Expose SkToBigInt for usage from other packages & repos

Add utils.ElementArrayToBigIntArray

.github/workflows/lint.yml

@@ -0,0 +1,16 @@
+on: [ push, pull_request ]
+name: Lint
+jobs:
+  lint:
+    runs-on: ubuntu-latest
+    steps:
+    - name: Install Go
+      uses: actions/setup-go@v1
+      with:
+        go-version: 1.14.x
+    - name: Checkout code
+      uses: actions/checkout@v2
+    - name: Lint
+      run: |
+        curl -sSfL https://raw.githubusercontent.com/golangci/golangci-lint/master/install.sh | sh -s -- -b $(go env GOPATH)/bin v1.24.0
+        $(go env GOPATH)/bin/golangci-lint run

.github/workflows/test.yml

@@ -0,0 +1,28 @@
+on: [ push, pull_request ]
+name: Test
+jobs:
+  test:
+    strategy:
+      matrix:
+        go-version: [ 1.13.x, 1.14.x ]
+        goarch: [ "amd64", "386" ]
+    runs-on: ubuntu-latest
+    steps:
+    - name: Install Go
+      uses: actions/setup-go@v1
+      with:
+        go-version: ${{ matrix.go-version }}
+      env:
+        GOARCH: ${{ matrix.goarch }}
+    - name: Checkout code
+      uses: actions/checkout@v2
+    - uses: actions/cache@v1
+      with:
+          path: ~/go/pkg/mod
+          key: ${{ runner.os }}-go-${{ hashFiles('**/go.sum') }}
+          restore-keys: |
+              ${{ runner.os }}-go-
+    - name: Test
+      env:
+        GOARCH: ${{ matrix.goarch }}
+      run: go test ./...

.travis.yml

@@ -4,5 +4,12 @@ language: go
 go:
   - "1.12"
 
+jobs:
+  include:
+    - name: "Unit Tests 64 bit arch"
+      env: GOARCH="amd64"
+    - name: "Unit Test 32 bit arch"
+      env: GOARCH="386"
+
 env:
   - GO111MODULE=on

README.md

@@ -1,4 +1,4 @@
-# go-iden3-crypto [![Go Report Card](https://goreportcard.com/badge/github.com/iden3/go-iden3-crypto)](https://goreportcard.com/report/github.com/iden3/go-iden3-crypto) [![Build Status](https://travis-ci.org/iden3/go-iden3-crypto.svg?branch=master)](https://travis-ci.org/iden3/go-iden3-crypto) [![GoDoc](https://godoc.org/github.com/iden3/go-iden3-crypto?status.svg)](https://godoc.org/github.com/iden3/go-iden3-crypto)
+# go-iden3-crypto [![Go Report Card](https://goreportcard.com/badge/github.com/iden3/go-iden3-crypto)](https://goreportcard.com/report/github.com/iden3/go-iden3-crypto) [![Test Status](https://github.com/iden3/go-iden3-crypto/workflows/Test/badge.svg)](https://github.com/iden3/go-iden3-crypto/actions?query=workflow%3ATest) [![Lint Status](https://github.com/iden3/go-iden3-crypto/workflows/Lint/badge.svg)](https://github.com/iden3/go-iden3-crypto/actions?query=workflow%3ALint) [![GoDoc](https://godoc.org/github.com/iden3/go-iden3-crypto?status.svg)](https://godoc.org/github.com/iden3/go-iden3-crypto)
 
 Go implementation of some cryptographic primitives (that fit inside the SNARK field) used in iden3
 

babyjub/babyjub.go

@@ -154,10 +154,7 @@ func (p *Point) InSubGroup() bool {
 // PointCoordSign returns the sign of the curve point coordinate.  It returns
 // false if the sign is positive and false if the sign is negative.
 func PointCoordSign(c *big.Int) bool {
-	if c.Cmp(new(big.Int).Rsh(constants.Q, 1)) == 1 {
+	return c.Cmp(new(big.Int).Rsh(constants.Q, 1)) == 1
-		return true
-	}
-	return false
 }
 
 func PackPoint(ay *big.Int, sign bool) [32]byte {

babyjub/babyjub_test.go

@@ -3,8 +3,10 @@ package babyjub
 import (
 	"encoding/hex"
 	"math/big"
+	"math/rand"
 	"testing"
 
+	"github.com/iden3/go-iden3-crypto/constants"
 	"github.com/iden3/go-iden3-crypto/utils"
 	"github.com/stretchr/testify/assert"
 )
@@ -231,3 +233,74 @@ func TestCompressDecompressRnd(t *testing.T) {
 		assert.Equal(t, p1, p2)
 	}
 }
+
+func BenchmarkBabyjub(b *testing.B) {
+	const n = 256
+
+	rnd := rand.New(rand.NewSource(42))
+
+	var badpoints [n]*Point
+	for i := 0; i < n; i++ {
+		x := new(big.Int).Rand(rnd, constants.Q)
+		y := new(big.Int).Rand(rnd, constants.Q)
+		badpoints[i] = &Point{X: x, Y: y}
+	}
+
+	var points [n]*Point
+	baseX := utils.NewIntFromString(
+		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
+	baseY := utils.NewIntFromString(
+		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
+	base := &Point{X: baseX, Y: baseY}
+	for i := 0; i < n; i++ {
+		s := new(big.Int).Rand(rnd, constants.Q)
+		points[i] = NewPoint().Mul(s, base)
+	}
+
+	var scalars [n]*big.Int
+	for i := 0; i < n; i++ {
+		scalars[i] = new(big.Int).Rand(rnd, constants.Q)
+	}
+
+	b.Run("AddConst", func(b *testing.B) {
+		p0 := &Point{X: big.NewInt(0), Y: big.NewInt(1)}
+		p1 := &Point{X: big.NewInt(0), Y: big.NewInt(1)}
+
+		p2 := NewPoint()
+		for i := 0; i < b.N; i++ {
+			p2.Add(p0, p1)
+		}
+	})
+
+	b.Run("AddRnd", func(b *testing.B) {
+		res := NewPoint()
+		for i := 0; i < b.N; i++ {
+			res.Add(points[i%(n/2)], points[i%(n/2)+1])
+		}
+	})
+
+	b.Run("MulRnd", func(b *testing.B) {
+		res := NewPoint()
+		for i := 0; i < b.N; i++ {
+			res.Mul(scalars[i%n], points[i%n])
+		}
+	})
+
+	b.Run("Compress", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			points[i%n].Compress()
+		}
+	})
+
+	b.Run("InCurve", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			badpoints[i%n].InCurve()
+		}
+	})
+
+	b.Run("InSubGroup", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			points[i%n].InCurve()
+		}
+	})
+}

babyjub/eddsa.go

@@ -36,6 +36,13 @@ func NewRandPrivKey() PrivateKey {
 // Scalar converts a private key into the scalar value s following the EdDSA
 // standard, and using blake-512 hash.
 func (k *PrivateKey) Scalar() *PrivKeyScalar {
+	s := SkToBigInt(k)
+	return NewPrivKeyScalar(s)
+}
+
+// SkToBigInt converts a private key into the *big.Int value following the
+// EdDSA standard, and using blake-512 hash
+func SkToBigInt(k *PrivateKey) *big.Int {
 	sBuf := Blake512(k[:])
 	sBuf32 := [32]byte{}
 	copy(sBuf32[:], sBuf[:32])
@@ -43,7 +50,7 @@ func (k *PrivateKey) Scalar() *PrivKeyScalar {
 	s := new(big.Int)
 	utils.SetBigIntFromLEBytes(s, sBuf32[:])
 	s.Rsh(s, 3)
-	return NewPrivKeyScalar(s)
+	return s
 }
 
 // Pub returns the public key corresponding to a private key.
@@ -222,11 +229,13 @@ 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}
+
-	hm, err := poseidon.Hash(hmInput) // hm = H1(8*R.x, 8*R.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.PoseidonHash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
 	if err != nil {
 		panic(err)
 	}
+
 	S := new(big.Int).Lsh(k.Scalar().BigInt(), 3)
 	S = S.Mul(hm, S)
 	S.Add(r, S)
@@ -238,8 +247,8 @@ 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)
 	}

babyjub/eddsa_test.go

@@ -1,7 +1,6 @@
 package babyjub
 
 import (
-	"crypto/rand"
 	"encoding/hex"
 	"fmt"
 	"math/big"
@@ -10,24 +9,23 @@ import (
 	"github.com/iden3/go-iden3-crypto/constants"
 	"github.com/iden3/go-iden3-crypto/utils"
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
 )
 
-func genInputs() (*PrivateKey, *big.Int) {
+func TestPublicKey(t *testing.T) {
-	k := NewRandPrivKey()
+	var k PrivateKey
-	fmt.Println("k", hex.EncodeToString(k[:]))
+	for i := 0; i < 32; i++ {
-
+		k[i] = byte(i)
-	msgBuf := [32]byte{}
+	}
-	rand.Read(msgBuf[:])
+	pk := k.Public()
-	msg := utils.SetBigIntFromLEBytes(new(big.Int), msgBuf[:])
+	assert.True(t, pk.X.Cmp(constants.Q) == -1)
-	msg.Mod(msg, constants.Q)
+	assert.True(t, pk.Y.Cmp(constants.Q) == -1)
-	fmt.Println("msg", msg)
-
-	return &k, msg
 }
 
 func TestSignVerifyMimc7(t *testing.T) {
 	var k PrivateKey
-	hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	_, err := hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	require.Nil(t, err)
 	msgBuf, err := hex.DecodeString("00010203040506070809")
 	if err != nil {
 		panic(err)
@@ -71,7 +69,8 @@ func TestSignVerifyMimc7(t *testing.T) {
 
 func TestSignVerifyPoseidon(t *testing.T) {
 	var k PrivateKey
-	hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	_, err := hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	require.Nil(t, err)
 	msgBuf, err := hex.DecodeString("00010203040506070809")
 	if err != nil {
 		panic(err)
@@ -115,7 +114,8 @@ func TestSignVerifyPoseidon(t *testing.T) {
 
