point().Mul(abinv)
+	cG := G.Mul(u.C)
+	u.F = bR.Add(abQ).Add(cG)
+	// TODO check F==O
+
+	r := new(big.Int).Mod(u.F.X, N)
+
+	// m' = br(m)+a
+	br := new(big.Int).Mul(u.B, r)
+	brm := new(big.Int).Mul(br, m)
+	mBlinded := new(big.Int).Add(brm, u.A)
+	mBlinded = new(big.Int).Mod(mBlinded, N)
+	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 = b^-1 s' + c
+	binv := new(big.Int).ModInverse(u.B, N)
+	bs := new(big.Int).Mul(binv, sBlind)
+	s := new(big.Int).Add(bs, u.C)
+	s = new(big.Int).Mod(s, N)
+
+	return &Signature{
+		S: s,
+		F: u.F,
+	}
+}
+
+// Verify checks the signature of the message m for the given PublicKey
+func Verify(m *big.Int, signature *Signature, q *PublicKey) bool {
+	// TODO add pending checks
+	sG := G.Mul(signature.S) // sG
+
+	r := new(big.Int).Mod(signature.F.X, N) // r = Fx mod N
+	rm := new(big.Int).Mul(r, m)
+	rm = new(big.Int).Mod(rm, N)
+	rmQ := q.Point().Mul(rm)
+	rmQF := rmQ.Add(signature.F) // rmQ + F
+
+	// check sG == rmQ + F
+	if bytes.Equal(sG.X.Bytes(), rmQF.X.Bytes()) &&
+		bytes.Equal(sG.Y.Bytes(), rmQF.Y.Bytes()) {
+		return true
+	}
+	return false
+}

v0/blindsecp256k1v0_test.go

@@ -0,0 +1,30 @@
+package blindsecp256k1v0
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestFlow(t *testing.T) {
+	// message to be signed
+	msg := new(big.Int).SetBytes([]byte("test"))
+
+	// create new signer
+	signerPrivateData := NewSigner()
+	signerPublicData := signerPrivateData.PublicData()
+
+	// user blinds the msg
+	msgBlinded, user := Blind(msg, signerPublicData)
+
+	// signer signs the blinded message
+	sBlind := signerPrivateData.BlindSign(msgBlinded)
+
+	// user unblinds the blinded signature
+	sig := Unblind(sBlind, msg, user)
+
+	// signature can be verified with signer PublicKey (Q)
+	verified := Verify(msg, sig, signerPublicData.Q)
+	assert.True(t, verified)
+}

wasm/blindsecp256k1-wasm.go

@@ -5,6 +5,8 @@ import (
 	"fmt"
 	"math/big"
 	"syscall/js"
+
+	blindsecp256k1v0 "blindsecp256k1/v0"
 )
 
 func main() {
@@ -15,6 +17,12 @@ func main() {
 }
 
 func registerCallbacks() {
+	// blindv0 & unblindv0 uses:
+	// http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf
+	js.Global().Set("blindv0", js.FuncOf(blindv0))
+	js.Global().Set("unblindv0", js.FuncOf(unblindv0))
+
+	// blind & unblind uses: https://sci-hub.do/10.1109/ICCKE.2013.6682844
 	js.Global().Set("blind", js.FuncOf(blind))
 	js.Global().Set("unblind", js.FuncOf(unblind))
 }
@@ -27,6 +35,77 @@ func stringToBigInt(s string) *big.Int {
 	return b
 }
 
