Add utils.ElementArrayToBigIntArray

Add github actions and remove travis

.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 ./...

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/eddsa_test.go

@@ -1,7 +1,6 @@
 package babyjub
 
 import (
-	"crypto/rand"
 	"encoding/hex"
 	"fmt"
 	"math/big"
@@ -10,25 +9,13 @@ 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) {
-	k := NewRandPrivKey()
-	fmt.Println("k", hex.EncodeToString(k[:]))
-
-	msgBuf := [32]byte{}
-	rand.Read(msgBuf[:])
-	msg := utils.SetBigIntFromLEBytes(new(big.Int), msgBuf[:])
-	msg.Mod(msg, constants.Q)
-	fmt.Println("msg", msg)
-
-	return &k, msg
-}
-
 func TestPublicKey(t *testing.T) {
 	var k PrivateKey
-	for i := 0; i < 256; i++ {
+	for i := 0; i < 32; i++ {
-		hex.Decode(k[:], []byte{byte(i)})
+		k[i] = byte(i)
 	}
 	pk := k.Public()
 	assert.True(t, pk.X.Cmp(constants.Q) == -1)
@@ -37,7 +24,8 @@ func TestPublicKey(t *testing.T) {
 
 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)
@@ -81,7 +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)
@@ -125,7 +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))
@@ -144,7 +134,8 @@ func TestCompressDecompress(t *testing.T) {
 
 func BenchmarkBabyjubEddsa(b *testing.B) {
 	var k PrivateKey
-	hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	_, err := hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	require.Nil(b, err)
 	pk := k.Public()
 
 	const n = 256

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)
 }

ff/arith.go

@@ -12,19 +12,14 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by goff (v0.2.0) DO NOT EDIT
+// Code generated by goff DO NOT EDIT
 
-// Package ff contains field arithmetic operations
 package ff
 
 import (
 	"math/bits"
-
-	"golang.org/x/sys/cpu"
 )
 
-var supportAdx = cpu.X86.HasADX && cpu.X86.HasBMI2
-
 func madd(a, b, t, u, v uint64) (uint64, uint64, uint64) {
 	var carry uint64
 	hi, lo := bits.Mul64(a, b)

ff/element.go

@@ -12,33 +12,29 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by goff (v0.2.0) DO NOT EDIT
+// 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 contains field arithmetic operations
+// Package ff (generated by goff) contains field arithmetics operations
 package ff
 
-// /!\ WARNING /!\
-// this code has not been audited and is provided as-is. In particular,
-// there is no security guarantees such as constant time implementation
-// or side-channel attack resistance
-// /!\ WARNING /!\
-
 import (
 	"crypto/rand"
 	"encoding/binary"
 	"io"
 	"math/big"
 	"math/bits"
-	"strconv"
 	"sync"
+
 	"unsafe"
 )
 
 // Element represents a field element stored on 4 words (uint64)
 // Element are assumed to be in Montgomery form in all methods
-// field modulus q =
-//
-// 21888242871839275222246405745257275088548364400416034343698204186575808495617
 type Element [4]uint64
 
 // ElementLimbs number of 64 bits words needed to represent Element
@@ -315,7 +311,6 @@ func (z *Element) SetRandom() *Element {
 	z[3] %= 3486998266802970665
 
 	// if z > q --> z -= q
-	// note: this is NOT constant time
 	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)
@@ -327,38 +322,6 @@ func (z *Element) SetRandom() *Element {
 	return z
 }
 
-// One returns 1 (in montgommery form)
-func One() Element {
-	var one Element
-	one.SetOne()
-	return one
-}
-
-// FromInterface converts i1 from uint64, int, string, or Element, big.Int into Element
-// panic if provided type is not supported
-func FromInterface(i1 interface{}) Element {
-	var val Element
-
-	switch c1 := i1.(type) {
-	case uint64:
-		val.SetUint64(c1)
-	case int:
-		val.SetString(strconv.Itoa(c1))
-	case string:
-		val.SetString(c1)
-	case big.Int:
-		val.SetBigInt(&c1)
-	case Element:
-		val = c1
-	case *Element:
-		val.Set(c1)
-	default:
-		panic("invalid type")
-	}
-
-	return val
-}
-
 // Add z = x + y mod q
 func (z *Element) Add(x, y *Element) *Element {
 	var carry uint64
@@ -369,7 +332,6 @@ func (z *Element) Add(x, y *Element) *Element {
 	z[3], _ = bits.Add64(x[3], y[3], carry)
 
 	// if z > q --> z -= q
-	// note: this is NOT constant time
 	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)
@@ -390,7 +352,6 @@ func (z *Element) AddAssign(x *Element) *Element {
 	z[3], _ = bits.Add64(z[3], x[3], carry)
 
 	// if z > q --> z -= q
-	// note: this is NOT constant time
 	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)
@@ -411,7 +372,6 @@ func (z *Element) Double(x *Element) *Element {
 	z[3], _ = bits.Add64(x[3], x[3], carry)
 
 	// if z > q --> z -= q
-	// note: this is NOT constant time
 	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)
@@ -456,31 +416,18 @@ func (z *Element) SubAssign(x *Element) *Element {
 	return z
 }
 