 func TestCompressDecompress(t *testing.T) {
 	var k PrivateKey
-	hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	_, err := hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	require.Nil(t, err)
 	pk := k.Public()
 	for i := 0; i < 64; i++ {
 		msgBuf, err := hex.DecodeString(fmt.Sprintf("000102030405060708%02d", i))
@@ -131,3 +131,55 @@ func TestCompressDecompress(t *testing.T) {
 		assert.Equal(t, true, ok)
 	}
 }
+
+func BenchmarkBabyjubEddsa(b *testing.B) {
+	var k PrivateKey
+	_, err := hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	require.Nil(b, err)
+	pk := k.Public()
+
+	const n = 256
+
+	msgBuf, err := hex.DecodeString("00010203040506070809")
+	if err != nil {
+		panic(err)
+	}
+	msg := utils.SetBigIntFromLEBytes(new(big.Int), msgBuf)
+	var msgs [n]*big.Int
+	for i := 0; i < n; i++ {
+		msgs[i] = new(big.Int).Add(msg, big.NewInt(int64(i)))
+	}
+	var sigs [n]*Signature
+
+	b.Run("SignMimc7", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			k.SignMimc7(msgs[i%n])
+		}
+	})
+
+	for i := 0; i < n; i++ {
+		sigs[i%n] = k.SignMimc7(msgs[i%n])
+	}
+
+	b.Run("VerifyMimc7", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			pk.VerifyMimc7(msgs[i%n], sigs[i%n])
+		}
+	})
+
+	b.Run("SignPoseidon", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			k.SignPoseidon(msgs[i%n])
+		}
+	})
+
+	for i := 0; i < n; i++ {
+		sigs[i%n] = k.SignPoseidon(msgs[i%n])
+	}
+
+	b.Run("VerifyPoseidon", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			pk.VerifyPoseidon(msgs[i%n], sigs[i%n])
+		}
+	})
+}

babyjub/helpers.go

@@ -8,6 +8,9 @@ import (
 // the original blake from the SHA3 competition and not the new blake2 version.
 func Blake512(m []byte) []byte {
 	h := blake512.New()
-	h.Write(m[:])
+	_, err := h.Write(m[:])
+	if err != nil {
+		panic(err)
+	}
 	return h.Sum(nil)
 }

constants/constants.go

@@ -1,12 +1,15 @@
 package constants
 
 import (
-	"github.com/iden3/go-iden3-crypto/utils"
+	"fmt"
 	"math/big"
+
+	"github.com/iden3/go-iden3-crypto/ff"
 )
 
 // Q is the order of the integer field (Zq) that fits inside the SNARK.
 var Q *big.Int
+var QE *ff.Element
 
 // Zero is 0.
 var Zero *big.Int
@@ -21,6 +24,11 @@ func init() {
 	Zero = big.NewInt(0)
 	One = big.NewInt(1)
 	MinusOne = big.NewInt(-1)
-	Q = utils.NewIntFromString(
+
-		"21888242871839275222246405745257275088548364400416034343698204186575808495617")
+	qString := "21888242871839275222246405745257275088548364400416034343698204186575808495617"
+	var ok bool
+	Q, ok = new(big.Int).SetString(qString, 10)
+	if !ok {
+		panic(fmt.Sprintf("Bad base 10 string %s", qString))
+	}
 }

ff/arith.go

@@ -0,0 +1,122 @@
+// Copyright 2020 ConsenSys AG
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by goff DO NOT EDIT
+
+package ff
+
+import (
+	"math/bits"
+)
+
+func madd(a, b, t, u, v uint64) (uint64, uint64, uint64) {
+	var carry uint64
+	hi, lo := bits.Mul64(a, b)
+	v, carry = bits.Add64(lo, v, 0)
+	u, carry = bits.Add64(hi, u, carry)
+	t, _ = bits.Add64(t, 0, carry)
+	return t, u, v
+}
+
+// madd0 hi = a*b + c (discards lo bits)
+func madd0(a, b, c uint64) (hi uint64) {
+	var carry, lo uint64
+	hi, lo = bits.Mul64(a, b)
+	_, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd1 hi, lo = a*b + c
+func madd1(a, b, c uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd2 hi, lo = a*b + c + d
+func madd2(a, b, c, d uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	c, carry = bits.Add64(c, d, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd2s superhi, hi, lo = 2*a*b + c + d + e
+func madd2s(a, b, c, d, e uint64) (superhi, hi, lo uint64) {
+	var carry, sum uint64
+
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, lo, 0)
+	hi, superhi = bits.Add64(hi, hi, carry)
+
+	sum, carry = bits.Add64(c, e, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, sum, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	hi, _ = bits.Add64(hi, 0, d)
+	return
+}
+
+func madd1s(a, b, d, e uint64) (superhi, hi, lo uint64) {
+	var carry uint64
+
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, lo, 0)
+	hi, superhi = bits.Add64(hi, hi, carry)
+	lo, carry = bits.Add64(lo, e, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	hi, _ = bits.Add64(hi, 0, d)
+	return
+}
+
+func madd2sb(a, b, c, e uint64) (superhi, hi, lo uint64) {
+	var carry, sum uint64
+
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, lo, 0)
+	hi, superhi = bits.Add64(hi, hi, carry)
+
+	sum, carry = bits.Add64(c, e, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, sum, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+func madd1sb(a, b, e uint64) (superhi, hi, lo uint64) {
+	var carry uint64
+
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, lo, 0)
+	hi, superhi = bits.Add64(hi, hi, carry)
+	lo, carry = bits.Add64(lo, e, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	c, carry = bits.Add64(c, d, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, e, carry)
+	return
+}