+func blindv0(this js.Value, values []js.Value) interface{} {
+	mStr := values[0].String()
+	signerQxStr := values[1].String()
+	signerQyStr := values[2].String()
+	signerRxStr := values[3].String()
+	signerRyStr := values[4].String()
+
+	m := stringToBigInt(mStr)
+	signerQx := stringToBigInt(signerQxStr)
+	signerQy := stringToBigInt(signerQyStr)
+	signerRx := stringToBigInt(signerRxStr)
+	signerRy := stringToBigInt(signerRyStr)
+
+	signerQ := &blindsecp256k1v0.PublicKey{
+		X: signerQx,
+		Y: signerQy,
+	}
+	signerR := &blindsecp256k1v0.Point{
+		X: signerRx,
+		Y: signerRy,
+	}
+
+	signer := &blindsecp256k1v0.SignerPublicData{signerQ, signerR}
+	mBlinded, user := blindsecp256k1v0.Blind(m, signer)
+
+	r := make(map[string]interface{})
+	r["mBlinded"] = mBlinded.String()
+	r["uA"] = user.A.String()
+	r["uB"] = user.B.String()
+	r["uC"] = user.C.String()
+	r["uC"] = user.C.String()
+	r["uFx"] = user.F.X.String()
+	r["uFy"] = user.F.Y.String()
+	return r
+}
+
+func unblindv0(this js.Value, values []js.Value) interface{} {
+	sBlindStr := values[0].String()
+	mStr := values[1].String()
+	uBStr := values[2].String()
+	uCStr := values[3].String()
+	uFxStr := values[4].String()
+	uFyStr := values[5].String()
+
+	sBlind := stringToBigInt(sBlindStr)
+	m := stringToBigInt(mStr)
+	uB := stringToBigInt(uBStr)
+	uC := stringToBigInt(uCStr)
+	uFx := stringToBigInt(uFxStr)
+	uFy := stringToBigInt(uFyStr)
+
+	uF := &blindsecp256k1v0.Point{
+		X: uFx,
+		Y: uFy,
+	}
+
+	u := &blindsecp256k1v0.UserSecretData{
+		// A not needed to Unblind
+		B: uB,
+		C: uC,
+		F: uF,
+	}
+
+	sig := blindsecp256k1v0.Unblind(sBlind, m, u)
+
+	r := make(map[string]interface{})
+	r["s"] = sig.S.String()
+	r["fx"] = sig.F.X.String()
+	r["fy"] = sig.F.Y.String()
+	return r
+}
 func blind(this js.Value, values []js.Value) interface{} {
 	mStr := values[0].String()
 	signerQxStr := values[1].String()
@@ -56,8 +135,6 @@ func blind(this js.Value, values []js.Value) interface{} {
 	r["mBlinded"] = mBlinded.String()
 	r["uA"] = user.A.String()
 	r["uB"] = user.B.String()
-	r["uC"] = user.C.String()
-	r["uC"] = user.C.String()
 	r["uFx"] = user.F.X.String()
 	r["uFy"] = user.F.Y.String()
 	return r
@@ -66,15 +143,15 @@ func blind(this js.Value, values []js.Value) interface{} {
 func unblind(this js.Value, values []js.Value) interface{} {
 	sBlindStr := values[0].String()
 	mStr := values[1].String()
-	uBStr := values[2].String()
-	uCStr := values[3].String()
+	uAStr := values[2].String()
+	uBStr := values[3].String()
 	uFxStr := values[4].String()
 	uFyStr := values[5].String()
 
 	sBlind := stringToBigInt(sBlindStr)
 	m := stringToBigInt(mStr)
+	uA := stringToBigInt(uAStr)
 	uB := stringToBigInt(uBStr)
-	uC := stringToBigInt(uCStr)
 	uFx := stringToBigInt(uFxStr)
 	uFy := stringToBigInt(uFyStr)
 
@@ -84,9 +161,8 @@ func unblind(this js.Value, values []js.Value) interface{} {
 	}
 
 	u := &blindsecp256k1.UserSecretData{
-		// A not needed to Unblind
+		A: uA,
 		B: uB,
-		C: uC,
 		F: uF,
 	}
 

wasm/webtest/index.js

@@ -1,6 +1,7 @@
 function test() {
 	let m = "1952805748";
 
+	console.log("using: https://sci-hub.do/10.1109/ICCKE.2013.6682844");
 	// Q & R would be received from the Signer
 	let signerQx = "26613296432153871833441195158297038913673464785502568519907582377915678491093";
 	let signerQy = "81940194042971427014176158889809922552127995083760111384335138546589994227275";
@@ -11,6 +12,16 @@ function test() {
 
 	// sBlind would be received from the Signer
 	let sBlind = "7240298625621589352655632414257224668430424461224914067754717095121139699933353374227084479180038954015287518505167995306229258561275087198611946596619855";
-	let unblindRes = unblind(sBlind, m, blindRes.uB, blindRes.uC, blindRes.uFx, blindRes.uFy);
+	let unblindRes = unblind(sBlind, m, blindRes.uA, blindRes.uB, blindRes.uFx, blindRes.uFy);
 	console.log("unblind", unblindRes);
+
+	// ---
+	// v0
+	console.log("using: http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf");
+	// Q & R would be received from the Signer
+	blindRes = blindv0(m, signerQx, signerQy, signerRx, signerRy);
+	console.log("blindv0", blindRes);
+	// sBlind would be received from the Signer
+	unblindRes = unblindv0(sBlind, m, blindRes.uB, blindRes.uC, blindRes.uFx, blindRes.uFy);
+	console.log("unblindv0", unblindRes);
 }