Update BabyJubJub signature with Poseidon

Optimize Poseidon

babyjub/eddsa.go

@@ -222,8 +222,8 @@ func (k *PrivateKey) SignPoseidon(msg *big.Int) *Signature {
 	r.Mod(r, SubOrder)
 	R8 := NewPoint().Mul(r, B8) // R8 = r * 8 * B
 	A := k.Public().Point()
-	hmInput := []*big.Int{R8.X, R8.Y, A.X, A.Y, msg}
+	hmInput := [poseidon.T]*big.Int{R8.X, R8.Y, A.X, A.Y, msg, big.NewInt(int64(0))}
-	hm, err := poseidon.Hash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
+	hm, err := poseidon.PoseidonHash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
 	if err != nil {
 		panic(err)
 	}
@@ -238,8 +238,8 @@ func (k *PrivateKey) SignPoseidon(msg *big.Int) *Signature {
 // VerifyPoseidon verifies the signature of a message encoded as a big.Int in Zq
 // using blake-512 hash for buffer hashing and Poseidon for big.Int hashing.
 func (p *PublicKey) VerifyPoseidon(msg *big.Int, sig *Signature) bool {
-	hmInput := []*big.Int{sig.R8.X, sig.R8.Y, p.X, p.Y, msg}
+	hmInput := [poseidon.T]*big.Int{sig.R8.X, sig.R8.Y, p.X, p.Y, msg, big.NewInt(int64(0))}
-	hm, err := poseidon.Hash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
+	hm, err := poseidon.PoseidonHash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
 	if err != nil {
 		panic(err)
 	}

poseidon/poseidon.go

@@ -6,8 +6,7 @@ import (
 	"math/big"
 	"strconv"
 
-	_constants "github.com/iden3/go-iden3-crypto/constants"
+	"github.com/iden3/go-iden3-crypto/constants"
-	"github.com/iden3/go-iden3-crypto/field"
 	"github.com/iden3/go-iden3-crypto/utils"
 	"golang.org/x/crypto/blake2b"
 )
@@ -17,23 +16,20 @@ const NROUNDSF = 8
 const NROUNDSP = 57
 const T = 6
 
-var constants = generateConstantsData()
+var constC []*big.Int
+var constM [T][T]*big.Int
 
-type constantsData struct {
+func Zero() *big.Int {
-	fqR field.Fq
+	return new(big.Int)
-	c   []*big.Int
-	m   [][]*big.Int
 }
 
-func generateConstantsData() constantsData {
+func modQ(v *big.Int) {
-	var constants constantsData
+	v.Mod(v, constants.Q)
+}
 
-	fqR := field.NewFq(_constants.Q)
+func init() {
-	constants.fqR = fqR
+	constC = getPseudoRandom(SEED+"_constants", NROUNDSF+NROUNDSP)
-	constants.c = getPseudoRandom(fqR, SEED+"_constants", NROUNDSF+NROUNDSP)
+	constM = getMDS()
-	constants.m = getMDS(fqR)
-
-	return constants
 }
 
 func leByteArrayToBigInt(b []byte) *big.Int {
@@ -45,14 +41,13 @@ func leByteArrayToBigInt(b []byte) *big.Int {
 	return res
 }
 
-func getPseudoRandom(fqR field.Fq, seed string, n int) []*big.Int {
+func getPseudoRandom(seed string, n int) []*big.Int {
-	var res []*big.Int
+	res := make([]*big.Int, n)
 	hash := blake2b.Sum256([]byte(seed))
-	for len(res) < n {
+	for i := 0; i < n; i++ {
-		hashBigInt := new(big.Int)
+		hashBigInt := Zero()
-		newN := fqR.Affine(utils.SetBigIntFromLEBytes(hashBigInt, hash[:]))
+		res[i] = utils.SetBigIntFromLEBytes(hashBigInt, hash[:])
-		// newN := fqR.Affine(leByteArrayToBigInt(hash[:]))
+		modQ(res[i])
-		res = append(res, newN)
 		hash = blake2b.Sum256(hash[:])
 	}
 	return res
@@ -67,20 +62,20 @@ func nonceToString(n int) string {
 }
 