ff/element.go

@@ -0,0 +1,792 @@
+// Copyright 2020 ConsenSys AG
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// field modulus q =
+//
+// 21888242871839275222246405745257275088548364400416034343698204186575808495617
+// Code generated by goff DO NOT EDIT
+// goff version:  - build:
+// Element are assumed to be in Montgomery form in all methods
+
+// Package ff (generated by goff) contains field arithmetics operations
+package ff
+
+import (
+	"crypto/rand"
+	"encoding/binary"
+	"io"
+	"math/big"
+	"math/bits"
+	"sync"
+
+	"unsafe"
+)
+
+// Element represents a field element stored on 4 words (uint64)
+// Element are assumed to be in Montgomery form in all methods
+type Element [4]uint64
+
+// ElementLimbs number of 64 bits words needed to represent Element
+const ElementLimbs = 4
+
+// ElementBits number bits needed to represent Element
+const ElementBits = 254
+
+// SetUint64 z = v, sets z LSB to v (non-Montgomery form) and convert z to Montgomery form
+func (z *Element) SetUint64(v uint64) *Element {
+	z[0] = v
+	z[1] = 0
+	z[2] = 0
+	z[3] = 0
+	return z.ToMont()
+}
+
+// Set z = x
+func (z *Element) Set(x *Element) *Element {
+	z[0] = x[0]
+	z[1] = x[1]
+	z[2] = x[2]
+	z[3] = x[3]
+	return z
+}
+
+// SetZero z = 0
+func (z *Element) SetZero() *Element {
+	z[0] = 0
+	z[1] = 0
+	z[2] = 0
+	z[3] = 0
+	return z
+}
+
+// SetOne z = 1 (in Montgomery form)
+func (z *Element) SetOne() *Element {
+	z[0] = 12436184717236109307
+	z[1] = 3962172157175319849
+	z[2] = 7381016538464732718
+	z[3] = 1011752739694698287
+	return z
+}
+
+// Neg z = q - x
+func (z *Element) Neg(x *Element) *Element {
+	if x.IsZero() {
+		return z.SetZero()
+	}
+	var borrow uint64
+	z[0], borrow = bits.Sub64(4891460686036598785, x[0], 0)
+	z[1], borrow = bits.Sub64(2896914383306846353, x[1], borrow)
+	z[2], borrow = bits.Sub64(13281191951274694749, x[2], borrow)
+	z[3], _ = bits.Sub64(3486998266802970665, x[3], borrow)
+	return z
+}
+
+// Div z = x*y^-1 mod q
+func (z *Element) Div(x, y *Element) *Element {
+	var yInv Element
+	yInv.Inverse(y)
+	z.Mul(x, &yInv)
+	return z
+}
+
+// Equal returns z == x
+func (z *Element) Equal(x *Element) bool {
+	return (z[3] == x[3]) && (z[2] == x[2]) && (z[1] == x[1]) && (z[0] == x[0])
+}
+
+// IsZero returns z == 0
+func (z *Element) IsZero() bool {
+	return (z[3] | z[2] | z[1] | z[0]) == 0
+}
+
+// field modulus stored as big.Int
+var _elementModulusBigInt big.Int
+var onceelementModulus sync.Once
+
+func elementModulusBigInt() *big.Int {
+	onceelementModulus.Do(func() {
+		_elementModulusBigInt.SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
+	})
+	return &_elementModulusBigInt
+}
+
+// Inverse z = x^-1 mod q
+// Algorithm 16 in "Efficient Software-Implementation of Finite Fields with Applications to Cryptography"
+// if x == 0, sets and returns z = x
+func (z *Element) Inverse(x *Element) *Element {
+	if x.IsZero() {
+		return z.Set(x)
+	}
+
+	// initialize u = q
+	var u = Element{
+		4891460686036598785,
+		2896914383306846353,
+		13281191951274694749,
+		3486998266802970665,
+	}
+
+	// initialize s = r^2
+	var s = Element{
+		1997599621687373223,
+		6052339484930628067,
+		10108755138030829701,
+		150537098327114917,
+	}
+
+	// r = 0
+	r := Element{}
+
+	v := *x
+
+	var carry, borrow, t, t2 uint64
+	var bigger, uIsOne, vIsOne bool
+
+	for !uIsOne && !vIsOne {
+		for v[0]&1 == 0 {
+
+			// v = v >> 1
+			t2 = v[3] << 63
+			v[3] >>= 1
+			t = t2
+			t2 = v[2] << 63
+			v[2] = (v[2] >> 1) | t
+			t = t2
+			t2 = v[1] << 63
+			v[1] = (v[1] >> 1) | t
+			t = t2
+			v[0] = (v[0] >> 1) | t
+
+			if s[0]&1 == 1 {
+
+				// s = s + q
+				s[0], carry = bits.Add64(s[0], 4891460686036598785, 0)
+				s[1], carry = bits.Add64(s[1], 2896914383306846353, carry)
+				s[2], carry = bits.Add64(s[2], 13281191951274694749, carry)
+				s[3], _ = bits.Add64(s[3], 3486998266802970665, carry)
+
+			}
+
+			// s = s >> 1
+			t2 = s[3] << 63
+			s[3] >>= 1
+			t = t2
+			t2 = s[2] << 63
+			s[2] = (s[2] >> 1) | t
+			t = t2
+			t2 = s[1] << 63
+			s[1] = (s[1] >> 1) | t
+			t = t2
+			s[0] = (s[0] >> 1) | t
+
+		}
+		for u[0]&1 == 0 {
+
+			// u = u >> 1
+			t2 = u[3] << 63
+			u[3] >>= 1
+			t = t2
+			t2 = u[2] << 63
+			u[2] = (u[2] >> 1) | t
+			t = t2
+			t2 = u[1] << 63
+			u[1] = (u[1] >> 1) | t
+			t = t2
+			u[0] = (u[0] >> 1) | t
+
+			if r[0]&1 == 1 {
+
+				// r = r + q
+				r[0], carry = bits.Add64(r[0], 4891460686036598785, 0)
+				r[1], carry = bits.Add64(r[1], 2896914383306846353, carry)
+				r[2], carry = bits.Add64(r[2], 13281191951274694749, carry)
+				r[3], _ = bits.Add64(r[3], 3486998266802970665, carry)
+
+			}
+
+			// r = r >> 1
+			t2 = r[3] << 63
+			r[3] >>= 1
+			t = t2
+			t2 = r[2] << 63
+			r[2] = (r[2] >> 1) | t
+			t = t2
+			t2 = r[1] << 63
+			r[1] = (r[1] >> 1) | t
+			t = t2
+			r[0] = (r[0] >> 1) | t
+
+		}
+
+		// v >= u
+		bigger = !(v[3] < u[3] || (v[3] == u[3] && (v[2] < u[2] || (v[2] == u[2] && (v[1] < u[1] || (v[1] == u[1] && (v[0] < u[0])))))))
+
+		if bigger {
+
+			// v = v - u
+			v[0], borrow = bits.Sub64(v[0], u[0], 0)
+			v[1], borrow = bits.Sub64(v[1], u[1], borrow)
+			v[2], borrow = bits.Sub64(v[2], u[2], borrow)
+			v[3], _ = bits.Sub64(v[3], u[3], borrow)
+
+			// r >= s
+			bigger = !(r[3] < s[3] || (r[3] == s[3] && (r[2] < s[2] || (r[2] == s[2] && (r[1] < s[1] || (r[1] == s[1] && (r[0] < s[0])))))))
+
+			if bigger {
+
+				// s = s + q
+				s[0], carry = bits.Add64(s[0], 4891460686036598785, 0)
+				s[1], carry = bits.Add64(s[1], 2896914383306846353, carry)
+				s[2], carry = bits.Add64(s[2], 13281191951274694749, carry)
+				s[3], _ = bits.Add64(s[3], 3486998266802970665, carry)
+
+			}
+
+			// s = s - r
+			s[0], borrow = bits.Sub64(s[0], r[0], 0)
+			s[1], borrow = bits.Sub64(s[1], r[1], borrow)
+			s[2], borrow = bits.Sub64(s[2], r[2], borrow)
+			s[3], _ = bits.Sub64(s[3], r[3], borrow)
+
+		} else {
+
+			// u = u - v
+			u[0], borrow = bits.Sub64(u[0], v[0], 0)
+			u[1], borrow = bits.Sub64(u[1], v[1], borrow)
+			u[2], borrow = bits.Sub64(u[2], v[2], borrow)
+			u[3], _ = bits.Sub64(u[3], v[3], borrow)
+
+			// s >= r
+			bigger = !(s[3] < r[3] || (s[3] == r[3] && (s[2] < r[2] || (s[2] == r[2] && (s[1] < r[1] || (s[1] == r[1] && (s[0] < r[0])))))))
+
+			if bigger {
+
+				// r = r + q
+				r[0], carry = bits.Add64(r[0], 4891460686036598785, 0)
+				r[1], carry = bits.Add64(r[1], 2896914383306846353, carry)
+				r[2], carry = bits.Add64(r[2], 13281191951274694749, carry)
+				r[3], _ = bits.Add64(r[3], 3486998266802970665, carry)
+
+			}
+
+			// r = r - s
+			r[0], borrow = bits.Sub64(r[0], s[0], 0)
+			r[1], borrow = bits.Sub64(r[1], s[1], borrow)
+			r[2], borrow = bits.Sub64(r[2], s[2], borrow)
+			r[3], _ = bits.Sub64(r[3], s[3], borrow)
+
+		}
+		uIsOne = (u[0] == 1) && (u[3]|u[2]|u[1]) == 0
+		vIsOne = (v[0] == 1) && (v[3]|v[2]|v[1]) == 0
+	}
+
+	if uIsOne {
+		z.Set(&r)
+	} else {
+		z.Set(&s)
+	}
+
+	return z
+}
+
+// SetRandom sets z to a random element < q
+func (z *Element) SetRandom() *Element {
+	bytes := make([]byte, 32)
+	io.ReadFull(rand.Reader, bytes)
+	z[0] = binary.BigEndian.Uint64(bytes[0:8])
+	z[1] = binary.BigEndian.Uint64(bytes[8:16])
+	z[2] = binary.BigEndian.Uint64(bytes[16:24])
+	z[3] = binary.BigEndian.Uint64(bytes[24:32])
+	z[3] %= 3486998266802970665
+
+	// if z > q --> z -= q
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 4891460686036598785, 0)
+		z[1], b = bits.Sub64(z[1], 2896914383306846353, b)
+		z[2], b = bits.Sub64(z[2], 13281191951274694749, b)
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
+	}
+
+	return z
+}
+
+// Add z = x + y mod q
+func (z *Element) Add(x, y *Element) *Element {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], y[0], 0)
+	z[1], carry = bits.Add64(x[1], y[1], carry)
+	z[2], carry = bits.Add64(x[2], y[2], carry)
+	z[3], _ = bits.Add64(x[3], y[3], carry)
+
+	// if z > q --> z -= q
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 4891460686036598785, 0)
+		z[1], b = bits.Sub64(z[1], 2896914383306846353, b)
+		z[2], b = bits.Sub64(z[2], 13281191951274694749, b)
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
+	}
+	return z
+}
+
+// AddAssign z = z + x mod q
+func (z *Element) AddAssign(x *Element) *Element {
+	var carry uint64
+
+	z[0], carry = bits.Add64(z[0], x[0], 0)
+	z[1], carry = bits.Add64(z[1], x[1], carry)
+	z[2], carry = bits.Add64(z[2], x[2], carry)
+	z[3], _ = bits.Add64(z[3], x[3], carry)
+
+	// if z > q --> z -= q
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 4891460686036598785, 0)
+		z[1], b = bits.Sub64(z[1], 2896914383306846353, b)
+		z[2], b = bits.Sub64(z[2], 13281191951274694749, b)
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
+	}
+	return z
+}
+
+// Double z = x + x mod q, aka Lsh 1
+func (z *Element) Double(x *Element) *Element {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], x[0], 0)
+	z[1], carry = bits.Add64(x[1], x[1], carry)
+	z[2], carry = bits.Add64(x[2], x[2], carry)
+	z[3], _ = bits.Add64(x[3], x[3], carry)
+
+	// if z > q --> z -= q
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 4891460686036598785, 0)
+		z[1], b = bits.Sub64(z[1], 2896914383306846353, b)
+		z[2], b = bits.Sub64(z[2], 13281191951274694749, b)
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
+	}
+	return z
+}
+
+// Sub  z = x - y mod q
+func (z *Element) Sub(x, y *Element) *Element {
+	var b uint64
+	z[0], b = bits.Sub64(x[0], y[0], 0)
+	z[1], b = bits.Sub64(x[1], y[1], b)
+	z[2], b = bits.Sub64(x[2], y[2], b)
+	z[3], b = bits.Sub64(x[3], y[3], b)
+	if b != 0 {
+		var c uint64
+		z[0], c = bits.Add64(z[0], 4891460686036598785, 0)
+		z[1], c = bits.Add64(z[1], 2896914383306846353, c)
+		z[2], c = bits.Add64(z[2], 13281191951274694749, c)
+		z[3], _ = bits.Add64(z[3], 3486998266802970665, c)
+	}
+	return z
+}
+
+// SubAssign  z = z - x mod q
+func (z *Element) SubAssign(x *Element) *Element {
+	var b uint64
+	z[0], b = bits.Sub64(z[0], x[0], 0)
+	z[1], b = bits.Sub64(z[1], x[1], b)
+	z[2], b = bits.Sub64(z[2], x[2], b)
+	z[3], b = bits.Sub64(z[3], x[3], b)
+	if b != 0 {
+		var c uint64
+		z[0], c = bits.Add64(z[0], 4891460686036598785, 0)
+		z[1], c = bits.Add64(z[1], 2896914383306846353, c)
+		z[2], c = bits.Add64(z[2], 13281191951274694749, c)
+		z[3], _ = bits.Add64(z[3], 3486998266802970665, c)
+	}
+	return z
+}
+
+// Exp z = x^e mod q
+func (z *Element) Exp(x Element, e uint64) *Element {
+	if e == 0 {
+		return z.SetOne()
+	}
+
+	z.Set(&x)
+
+	l := bits.Len64(e) - 2
+	for i := l; i >= 0; i-- {
+		z.Square(z)
