From ec095bba839ce375599b509e9a4e30fb0127c336 Mon Sep 17 00:00:00 2001 From: arnaucube Date: Mon, 11 Jan 2021 21:08:46 +0100 Subject: [PATCH] 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 | 2 +- blindsecp256k1.go | 72 +++++------ go.mod | 1 + go.sum | 194 ++++++++++++++++++++++++++++ v0/README.md | 5 + v0/blindsecp256k1v0.go | 214 +++++++++++++++++++++++++++++++ v0/blindsecp256k1v0_test.go | 30 +++++ wasm/blindsecp256k1-wasm.go | 90 ++++++++++++- wasm/webtest/blindsecp256k1.wasm | Bin 4188393 -> 6091254 bytes wasm/webtest/index.js | 13 +- 10 files changed, 576 insertions(+), 45 deletions(-) create mode 100644 v0/README.md create mode 100644 v0/blindsecp256k1v0.go create mode 100644 v0/blindsecp256k1v0_test.go diff --git a/README.md b/README.md index 9b2869b..fdf202b 100644 --- a/README.md +++ b/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. diff --git a/blindsecp256k1.go b/blindsecp256k1.go index 0f5136b..96d7f7b 100644 --- a/blindsecp256k1.go +++ b/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 diff --git a/go.mod b/go.mod index 8b6ff38..7d51625 100644 --- a/go.mod +++ b/go.mod @@ -4,5 +4,6 @@ go 1.14 require ( 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h1:DsYFclhRJ6vuDpmuTbkuFWG+y2sxOXAzmJt81HFBacw= diff --git a/v0/README.md b/v0/README.md new file mode 100644 index 0000000..c827578 --- /dev/null +++ b/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 diff --git a/v0/blindsecp256k1v0.go b/v0/blindsecp256k1v0.go new file mode 100644 index 0000000..87dbcd3 --- /dev/null +++ b/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 +} diff --git a/v0/blindsecp256k1v0_test.go b/v0/blindsecp256k1v0_test.go new file mode 100644 index 0000000..5d616c6 --- /dev/null +++ b/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) +} diff --git a/wasm/blindsecp256k1-wasm.go b/wasm/blindsecp256k1-wasm.go index 5dad320..8e2553c 100644 --- a/wasm/blindsecp256k1-wasm.go +++ b/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: 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