 // https://eprint.iacr.org/2019/458.pdf pag.8
-func getMDS(fqR field.Fq) [][]*big.Int {
+func getMDS() [T][T]*big.Int {
 	nonce := 0
-	cauchyMatrix := getPseudoRandom(fqR, SEED+"_matrix_"+nonceToString(nonce), T*2)
+	cauchyMatrix := getPseudoRandom(SEED+"_matrix_"+nonceToString(nonce), T*2)
 	for !checkAllDifferent(cauchyMatrix) {
 		nonce += 1
-		cauchyMatrix = getPseudoRandom(fqR, SEED+"_matrix_"+nonceToString(nonce), T*2)
+		cauchyMatrix = getPseudoRandom(SEED+"_matrix_"+nonceToString(nonce), T*2)
 	}
-	var m [][]*big.Int
+	var m [T][T]*big.Int
 	for i := 0; i < T; i++ {
-		var mi []*big.Int
+		// var mi []*big.Int
 		for j := 0; j < T; j++ {
-			mi = append(mi, fqR.Inverse(fqR.Sub(cauchyMatrix[i], cauchyMatrix[T+j])))
+			m[i][j] = new(big.Int).Sub(cauchyMatrix[i], cauchyMatrix[T+j])
+			m[i][j].ModInverse(m[i][j], constants.Q)
 		}
-		m = append(m, mi)
 	}
 	return m
 }
@@ -100,61 +95,64 @@ func checkAllDifferent(v []*big.Int) bool {
 }
 
 // ark computes Add-Round Key, from the paper https://eprint.iacr.org/2019/458.pdf
-func ark(state []*big.Int, c *big.Int) []*big.Int {
+func ark(state [T]*big.Int, c *big.Int) {
 	for i := 0; i < T; i++ {
-		state[i] = constants.fqR.Add(state[i], c)
+		modQ(state[i].Add(state[i], c))
 	}
-	return state
 }
 
 // cubic performs x^5 mod p
 // https://eprint.iacr.org/2019/458.pdf page 8
-func cubic(a *big.Int) *big.Int {
+var five = big.NewInt(5)
-	return constants.fqR.Mul(a, constants.fqR.Square(constants.fqR.Square(a)))
+
+func cubic(a *big.Int) {
+	a.Exp(a, five, constants.Q)
 }
 
 // sbox https://eprint.iacr.org/2019/458.pdf page 6
-func sbox(state []*big.Int, i int) []*big.Int {
+func sbox(state [T]*big.Int, i int) {
 	if (i < NROUNDSF/2) || (i >= NROUNDSF/2+NROUNDSP) {
 		for j := 0; j < T; j++ {
-			state[j] = cubic(state[j])
+			cubic(state[j])
 		}
 	} else {
-		state[0] = cubic(state[0])
+		cubic(state[0])
 	}
-	return state
 }
 
 // mix returns [[matrix]] * [vector]
-func mix(state []*big.Int, m [][]*big.Int) []*big.Int {
+func mix(state [T]*big.Int, newState [T]*big.Int, m [T][T]*big.Int) {
-	var newState []*big.Int
+	mul := Zero()
-	for i := 0; i < len(state); i++ {
+	for i := 0; i < T; i++ {
-		newState = append(newState, constants.fqR.Zero())
+		newState[i].SetInt64(0)
-		for j := 0; j < len(state); j++ {
+		for j := 0; j < T; j++ {
-			newState[i] = constants.fqR.Add(newState[i], constants.fqR.Mul(m[i][j], state[j]))
+			modQ(mul.Mul(m[i][j], state[j]))
+			newState[i].Add(newState[i], mul)
 		}
+		modQ(newState[i])
 	}
-	return newState
 }
 
 // PoseidonHash computes the Poseidon hash for the given inputs
-func PoseidonHash(inp []*big.Int) (*big.Int, error) {
+func PoseidonHash(inp [T]*big.Int) (*big.Int, error) {
-	if len(inp) == 0 || len(inp) > T {
+	if !utils.CheckBigIntArrayInField(inp[:], constants.Q) {
-		return nil, errors.New("wrong inputs length")
-	}
-	if !utils.CheckBigIntArrayInField(inp, constants.fqR.Q) {
 		return nil, errors.New("inputs values not inside Finite Field")
 	}
-	state := inp
+	state := [T]*big.Int{}
-	for i := len(inp); i < T; i++ {
+	for i := 0; i < T; i++ {
-		state = append(state, constants.fqR.Zero())
+		state[i] = new(big.Int).Set(inp[i])
 	}
 