+		if e&(1<<uint(i)) != 0 {
+			z.MulAssign(&x)
+		}
+	}
+	return z
+}
+
+// FromMont converts z in place (i.e. mutates) from Montgomery to regular representation
+// sets and returns z = z * 1
+func (z *Element) FromMont() *Element {
+
+	// the following lines implement z = z * 1
+	// with a modified CIOS montgomery multiplication
+	{
+		// m = z[0]n'[0] mod W
+		m := z[0] * 14042775128853446655
+		C := madd0(m, 4891460686036598785, z[0])
+		C, z[0] = madd2(m, 2896914383306846353, z[1], C)
+		C, z[1] = madd2(m, 13281191951274694749, z[2], C)
+		C, z[2] = madd2(m, 3486998266802970665, z[3], C)
+		z[3] = C
+	}
+	{
+		// m = z[0]n'[0] mod W
+		m := z[0] * 14042775128853446655
+		C := madd0(m, 4891460686036598785, z[0])
+		C, z[0] = madd2(m, 2896914383306846353, z[1], C)
+		C, z[1] = madd2(m, 13281191951274694749, z[2], C)
+		C, z[2] = madd2(m, 3486998266802970665, z[3], C)
+		z[3] = C
+	}
+	{
+		// m = z[0]n'[0] mod W
+		m := z[0] * 14042775128853446655
+		C := madd0(m, 4891460686036598785, z[0])
+		C, z[0] = madd2(m, 2896914383306846353, z[1], C)
+		C, z[1] = madd2(m, 13281191951274694749, z[2], C)
+		C, z[2] = madd2(m, 3486998266802970665, z[3], C)
+		z[3] = C
+	}
+	{
+		// m = z[0]n'[0] mod W
+		m := z[0] * 14042775128853446655
+		C := madd0(m, 4891460686036598785, z[0])
+		C, z[0] = madd2(m, 2896914383306846353, z[1], C)
+		C, z[1] = madd2(m, 13281191951274694749, z[2], C)
+		C, z[2] = madd2(m, 3486998266802970665, z[3], C)
+		z[3] = C
+	}
+
+	// if z > q --> z -= q
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 4891460686036598785, 0)
+		z[1], b = bits.Sub64(z[1], 2896914383306846353, b)
+		z[2], b = bits.Sub64(z[2], 13281191951274694749, b)
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
+	}
+	return z
+}
+
+// ToMont converts z to Montgomery form
+// sets and returns z = z * r^2
+func (z *Element) ToMont() *Element {
+	var rSquare = Element{
+		1997599621687373223,
+		6052339484930628067,
+		10108755138030829701,
+		150537098327114917,
+	}
+	return z.MulAssign(&rSquare)
+}
+
+// ToRegular returns z in regular form (doesn't mutate z)
+func (z Element) ToRegular() Element {
+	return *z.FromMont()
+}
+
+// String returns the string form of an Element in Montgomery form
+func (z *Element) String() string {
+	var _z big.Int
+	return z.ToBigIntRegular(&_z).String()
+}
+
+// ToBigInt returns z as a big.Int in Montgomery form
+func (z *Element) ToBigInt(res *big.Int) *big.Int {
+	if bits.UintSize == 64 {
+		bits := (*[4]big.Word)(unsafe.Pointer(z))
+		return res.SetBits(bits[:])
+	} else {
+		var bits [8]big.Word
+		for i := 0; i < len(z); i++ {
+			bits[i*2] = big.Word(z[i])
+			bits[i*2+1] = big.Word(z[i] >> 32)
+		}
+		return res.SetBits(bits[:])
+	}
+}
+
+// ToBigIntRegular returns z as a big.Int in regular form
+func (z Element) ToBigIntRegular(res *big.Int) *big.Int {
+	z.FromMont()
+	if bits.UintSize == 64 {
+		bits := (*[4]big.Word)(unsafe.Pointer(&z))
+		return res.SetBits(bits[:])
+	} else {
+		var bits [8]big.Word
+		for i := 0; i < len(z); i++ {
+			bits[i*2] = big.Word(z[i])
+			bits[i*2+1] = big.Word(z[i] >> 32)
+		}
+		return res.SetBits(bits[:])
+	}
+}
+
+// SetBigInt sets z to v (regular form) and returns z in Montgomery form
+func (z *Element) SetBigInt(v *big.Int) *Element {
+	z.SetZero()
+
+	zero := big.NewInt(0)
+	q := elementModulusBigInt()
+
+	// copy input
+	vv := new(big.Int).Set(v)
+
+	// while v < 0, v+=q
+	for vv.Cmp(zero) == -1 {
+		vv.Add(vv, q)
+	}
+	// while v > q, v-=q
+	for vv.Cmp(q) == 1 {
+		vv.Sub(vv, q)
+	}
+	// if v == q, return 0
+	if vv.Cmp(q) == 0 {
+		return z
+	}
+	// v should
+	vBits := vv.Bits()
+	if bits.UintSize == 64 {
+		for i := 0; i < len(vBits); i++ {
+			z[i] = uint64(vBits[i])
+		}
+	} else {
+		for i := 0; i < len(vBits); i++ {
+			if i%2 == 0 {
+				z[i/2] = uint64(vBits[i])
+			} else {
+				z[i/2] |= uint64(vBits[i]) << 32
+			}
+		}
+	}
+	return z.ToMont()
+}
+
+// SetString creates a big.Int with s (in base 10) and calls SetBigInt on z
+func (z *Element) SetString(s string) *Element {
+	x, ok := new(big.Int).SetString(s, 10)
+	if !ok {
+		panic("Element.SetString failed -> can't parse number in base10 into a big.Int")
+	}
+	return z.SetBigInt(x)
+}
+
+// Mul z = x * y mod q
+func (z *Element) Mul(x, y *Element) *Element {
+
+	var t [4]uint64
+	var c [3]uint64
+	{
+		// round 0
+		v := x[0]
+		c[1], c[0] = bits.Mul64(v, y[0])
+		m := c[0] * 14042775128853446655
+		c[2] = madd0(m, 4891460686036598785, c[0])
+		c[1], c[0] = madd1(v, y[1], c[1])
+		c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0])
+		c[1], c[0] = madd1(v, y[2], c[1])
+		c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0])
+		c[1], c[0] = madd1(v, y[3], c[1])
+		t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
+	}
+	{
+		// round 1
+		v := x[1]
+		c[1], c[0] = madd1(v, y[0], t[0])
+		m := c[0] * 14042775128853446655
+		c[2] = madd0(m, 4891460686036598785, c[0])
+		c[1], c[0] = madd2(v, y[1], c[1], t[1])
+		c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0])
+		c[1], c[0] = madd2(v, y[2], c[1], t[2])
+		c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0])
+		c[1], c[0] = madd2(v, y[3], c[1], t[3])
+		t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
+	}
+	{
+		// round 2
+		v := x[2]
+		c[1], c[0] = madd1(v, y[0], t[0])
+		m := c[0] * 14042775128853446655
+		c[2] = madd0(m, 4891460686036598785, c[0])
+		c[1], c[0] = madd2(v, y[1], c[1], t[1])
+		c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0])
+		c[1], c[0] = madd2(v, y[2], c[1], t[2])
+		c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0])
+		c[1], c[0] = madd2(v, y[3], c[1], t[3])
+		t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
+	}
+	{
+		// round 3
+		v := x[3]
+		c[1], c[0] = madd1(v, y[0], t[0])
+		m := c[0] * 14042775128853446655
+		c[2] = madd0(m, 4891460686036598785, c[0])
+		c[1], c[0] = madd2(v, y[1], c[1], t[1])
+		c[2], z[0] = madd2(m, 2896914383306846353, c[2], c[0])
+		c[1], c[0] = madd2(v, y[2], c[1], t[2])
+		c[2], z[1] = madd2(m, 13281191951274694749, c[2], c[0])
+		c[1], c[0] = madd2(v, y[3], c[1], t[3])
+		z[3], z[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
+	}
+
+	// if z > q --> z -= q
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 4891460686036598785, 0)
+		z[1], b = bits.Sub64(z[1], 2896914383306846353, b)
+		z[2], b = bits.Sub64(z[2], 13281191951274694749, b)
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
+	}
+	return z
+}
+
+// MulAssign z = z * x mod q
+func (z *Element) MulAssign(x *Element) *Element {
+
+	var t [4]uint64
+	var c [3]uint64
+	{
+		// round 0
+		v := z[0]
+		c[1], c[0] = bits.Mul64(v, x[0])
+		m := c[0] * 14042775128853446655
+		c[2] = madd0(m, 4891460686036598785, c[0])
+		c[1], c[0] = madd1(v, x[1], c[1])
+		c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0])
+		c[1], c[0] = madd1(v, x[2], c[1])
+		c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0])
+		c[1], c[0] = madd1(v, x[3], c[1])
+		t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
+	}
+	{
+		// round 1
+		v := z[1]
+		c[1], c[0] = madd1(v, x[0], t[0])
+		m := c[0] * 14042775128853446655
+		c[2] = madd0(m, 4891460686036598785, c[0])
+		c[1], c[0] = madd2(v, x[1], c[1], t[1])
+		c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0])
+		c[1], c[0] = madd2(v, x[2], c[1], t[2])
+		c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0])
+		c[1], c[0] = madd2(v, x[3], c[1], t[3])
+		t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
+	}
+	{
+		// round 2
+		v := z[2]
+		c[1], c[0] = madd1(v, x[0], t[0])
+		m := c[0] * 14042775128853446655
+		c[2] = madd0(m, 4891460686036598785, c[0])
+		c[1], c[0] = madd2(v, x[1], c[1], t[1])
+		c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0])
+		c[1], c[0] = madd2(v, x[2], c[1], t[2])
+		c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0])
+		c[1], c[0] = madd2(v, x[3], c[1], t[3])
+		t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
+	}
+	{
+		// round 3
+		v := z[3]
+		c[1], c[0] = madd1(v, x[0], t[0])
+		m := c[0] * 14042775128853446655
+		c[2] = madd0(m, 4891460686036598785, c[0])
+		c[1], c[0] = madd2(v, x[1], c[1], t[1])
+		c[2], z[0] = madd2(m, 2896914383306846353, c[2], c[0])
+		c[1], c[0] = madd2(v, x[2], c[1], t[2])
+		c[2], z[1] = madd2(m, 13281191951274694749, c[2], c[0])
+		c[1], c[0] = madd2(v, x[3], c[1], t[3])
+		z[3], z[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
+	}
+
+	// if z > q --> z -= q
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 4891460686036598785, 0)
+		z[1], b = bits.Sub64(z[1], 2896914383306846353, b)
+		z[2], b = bits.Sub64(z[2], 13281191951274694749, b)
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
+	}
+	return z
+}
+
+// Square z = x * x mod q
+func (z *Element) Square(x *Element) *Element {
+
+	var p [4]uint64
+
+	var u, v uint64
+	{
+		// round 0
+		u, p[0] = bits.Mul64(x[0], x[0])
+		m := p[0] * 14042775128853446655
+		C := madd0(m, 4891460686036598785, p[0])
+		var t uint64
+		t, u, v = madd1sb(x[0], x[1], u)
+		C, p[0] = madd2(m, 2896914383306846353, v, C)
+		t, u, v = madd1s(x[0], x[2], t, u)
+		C, p[1] = madd2(m, 13281191951274694749, v, C)
+		_, u, v = madd1s(x[0], x[3], t, u)
+		p[3], p[2] = madd3(m, 3486998266802970665, v, C, u)
+	}
+	{
+		// round 1
+		m := p[0] * 14042775128853446655
+		C := madd0(m, 4891460686036598785, p[0])
+		u, v = madd1(x[1], x[1], p[1])
+		C, p[0] = madd2(m, 2896914383306846353, v, C)
+		var t uint64
+		t, u, v = madd2sb(x[1], x[2], p[2], u)
+		C, p[1] = madd2(m, 13281191951274694749, v, C)
+		_, u, v = madd2s(x[1], x[3], p[3], t, u)
+		p[3], p[2] = madd3(m, 3486998266802970665, v, C, u)
+	}
+	{
+		// round 2
+		m := p[0] * 14042775128853446655
+		C := madd0(m, 4891460686036598785, p[0])
+		C, p[0] = madd2(m, 2896914383306846353, p[1], C)
+		u, v = madd1(x[2], x[2], p[2])
+		C, p[1] = madd2(m, 13281191951274694749, v, C)
+		_, u, v = madd2sb(x[2], x[3], p[3], u)
+		p[3], p[2] = madd3(m, 3486998266802970665, v, C, u)
+	}
+	{
+		// round 3
+		m := p[0] * 14042775128853446655
+		C := madd0(m, 4891460686036598785, p[0])
+		C, z[0] = madd2(m, 2896914383306846353, p[1], C)
+		C, z[1] = madd2(m, 13281191951274694749, p[2], C)
+		u, v = madd1(x[3], x[3], p[3])
+		z[3], z[2] = madd3(m, 3486998266802970665, v, C, u)
+	}
+
+	// if z > q --> z -= q
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 4891460686036598785, 0)
+		z[1], b = bits.Sub64(z[1], 2896914383306846353, b)
+		z[2], b = bits.Sub64(z[2], 13281191951274694749, b)
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
+	}
+	return z
+}

ff/element_test.go

@@ -0,0 +1,234 @@
+// Code generated by goff DO NOT EDIT
+package ff
+
+import (
+	"crypto/rand"
+	"math/big"
+	mrand "math/rand"
+	"testing"
+)
+
+func TestELEMENTCorrectnessAgainstBigInt(t *testing.T) {
+	modulus, _ := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
+	cmpEandB := func(e *Element, b *big.Int, name string) {
+		var _e big.Int
+		if e.FromMont().ToBigInt(&_e).Cmp(b) != 0 {
+			t.Fatal(name, "failed")
+		}
+	}
+	var modulusMinusOne, one big.Int
+	one.SetUint64(1)
+
+	modulusMinusOne.Sub(modulus, &one)
+
+	for i := 0; i < 1000; i++ {
+
+		// sample 2 random big int
+		b1, _ := rand.Int(rand.Reader, modulus)
+		b2, _ := rand.Int(rand.Reader, modulus)
+		rExp := mrand.Uint64()
+
+		// adding edge cases
+		// TODO need more edge cases
+		switch i {
+		case 0:
+			rExp = 0
+			b1.SetUint64(0)
+		case 1:
+			b2.SetUint64(0)
+		case 2:
+			b1.SetUint64(0)
+			b2.SetUint64(0)
+		case 3:
+			rExp = 0
+		case 4:
+			rExp = 1
+		case 5:
+			rExp = ^uint64(0) // max uint
+		case 6:
+			rExp = 2
+			b1.Set(&modulusMinusOne)
+		case 7:
+			b2.Set(&modulusMinusOne)
+		case 8:
+			b1.Set(&modulusMinusOne)
+			b2.Set(&modulusMinusOne)
+		}
+
+		rbExp := new(big.Int).SetUint64(rExp)
+
+		var bMul, bAdd, bSub, bDiv, bNeg, bLsh, bInv, bExp, bSquare big.Int
+
+		// e1 = mont(b1), e2 = mont(b2)
+		var e1, e2, eMul, eAdd, eSub, eDiv, eNeg, eLsh, eInv, eExp, eSquare, eMulAssign, eSubAssign, eAddAssign Element
+		e1.SetBigInt(b1)
+		e2.SetBigInt(b2)
+
+		// (e1*e2).FromMont() === b1*b2 mod q ... etc
+		eSquare.Square(&e1)
+		eMul.Mul(&e1, &e2)
+		eMulAssign.Set(&e1)
+		eMulAssign.MulAssign(&e2)
+		eAdd.Add(&e1, &e2)
+		eAddAssign.Set(&e1)
+		eAddAssign.AddAssign(&e2)
+		eSub.Sub(&e1, &e2)
+		eSubAssign.Set(&e1)
+		eSubAssign.SubAssign(&e2)
+		eDiv.Div(&e1, &e2)
+		eNeg.Neg(&e1)
+		eInv.Inverse(&e1)
+		eExp.Exp(e1, rExp)
+		eLsh.Double(&e1)
+
+		// same operations with big int
+		bAdd.Add(b1, b2).Mod(&bAdd, modulus)
+		bMul.Mul(b1, b2).Mod(&bMul, modulus)
+		bSquare.Mul(b1, b1).Mod(&bSquare, modulus)
+		bSub.Sub(b1, b2).Mod(&bSub, modulus)
+		bDiv.ModInverse(b2, modulus)
+		bDiv.Mul(&bDiv, b1).
+			Mod(&bDiv, modulus)
+		bNeg.Neg(b1).Mod(&bNeg, modulus)
+
+		bInv.ModInverse(b1, modulus)
+		bExp.Exp(b1, rbExp, modulus)
+		bLsh.Lsh(b1, 1).Mod(&bLsh, modulus)
+
+		cmpEandB(&eSquare, &bSquare, "Square")
+		cmpEandB(&eMul, &bMul, "Mul")
+		cmpEandB(&eMulAssign, &bMul, "MulAssign")
+		cmpEandB(&eAdd, &bAdd, "Add")
+		cmpEandB(&eAddAssign, &bAdd, "AddAssign")
+		cmpEandB(&eSub, &bSub, "Sub")
+		cmpEandB(&eSubAssign, &bSub, "SubAssign")
+		cmpEandB(&eDiv, &bDiv, "Div")
+		cmpEandB(&eNeg, &bNeg, "Neg")
+		cmpEandB(&eInv, &bInv, "Inv")
+		cmpEandB(&eExp, &bExp, "Exp")
+		cmpEandB(&eLsh, &bLsh, "Lsh")
+	}
+}
+
+func TestELEMENTIsRandom(t *testing.T) {
+	for i := 0; i < 1000; i++ {
+		var x, y Element
+		x.SetRandom()
+		y.SetRandom()
+		if x.Equal(&y) {
+			t.Fatal("2 random numbers are unlikely to be equal")
+		}
+	}
+}
+
+// -------------------------------------------------------------------------------------------------
+// benchmarks
+// most benchmarks are rudimentary and should sample a large number of random inputs
+// or be run multiple times to ensure it didn't measure the fastest path of the function
+// TODO: clean up and push benchmarking branch
+
+var benchResElement Element
+
+func BenchmarkInverseELEMENT(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		benchResElement.Inverse(&x)
+	}
+
+}
+func BenchmarkExpELEMENT(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Exp(x, mrand.Uint64())
+	}
+}
+
+func BenchmarkDoubleELEMENT(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Double(&benchResElement)
+	}
+}
+
+func BenchmarkAddELEMENT(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Add(&x, &benchResElement)
+	}
+}
+
+func BenchmarkSubELEMENT(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Sub(&x, &benchResElement)
+	}
+}
+
+func BenchmarkNegELEMENT(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Neg(&benchResElement)
+	}
+}
+
+func BenchmarkDivELEMENT(b *testing.B) {
+	var x Element
+	x.SetRandom()
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Div(&x, &benchResElement)
+	}
+}
+
+func BenchmarkFromMontELEMENT(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.FromMont()
+	}
+}
+
+func BenchmarkToMontELEMENT(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.ToMont()
+	}
+}
+func BenchmarkSquareELEMENT(b *testing.B) {
+	benchResElement.SetRandom()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.Square(&benchResElement)
+	}
+}
+
+func BenchmarkMulAssignELEMENT(b *testing.B) {
+	x := Element{
+		1997599621687373223,
+		6052339484930628067,
+		10108755138030829701,
+		150537098327114917,
+	}
+	benchResElement.SetOne()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		benchResElement.MulAssign(&x)
+	}
+}

ff/util.go

@@ -0,0 +1,5 @@
+package ff
+
+func NewElement() *Element {
+	return &Element{}
+}