 	// ARK --> SBox --> M, https://eprint.iacr.org/2019/458.pdf pag.5
+	var newState [T]*big.Int
+	for i := 0; i < T; i++ {
+		newState[i] = Zero()
+	}
 	for i := 0; i < NROUNDSF+NROUNDSP; i++ {
-		state = ark(state, constants.c[i])
+		ark(state, constC[i])
-		state = sbox(state, i)
+		sbox(state, i)
-		state = mix(state, constants.m)
+		mix(state, newState, constM)
+		state, newState = newState, state
 	}
 	return state[0], nil
 }
@@ -162,28 +160,31 @@ func PoseidonHash(inp []*big.Int) (*big.Int, error) {
 // Hash performs the Poseidon hash over a *big.Int array
 // in chunks of 5 elements
 func Hash(arr []*big.Int) (*big.Int, error) {
-	if !utils.CheckBigIntArrayInField(arr, constants.fqR.Q) {
+	if !utils.CheckBigIntArrayInField(arr, constants.Q) {
 		return nil, errors.New("inputs values not inside Finite Field")
 	}
 
-	r := constants.fqR.Zero()
+	r := big.NewInt(1)
 	for i := 0; i < len(arr); i = i + T - 1 {
 		var toHash [T]*big.Int
-		for j := 0; j < T-1; j++ {
+		j := 0
-			if i+j < len(arr) {
+		for ; j < T-1; j++ {
-				toHash[j] = arr[i+j]
+			if i+j >= len(arr) {
-			} else {
+				break
-				toHash[j] = _constants.Zero
 			}
+			toHash[j] = arr[i+j]
 		}
-		toHash[T-1] = r
+		toHash[j] = r
-		ph, err := PoseidonHash(toHash[:])
+		j++
+		for ; j < T; j++ {
+			toHash[j] = constants.Zero
+		}
+
+		ph, err := PoseidonHash(toHash)
 		if err != nil {
 			return nil, err
 		}
-		r = constants.fqR.Add(
+		modQ(r.Add(r, ph))
-			r,
-			ph)
 	}
 
 	return r, nil
@@ -195,12 +196,12 @@ func HashBytes(b []byte) (*big.Int, error) {
 	n := 31
 	bElems := make([]*big.Int, 0, len(b)/n+1)
 	for i := 0; i < len(b)/n; i++ {
-		v := new(big.Int)
+		v := Zero()
 		utils.SetBigIntFromLEBytes(v, b[n*i:n*(i+1)])
 		bElems = append(bElems, v)
 	}
 	if len(b)%n != 0 {
-		v := new(big.Int)
+		v := Zero()
 		utils.SetBigIntFromLEBytes(v, b[(len(b)/n)*n:])
 		bElems = append(bElems, v)
 	}

poseidon/poseidon_test.go

@@ -20,13 +20,13 @@ func TestPoseidon(t *testing.T) {
 	b2 := big.NewInt(int64(2))
 	h, err := Hash([]*big.Int{b1, b2})
 	assert.Nil(t, err)
-	assert.Equal(t, "12242166908188651009877250812424843524687801523336557272219921456462821518061", h.String())
+	assert.Equal(t, "4932297968297298434239270129193057052722409868268166443802652458940273154855", h.String())
 
 	b3 := big.NewInt(int64(3))
 	b4 := big.NewInt(int64(4))
 	h, err = Hash([]*big.Int{b3, b4})
 	assert.Nil(t, err)
-	assert.Equal(t, "17185195740979599334254027721507328033796809509313949281114643312710535000993", h.String())
+	assert.Equal(t, "4635491972858758537477743930622086396911540895966845494943021655521913507504", h.String())
 
 	msg := []byte("Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.")
 	n := 31
@@ -43,7 +43,7 @@ func TestPoseidon(t *testing.T) {
 	}
 	hmsg, err := Hash(msgElems)
 	assert.Nil(t, err)
-	assert.Equal(t, "19204466598658860237115179437116112945222240370078952939676636700594938553268", hmsg.String())
+	assert.Equal(t, "16019700159595764790637132363672701294192939959594423814006267756172551741065", hmsg.String())
 
 	msg2 := []byte("Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet.")
 	msg2Elems := make([]*big.Int, 0, len(msg2)/n+1)
@@ -59,11 +59,11 @@ func TestPoseidon(t *testing.T) {
 	}
 	hmsg2, err := Hash(msg2Elems)
 	assert.Nil(t, err)
-	assert.Equal(t, "11846976426841208067103690249139614816718727366915557488657094868020932500524", hmsg2.String())
+	assert.Equal(t, "2978613163687734485261639854325792381691890647104372645321246092227111432722", hmsg2.String())
 
 	hmsg2, err = HashBytes(msg2)
 	assert.Nil(t, err)
-	assert.Equal(t, "11846976426841208067103690249139614816718727366915557488657094868020932500524", hmsg2.String())
+	assert.Equal(t, "2978613163687734485261639854325792381691890647104372645321246092227111432722", hmsg2.String())
 }
 
 func TestPoseidonBrokenChunks(t *testing.T) {