field/field.go

@@ -1,152 +0,0 @@
-// code originally taken from https://github.com/arnaucube/go-snark (https://github.com/arnaucube/go-snark/blob/master/fields/fq.go), pasted here to ensure compatibility among future changes
-
-package field
-
-import (
-	"bytes"
-	"crypto/rand"
-	"math/big"
-)
-
-// Fq is the Z field over modulus Q
-type Fq struct {
-	Q *big.Int // Q
-}
-
-// NewFq generates a new Fq
-func NewFq(q *big.Int) Fq {
-	return Fq{
-		q,
-	}
-}
-
-// Zero returns a Zero value on the Fq
-func (fq Fq) Zero() *big.Int {
-	return big.NewInt(int64(0))
-}
-
-// One returns a One value on the Fq
-func (fq Fq) One() *big.Int {
-	return big.NewInt(int64(1))
-}
-
-// Add performs an addition on the Fq
-func (fq Fq) Add(a, b *big.Int) *big.Int {
-	r := new(big.Int).Add(a, b)
-	return new(big.Int).Mod(r, fq.Q)
-}
-
-// Double performs a doubling on the Fq
-func (fq Fq) Double(a *big.Int) *big.Int {
-	r := new(big.Int).Add(a, a)
-	return new(big.Int).Mod(r, fq.Q)
-}
-
-// Sub performs a subtraction on the Fq
-func (fq Fq) Sub(a, b *big.Int) *big.Int {
-	r := new(big.Int).Sub(a, b)
-	return new(big.Int).Mod(r, fq.Q)
-}
-
-// Neg performs a negation on the Fq
-func (fq Fq) Neg(a *big.Int) *big.Int {
-	m := new(big.Int).Neg(a)
-	return new(big.Int).Mod(m, fq.Q)
-}
-
-// Mul performs a multiplication on the Fq
-func (fq Fq) Mul(a, b *big.Int) *big.Int {
-	m := new(big.Int).Mul(a, b)
-	return new(big.Int).Mod(m, fq.Q)
-}
-
-func (fq Fq) MulScalar(base, e *big.Int) *big.Int {
-	return fq.Mul(base, e)
-}
-
-// Inverse returns the inverse on the Fq
-func (fq Fq) Inverse(a *big.Int) *big.Int {
-	return new(big.Int).ModInverse(a, fq.Q)
-}
-
-// Div performs the division over the finite field
-func (fq Fq) Div(a, b *big.Int) *big.Int {
-	d := fq.Mul(a, fq.Inverse(b))
-	return new(big.Int).Mod(d, fq.Q)
-}
-
-// Square performs a square operation on the Fq
-func (fq Fq) Square(a *big.Int) *big.Int {
-	m := new(big.Int).Mul(a, a)
-	return new(big.Int).Mod(m, fq.Q)
-}
-
-// Exp performs the exponential over Fq
-func (fq Fq) Exp(base *big.Int, e *big.Int) *big.Int {
-	res := fq.One()
-	rem := fq.Copy(e)
-	exp := base
-
-	for !bytes.Equal(rem.Bytes(), big.NewInt(int64(0)).Bytes()) {
-		if BigIsOdd(rem) {
-			res = fq.Mul(res, exp)
-		}
-		exp = fq.Square(exp)
-		rem = new(big.Int).Rsh(rem, 1)
-	}
-	return res
-}
-
-func (fq Fq) Rand() (*big.Int, error) {
-
-	maxbits := fq.Q.BitLen()
-	b := make([]byte, (maxbits/8)-1)
-	_, err := rand.Read(b)
-	if err != nil {
-		return nil, err
-	}
-	r := new(big.Int).SetBytes(b)
-	rq := new(big.Int).Mod(r, fq.Q)
-
-	// r over q, nil
-	return rq, nil
-}
-
-func (fq Fq) IsZero(a *big.Int) bool {
-	return bytes.Equal(a.Bytes(), fq.Zero().Bytes())
-}
-
-func (fq Fq) Copy(a *big.Int) *big.Int {
-	return new(big.Int).SetBytes(a.Bytes())
-}
-
-func (fq Fq) Affine(a *big.Int) *big.Int {
-	nq := fq.Neg(fq.Q)
-
-	aux := a
-	if aux.Cmp(big.NewInt(int64(0))) == -1 { // negative value
-		if aux.Cmp(nq) != 1 { // aux less or equal nq
-			aux = new(big.Int).Mod(aux, fq.Q)
-		}
-		if aux.Cmp(big.NewInt(int64(0))) == -1 { // negative value
-			aux = new(big.Int).Add(aux, fq.Q)
-		}
-	} else {
-		if aux.Cmp(fq.Q) != -1 { // aux greater or equal nq
-			aux = new(big.Int).Mod(aux, fq.Q)
-		}
-	}
-	return aux
-}
-
-func (fq Fq) Equal(a, b *big.Int) bool {
-	aAff := fq.Affine(a)
-	bAff := fq.Affine(b)
-	return bytes.Equal(aAff.Bytes(), bAff.Bytes())
-}
-
-func BigIsOdd(n *big.Int) bool {
-	one := big.NewInt(int64(1))
-	and := new(big.Int).And(n, one)
-	return bytes.Equal(and.Bytes(), big.NewInt(int64(1)).Bytes())
-}

field/field_test.go

@@ -1,39 +0,0 @@
-// code originally taken from https://github.com/arnaucube/go-snark (https://github.com/arnaucube/go-snark/blob/master/fields/fq.go), pasted here to ensure compatibility among future changes
-
-package field
-
-import (
-	"math/big"
-	"testing"
-
-	"github.com/stretchr/testify/assert"
-)
-
-func iToBig(a int) *big.Int {
-	return big.NewInt(int64(a))
-}
-
-func TestFq1(t *testing.T) {
-	fq1 := NewFq(iToBig(7))
-
-	res := fq1.Add(iToBig(4), iToBig(4))
-	assert.Equal(t, iToBig(1), fq1.Affine(res))
-
-	res = fq1.Double(iToBig(5))
-	assert.Equal(t, iToBig(3), fq1.Affine(res))
-
-	res = fq1.Sub(iToBig(5), iToBig(7))
-	assert.Equal(t, iToBig(5), fq1.Affine(res))
-
-	res = fq1.Neg(iToBig(5))
-	assert.Equal(t, iToBig(2), fq1.Affine(res))
-
-	res = fq1.Mul(iToBig(5), iToBig(11))
-	assert.Equal(t, iToBig(6), fq1.Affine(res))
-
-	res = fq1.Inverse(iToBig(4))
-	assert.Equal(t, iToBig(2), res)
-
-	res = fq1.Square(iToBig(5))
-	assert.Equal(t, iToBig(4), res)
-}

go.mod

@@ -4,7 +4,7 @@ go 1.12
 
 require (
 	github.com/dchest/blake512 v1.0.0
-	github.com/ethereum/go-ethereum v1.8.27
+	github.com/ethereum/go-ethereum v1.9.12
-	github.com/stretchr/testify v1.3.0
+	github.com/stretchr/testify v1.4.0
-	golang.org/x/crypto v0.0.0-20190621222207-cc06ce4a13d4
+	golang.org/x/crypto v0.0.0-20200311171314-f7b00557c8c4
 )

go.sum

@@ -1,20 +1,172 @@
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mimc7/mimc7.go

@@ -6,7 +6,7 @@ import (
 
 	"github.com/ethereum/go-ethereum/crypto"
 	_constants "github.com/iden3/go-iden3-crypto/constants"
-	"github.com/iden3/go-iden3-crypto/field"
+	"github.com/iden3/go-iden3-crypto/ff"
 	"github.com/iden3/go-iden3-crypto/utils"
 )
 
@@ -15,73 +15,72 @@ const SEED = "mimc"
 var constants = generateConstantsData()
 
 type constantsData struct {
-	maxFieldVal *big.Int
+	seedHash *big.Int
-	seedHash    *big.Int
+	iv       *big.Int
-	iv          *big.Int
+	nRounds  int
-	fqR         field.Fq
+	cts      []*ff.Element
-	nRounds     int
-	cts         []*big.Int
 }
 
 func generateConstantsData() constantsData {
 	var constants constantsData
 
-	fqR := field.NewFq(_constants.Q)
-	constants.fqR = fqR
-
-	// maxFieldVal is the R value of the Finite Field
-	constants.maxFieldVal = constants.fqR.Q
-
 	constants.seedHash = new(big.Int).SetBytes(crypto.Keccak256([]byte(SEED)))
 	c := new(big.Int).SetBytes(crypto.Keccak256([]byte(SEED + "_iv")))
-	constants.iv = new(big.Int).Mod(c, constants.maxFieldVal)
+	constants.iv = new(big.Int).Mod(c, _constants.Q)
 
 	constants.nRounds = 91
-	cts := getConstants(constants.fqR, SEED, constants.nRounds)
+	cts := getConstants(SEED, constants.nRounds)
 	constants.cts = cts
 	return constants
 }
 
-func getConstants(fqR field.Fq, seed string, nRounds int) []*big.Int {
+func getConstants(seed string, nRounds int) []*ff.Element {
-	cts := make([]*big.Int, nRounds)
+	cts := make([]*ff.Element, nRounds)
-	cts[0] = big.NewInt(int64(0))
+	cts[0] = ff.NewElement()
 	c := new(big.Int).SetBytes(crypto.Keccak256([]byte(SEED)))
 	for i := 1; i < nRounds; i++ {
 		c = new(big.Int).SetBytes(crypto.Keccak256(c.Bytes()))
 
-		n := fqR.Affine(c)
+		n := new(big.Int).Mod(c, _constants.Q)
-		cts[i] = n
+		cts[i] = ff.NewElement().SetBigInt(n)
 	}
 	return cts
 }
 
 // MIMC7HashGeneric performs the MIMC7 hash over a *big.Int, in a generic way, where it can be specified the Finite Field over R, and the number of rounds
-func MIMC7HashGeneric(fqR field.Fq, xIn, k *big.Int, nRounds int) *big.Int {
+func MIMC7HashGeneric(xInBI, kBI *big.Int, nRounds int) *big.Int {
-	cts := getConstants(fqR, SEED, nRounds)
+	xIn := ff.NewElement().SetBigInt(xInBI)
-	var r *big.Int
+	k := ff.NewElement().SetBigInt(kBI)
+
+	cts := getConstants(SEED, nRounds)
+	var r *ff.Element
 	for i := 0; i < nRounds; i++ {
-		var t *big.Int
+		var t *ff.Element
 		if i == 0 {
-			t = fqR.Add(xIn, k)
+			t = ff.NewElement().Add(xIn, k)
 		} else {
-			t = fqR.Add(fqR.Add(r, k), cts[i])
+			t = ff.NewElement().Add(ff.NewElement().Add(r, k), cts[i])
 		}
-		t2 := fqR.Square(t)
+		t2 := ff.NewElement().Square(t)
-		t4 := fqR.Square(t2)
+		t4 := ff.NewElement().Square(t2)
-		r = fqR.Mul(fqR.Mul(t4, t2), t)
+		r = ff.NewElement().Mul(ff.NewElement().Mul(t4, t2), t)
 	}
-	return fqR.Affine(fqR.Add(r, k))
+	rE := ff.NewElement().Add(r, k)
+
+	res := big.NewInt(0)
+	rE.ToBigIntRegular(res)
+	return res
 }
 
 // HashGeneric performs the MIMC7 hash over a *big.Int array, in a generic way, where it can be specified the Finite Field over R, and the number of rounds
-func HashGeneric(iv *big.Int, arr []*big.Int, fqR field.Fq, nRounds int) (*big.Int, error) {
+func HashGeneric(iv *big.Int, arr []*big.Int, nRounds int) (*big.Int, error) {
-	if !utils.CheckBigIntArrayInField(arr, constants.fqR.Q) {
+	if !utils.CheckBigIntArrayInField(arr) {
 		return nil, errors.New("inputs values not inside Finite Field")
 	}
 	r := iv
 	var err error
 	for i := 0; i < len(arr); i++ {
-		r = MIMC7HashGeneric(fqR, r, arr[i], nRounds)
+		r = MIMC7HashGeneric(r, arr[i], nRounds)
 		if err != nil {
 			return r, err
 		}
@@ -90,40 +89,48 @@ func HashGeneric(iv *big.Int, arr []*big.Int, fqR field.Fq, nRounds int) (*big.I
 }
 
 // MIMC7Hash performs the MIMC7 hash over a *big.Int, using the Finite Field over R and the number of rounds setted in the `constants` variable
-func MIMC7Hash(xIn, k *big.Int) *big.Int {
+func MIMC7Hash(xInBI, kBI *big.Int) *big.Int {
-	var r *big.Int
+	xIn := ff.NewElement().SetBigInt(xInBI)
+	k := ff.NewElement().SetBigInt(kBI)
+
+	var r *ff.Element
 	for i := 0; i < constants.nRounds; i++ {
-		var t *big.Int
+		var t *ff.Element
 		if i == 0 {
-			t = constants.fqR.Add(xIn, k)
+			t = ff.NewElement().Add(xIn, k)
 		} else {
-			t = constants.fqR.Add(constants.fqR.Add(r, k), constants.cts[i])
+			t = ff.NewElement().Add(ff.NewElement().Add(r, k), constants.cts[i])
 		}
-		t2 := constants.fqR.Square(t)
+		t2 := ff.NewElement().Square(t)
-		t4 := constants.fqR.Square(t2)
+		t4 := ff.NewElement().Square(t2)
-		r = constants.fqR.Mul(constants.fqR.Mul(t4, t2), t)
+		r = ff.NewElement().Mul(ff.NewElement().Mul(t4, t2), t)
 	}
-	return constants.fqR.Affine(constants.fqR.Add(r, k))
+	rE := ff.NewElement().Add(r, k)
+
+	res := big.NewInt(0)
+	rE.ToBigIntRegular(res)
+	return res
 }
 
 // Hash performs the MIMC7 hash over a *big.Int array
 func Hash(arr []*big.Int, key *big.Int) (*big.Int, error) {
-	if !utils.CheckBigIntArrayInField(arr, constants.fqR.Q) {
+	if !utils.CheckBigIntArrayInField(arr) {
 		return nil, errors.New("inputs values not inside Finite Field")
 	}
 	var r *big.Int
 	if key == nil {
-		r = constants.fqR.Zero()
+		r = big.NewInt(0)
 	} else {
 		r = key
 	}
 	for i := 0; i < len(arr); i++ {
-		r = constants.fqR.Add(
+		r = new(big.Int).Add(
-			constants.fqR.Add(
+			new(big.Int).Add(
 				r,
 				arr[i],
 			),
 			MIMC7Hash(arr[i], r))
+		r = new(big.Int).Mod(r, _constants.Q)
 	}
 	return r, nil
 }

mimc7/mimc7_test.go

@@ -6,7 +6,6 @@ import (
 	"testing"
 
 	"github.com/ethereum/go-ethereum/crypto"
-	"github.com/iden3/go-iden3-crypto/field"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -22,16 +21,12 @@ func TestMIMC7Generic(t *testing.T) {
 	b2 := big.NewInt(int64(2))
 	b3 := big.NewInt(int64(3))
 
-	r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
-	assert.True(t, ok)
-	fqR := field.NewFq(r)
-
 	bigArray := []*big.Int{b1, b2, b3}
 
 	// Generic Hash
-	mhg := MIMC7HashGeneric(fqR, b1, b2, 91)
+	mhg := MIMC7HashGeneric(b1, b2, 91)
 	assert.Equal(t, "10594780656576967754230020536574539122676596303354946869887184401991294982664", mhg.String())
-	hg, err := HashGeneric(fqR.Zero(), bigArray, fqR, 91)
+	hg, err := HashGeneric(big.NewInt(0), bigArray, 91)
 	assert.Nil(t, err)
 	assert.Equal(t, "6464402164086696096195815557694604139393321133243036833927490113253119343397", (*big.Int)(hg).String())
 }
@@ -91,9 +86,7 @@ func BenchmarkMIMC7(b *testing.B) {
 	b41 := big.NewInt(int64(41))
 	bigArray4 := []*big.Int{b12, b45, b78, b41}
 
-	var h4 *big.Int
 	for i := 0; i < b.N; i++ {
-		h4, _ = Hash(bigArray4, nil)
+		Hash(bigArray4, nil) //nolint:errcheck
 	}
-	println(h4)
 }

poseidon/poseidon.go

@@ -1,13 +1,12 @@
 package poseidon
 
 import (
-	"bytes"
 	"errors"
 	"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/ff"
 	"github.com/iden3/go-iden3-crypto/utils"
 	"golang.org/x/crypto/blake2b"
 )
@@ -17,42 +16,28 @@ const NROUNDSF = 8
 const NROUNDSP = 57
 const T = 6
 
-var constants = generateConstantsData()
+var constC []*ff.Element
+var constM [T][T]*ff.Element
 
-type constantsData struct {
+func Zero() *ff.Element {
-	fqR field.Fq
+	return ff.NewElement()
-	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)
-	constants.fqR = fqR
-	constants.c = getPseudoRandom(fqR, SEED+"_constants", NROUNDSF+NROUNDSP)
-	constants.m = getMDS(fqR)
-
-	return constants
 }
 
-func leByteArrayToBigInt(b []byte) *big.Int {
+func init() {
-	res := big.NewInt(0)
+	constC = getPseudoRandom(SEED+"_constants", NROUNDSF+NROUNDSP)
-	for i := 0; i < len(b); i++ {
+	constM = getMDS()
-		n := big.NewInt(int64(b[i]))
-		res = new(big.Int).Add(res, new(big.Int).Lsh(n, uint(i*8)))
-	}
-	return res
 }
 
-func getPseudoRandom(fqR field.Fq, seed string, n int) []*big.Int {
+func getPseudoRandom(seed string, n int) []*ff.Element {
-	var res []*big.Int
+	res := make([]*ff.Element, n)
 	hash := blake2b.Sum256([]byte(seed))
-	for len(res) < n {
+	for i := 0; i < n; i++ {
-		hashBigInt := new(big.Int)
+		hashBigInt := big.NewInt(int64(0))
-		newN := fqR.Affine(utils.SetBigIntFromLEBytes(hashBigInt, hash[:]))
+		res[i] = ff.NewElement().SetBigInt(utils.SetBigIntFromLEBytes(hashBigInt, hash[:]))
-		// newN := fqR.Affine(leByteArrayToBigInt(hash[:]))
-		res = append(res, newN)
 		hash = blake2b.Sum256(hash[:])
 	}
 	return res
@@ -67,31 +52,30 @@ 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]*ff.Element {
 	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]*ff.Element
 	for i := 0; i < T; i++ {
-		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] = ff.NewElement().Sub(cauchyMatrix[i], cauchyMatrix[T+j])
+			m[i][j].Inverse(m[i][j])
 		}
-		m = append(m, mi)
 	}
 	return m
 }
 
-func checkAllDifferent(v []*big.Int) bool {
+func checkAllDifferent(v []*ff.Element) bool {
 	for i := 0; i < len(v); i++ {
-		if bytes.Equal(v[i].Bytes(), big.NewInt(int64(0)).Bytes()) {
+		if v[i].Equal(ff.NewElement()) {
 			return false
 		}
 		for j := i + 1; j < len(v); j++ {
-			if bytes.Equal(v[i].Bytes(), v[j].Bytes()) {
+			if v[i].Equal(v[j]) {
 				return false
 			}
 		}
@@ -100,89 +84,94 @@ 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]*ff.Element, c *ff.Element) {
-	for i := 0; i < len(state); i++ {
+	for i := 0; i < T; i++ {
-		state[i] = constants.fqR.Add(state[i], c)
+		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 {
+
-	return constants.fqR.Mul(a, constants.fqR.Square(constants.fqR.Square(a)))
+func cubic(a *ff.Element) {
+	a.Exp(*a, 5)
 }
 
 // sbox https://eprint.iacr.org/2019/458.pdf page 6
-func sbox(state []*big.Int, i int) []*big.Int {
+func sbox(state [T]*ff.Element, 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]*ff.Element, newState [T]*ff.Element, m [T][T]*ff.Element) {
-	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].SetUint64(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]))
+			mul.Mul(m[i][j], state[j])
+			newState[i].Add(newState[i], mul)
 		}
 	}
-	return newState
 }
 
 // PoseidonHash computes the Poseidon hash for the given inputs
-func PoseidonHash(inp []*big.Int) (*big.Int, error) {
+func PoseidonHash(inpBI [T]*big.Int) (*big.Int, error) {
-	if len(inp) == 0 || len(inp) > T {
+	if !utils.CheckBigIntArrayInField(inpBI[:]) {
-		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
+	inp := utils.BigIntArrayToElementArray(inpBI[:])
-	for i := len(inp); i < T; i++ {
+	state := [T]*ff.Element{}
-		state = append(state, constants.fqR.Zero())
+	for i := 0; i < T; i++ {
+		state[i] = ff.NewElement().Set(inp[i])
 	}
 
 	// ARK --> SBox --> M, https://eprint.iacr.org/2019/458.pdf pag.5
-	for i := 0; i < NROUNDSF+NROUNDSP; i++ {
+	var newState [T]*ff.Element
-		state = ark(state, constants.c[i])
+	for i := 0; i < T; i++ {
-		state = sbox(state, i)
+		newState[i] = Zero()
-		state = mix(state, constants.m)
 	}
-	return state[0], nil
+	for i := 0; i < NROUNDSF+NROUNDSP; i++ {
+		ark(state, constC[i])
+		sbox(state, i)
+		mix(state, newState, constM)
+		state, newState = newState, state
+	}
+	rE := state[0]
+	r := big.NewInt(0)
+	rE.ToBigIntRegular(r)
+	return r, nil
 }
 
-// Hash performs the Poseidon hash over a *big.Int array
+// Hash performs the Poseidon hash over a ff.Element array
 // in chunks of 5 elements
 func Hash(arr []*big.Int) (*big.Int, error) {
-	if !utils.CheckBigIntArrayInField(arr, constants.fqR.Q) {
+	r := big.NewInt(int64(1))
-		return nil, errors.New("inputs values not inside Finite Field")
+	for i := 0; i < len(arr); i = i + T - 1 {
-	}
+		var toHash [T]*big.Int
-
+		j := 0
-	r := constants.fqR.Zero()
+		for ; j < T-1; j++ {
-	for i := 0; i < len(arr); i = i + 5 {
+			if i+j >= len(arr) {
-		var fiveElems []*big.Int
+				break
-		for j := 0; j < 5; j++ {
-			if i+j < len(arr) {
-				fiveElems = append(fiveElems, arr[i+j])
-			} else {
-				fiveElems = append(fiveElems, big.NewInt(int64(0)))
 			}
+			toHash[j] = arr[i+j]
 		}
-		ph, err := PoseidonHash(fiveElems)
+		toHash[j] = r
+		j++
+		for ; j < T; j++ {
+			toHash[j] = big.NewInt(0)
+		}
+
+		ph, err := PoseidonHash(toHash)
 		if err != nil {
 			return nil, err
 		}
-		r = constants.fqR.Add(
+		modQ(r.Add(r, ph))
-			r,
-			ph)
 	}
 
 	return r, nil
@@ -194,12 +183,13 @@ 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 := big.NewInt(int64(0))
 		utils.SetBigIntFromLEBytes(v, b[n*i:n*(i+1)])
 		bElems = append(bElems, v)
+
 	}
 	if len(b)%n != 0 {
-		v := new(big.Int)
+		v := big.NewInt(int64(0))
 		utils.SetBigIntFromLEBytes(v, b[(len(b)/n)*n:])
 		bElems = append(bElems, v)
 	}

poseidon/poseidon_test.go

@@ -16,17 +16,29 @@ func TestBlake2bVersion(t *testing.T) {
 }
 
 func TestPoseidon(t *testing.T) {
-	b1 := big.NewInt(int64(1))
+	b1 := big.NewInt(1)
-	b2 := big.NewInt(int64(2))
+	b2 := big.NewInt(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))
+	b3 := big.NewInt(3)
-	b4 := big.NewInt(int64(4))
+	b4 := big.NewInt(4)
 	h, err = Hash([]*big.Int{b3, b4})
 	assert.Nil(t, err)
-	assert.Equal(t, "17185195740979599334254027721507328033796809509313949281114643312710535000993", h.String())
+	assert.Equal(t, "4635491972858758537477743930622086396911540895966845494943021655521913507504", h.String())
+
+	b5 := big.NewInt(5)
+	b6 := big.NewInt(6)
+	b7 := big.NewInt(7)
+	b8 := big.NewInt(8)
+	b9 := big.NewInt(9)
+	b10 := big.NewInt(10)
+	b11 := big.NewInt(11)
+	b12 := big.NewInt(12)
+	h, err = Hash([]*big.Int{b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12})
+	assert.Nil(t, err)
+	assert.Equal(t, "15278801138972282646981503374384603641625274360649669926363020545395022098027", 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 +55,7 @@ func TestPoseidon(t *testing.T) {
 	}
 	hmsg, err := Hash(msgElems)
 	assert.Nil(t, err)
-	assert.Equal(t, "11821124228916291136371255062457365369197326845706357273715164664419275913793", 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)
@@ -59,9 +71,52 @@ func TestPoseidon(t *testing.T) {
 	}
 	hmsg2, err := Hash(msg2Elems)
 	assert.Nil(t, err)
-	assert.Equal(t, "10747013384255785702102976082726575658403084163954725275481577373644732938016", hmsg2.String())
+	assert.Equal(t, "2978613163687734485261639854325792381691890647104372645321246092227111432722", hmsg2.String())
 
 	hmsg2, err = HashBytes(msg2)
 	assert.Nil(t, err)
-	assert.Equal(t, "10747013384255785702102976082726575658403084163954725275481577373644732938016", hmsg2.String())
+	assert.Equal(t, "2978613163687734485261639854325792381691890647104372645321246092227111432722", hmsg2.String())
+}
+
+func TestPoseidonBrokenChunks(t *testing.T) {
+	h1, err := Hash([]*big.Int{big.NewInt(0), big.NewInt(1), big.NewInt(2), big.NewInt(3), big.NewInt(4),
+		big.NewInt(5), big.NewInt(6), big.NewInt(7), big.NewInt(8), big.NewInt(9)})
+	assert.Nil(t, err)
+	h2, err := Hash([]*big.Int{big.NewInt(5), big.NewInt(6), big.NewInt(7), big.NewInt(8), big.NewInt(9),
+		big.NewInt(0), big.NewInt(1), big.NewInt(2), big.NewInt(3), big.NewInt(4)})
+	assert.Nil(t, err)
+	assert.NotEqual(t, h1, h2)
+}
+
+func TestPoseidonBrokenPadding(t *testing.T) {
+	h1, err := Hash([]*big.Int{big.NewInt(int64(1))})
+	assert.Nil(t, err)
+	h2, err := Hash([]*big.Int{big.NewInt(int64(1)), big.NewInt(int64(0))})
+	assert.Nil(t, err)
+	assert.NotEqual(t, h1, h2)
+}
+
+func BenchmarkPoseidon(b *testing.B) {
+	b12 := big.NewInt(int64(12))
+	b45 := big.NewInt(int64(45))
+	b78 := big.NewInt(int64(78))
+	b41 := big.NewInt(int64(41))
+	bigArray4 := []*big.Int{b12, b45, b78, b41}
+
+	for i := 0; i < b.N; i++ {
+		Hash(bigArray4) //nolint:errcheck
+	}
+}
+
+func BenchmarkPoseidonLarge(b *testing.B) {
+	b12 := utils.NewIntFromString("11384336176656855268977457483345535180380036354188103142384839473266348197733")
+	b45 := utils.NewIntFromString("11384336176656855268977457483345535180380036354188103142384839473266348197733")
+	b78 := utils.NewIntFromString("11384336176656855268977457483345535180380036354188103142384839473266348197733")
+	b41 := utils.NewIntFromString("11384336176656855268977457483345535180380036354188103142384839473266348197733")
+
+	bigArray4 := []*big.Int{b12, b45, b78, b41}
+
+	for i := 0; i < b.N; i++ {
+		Hash(bigArray4) //nolint:errcheck
+	}
 }

utils/showarchbits_test.go

@@ -0,0 +1,11 @@
+package utils
+
+import (
+	"fmt"
+	"math/bits"
+	"testing"
+)
+
+func TestShowArchBits(t *testing.T) {
+	fmt.Printf("Architecture is %v bits\n", bits.UintSize)
+}

utils/utils.go

@@ -6,6 +6,9 @@ import (
 	"fmt"
 	"math/big"
 	"strings"
+
+	"github.com/iden3/go-iden3-crypto/constants"
+	"github.com/iden3/go-iden3-crypto/ff"
 )
 
 // NewIntFromString creates a new big.Int from a decimal integer encoded as a
@@ -63,9 +66,7 @@ func HexEncode(bs []byte) string {
 
 // HexDecode decodes a hex string into an array of bytes.
 func HexDecode(h string) ([]byte, error) {
-	if strings.HasPrefix(h, "0x") {
+	h = strings.TrimPrefix(h, "0x")
-		h = h[2:]
-	}
 	return hex.DecodeString(h)
 }
 
@@ -87,20 +88,38 @@ func HexDecodeInto(dst []byte, h []byte) error {
 	return nil
 }
 
-// CheckBigIntInField checks if given big.Int fits in a Field Q element
+// CheckBigIntInField checks if given *big.Int fits in a Field Q element
-func CheckBigIntInField(a *big.Int, q *big.Int) bool {
+func CheckBigIntInField(a *big.Int) bool {
-	if a.Cmp(q) != -1 {
+	return a.Cmp(constants.Q) == -1
-		return false
-	}
-	return true
 }
 
-// CheckBigIntArrayInField checks if given big.Int fits in a Field Q element
+// CheckBigIntArrayInField checks if given *big.Int fits in a Field Q element
-func CheckBigIntArrayInField(arr []*big.Int, q *big.Int) bool {
+func CheckBigIntArrayInField(arr []*big.Int) bool {
 	for _, a := range arr {
-		if !CheckBigIntInField(a, q) {
+		if !CheckBigIntInField(a) {
 			return false
 		}
 	}
 	return true
 }
+
+// BigIntArrayToElementArray converts an array of *big.Int into an array of *ff.Element
+func BigIntArrayToElementArray(bi []*big.Int) []*ff.Element {
+	var o []*ff.Element
+	for i := range bi {
+		o = append(o, ff.NewElement().SetBigInt(bi[i]))
+	}
+	return o
+}
+
+// ElementArrayToBigIntArray converts an array of *ff.Element into an array of *big.Int
+func ElementArrayToBigIntArray(e []*ff.Element) []*big.Int {
+	var o []*big.Int
+	for i := range e {
+		ei := e[i]
+		bi := big.NewInt(0)
+		ei.ToBigIntRegular(bi)
+		o = append(o, bi)
+	}
+	return o
+}