-// Exp z = x^exponent mod q
+// Exp z = x^e mod q
-// (not optimized)
+func (z *Element) Exp(x Element, e uint64) *Element {
-// exponent (non-montgomery form) is ordered from least significant word to most significant word
+	if e == 0 {
-func (z *Element) Exp(x Element, exponent ...uint64) *Element {
-	r := 0
-	msb := 0
-	for i := len(exponent) - 1; i >= 0; i-- {
-		if exponent[i] == 0 {
-			r++
-		} else {
-			msb = (i * 64) + bits.Len64(exponent[i])
-			break
-		}
-	}
-	exponent = exponent[:len(exponent)-r]
-	if len(exponent) == 0 {
 		return z.SetOne()
 	}
 
 	z.Set(&x)
 
-	l := msb - 2
+	l := bits.Len64(e) - 2
 	for i := l; i >= 0; i-- {
 		z.Square(z)
-		if exponent[i/64]&(1<<uint(i%64)) != 0 {
+		if e&(1<<uint(i)) != 0 {
 			z.MulAssign(&x)
 		}
 	}
@@ -531,7 +478,6 @@ func (z *Element) FromMont() *Element {
 	}
 
 	// if z > q --> z -= q
-	// note: this is NOT constant time
 	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)
@@ -603,19 +549,6 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 	zero := big.NewInt(0)
 	q := elementModulusBigInt()
 
-	// fast path
-	c := v.Cmp(q)
-	if c == 0 {
-		return z
-	} else if c != 1 && v.Cmp(zero) != -1 {
-		// v should
-		vBits := v.Bits()
-		for i := 0; i < len(vBits); i++ {
-			z[i] = uint64(vBits[i])
-		}
-		return z.ToMont()
-	}
-
 	// copy input
 	vv := new(big.Int).Set(v)
 
@@ -658,97 +591,202 @@ func (z *Element) SetString(s string) *Element {
 	return z.SetBigInt(x)
 }
 
-// Legendre returns the Legendre symbol of z (either +1, -1, or 0.)
+// Mul z = x * y mod q
-func (z *Element) Legendre() int {
+func (z *Element) Mul(x, y *Element) *Element {
-	var l Element
-	// z^((q-1)/2)
-	l.Exp(*z,
-		11669102379873075200,
-		10671829228508198984,
-		15863968012492123182,
-		1743499133401485332,
-	)
 
-	if l.IsZero() {
+	var t [4]uint64
-		return 0
+	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 l == 1
+	// if z > q --> z -= q
-	if (l[3] == 1011752739694698287) && (l[2] == 7381016538464732718) && (l[1] == 3962172157175319849) && (l[0] == 12436184717236109307) {
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
-		return 1
+		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 -1
+	return z
 }
 
-// Sqrt z = √x mod q
+// MulAssign z = z * x mod q
-// if the square root doesn't exist (x is not a square mod q)
+func (z *Element) MulAssign(x *Element) *Element {
-// Sqrt leaves z unchanged and returns nil
-func (z *Element) Sqrt(x *Element) *Element {
-	// q ≡ 1 (mod 4)
-	// see modSqrtTonelliShanks in math/big/int.go
-	// using https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020786.02p0470a.pdf
 
-	var y, b, t, w Element
+	var t [4]uint64
-	// w = x^((s-1)/2))
+	var c [3]uint64
-	w.Exp(*x,
+	{
-		14829091926808964255,
+		// round 0
-		867720185306366531,
+		v := z[0]
-		688207751544974772,
+		c[1], c[0] = bits.Mul64(v, x[0])
-		6495040407,
+		m := c[0] * 14042775128853446655
-	)
+		c[2] = madd0(m, 4891460686036598785, c[0])
-
+		c[1], c[0] = madd1(v, x[1], c[1])
-	// y = x^((s+1)/2)) = w * x
+		c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0])
-	y.Mul(x, &w)
+		c[1], c[0] = madd1(v, x[2], c[1])
-
+		c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0])
-	// b = x^s = w * w * x = y * x
+		c[1], c[0] = madd1(v, x[3], c[1])
-	b.Mul(&w, &y)
+		t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1])
-
-	// g = nonResidue ^ s
-	var g = Element{
-		7164790868263648668,
-		11685701338293206998,
-		6216421865291908056,
-		1756667274303109607,
 	}
-	r := uint64(28)
+	{
-
+		// round 1
-	// compute legendre symbol
+		v := z[1]
-	// t = x^((q-1)/2) = r-1 squaring of x^s
+		c[1], c[0] = madd1(v, x[0], t[0])
-	t = b
+		m := c[0] * 14042775128853446655
-	for i := uint64(0); i < r-1; i++ {
+		c[2] = madd0(m, 4891460686036598785, c[0])
-		t.Square(&t)
+		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])
 	}
-	if t.IsZero() {
+	{
-		return z.SetZero()
+		// 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])
 	}
-	if !((t[3] == 1011752739694698287) && (t[2] == 7381016538464732718) && (t[1] == 3962172157175319849) && (t[0] == 12436184717236109307)) {
+	{
-		// t != 1, we don't have a square root
+		// round 3
-		return nil
+		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])
 	}
-	for {
-		var m uint64
-		t = b
 
-		// for t != 1
+	// if z > q --> z -= q
-		for !((t[3] == 1011752739694698287) && (t[2] == 7381016538464732718) && (t[1] == 3962172157175319849) && (t[0] == 12436184717236109307)) {
+	if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) {
-			t.Square(&t)
+		var b uint64
-			m++
+		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)
-		if m == 0 {
+		z[3], _ = bits.Sub64(z[3], 3486998266802970665, b)
-			return z.Set(&y)
-		}
-		// t = g^(2^(r-m-1)) mod q
-		ge := int(r - m - 1)
-		t = g
-		for ge > 0 {
-			t.Square(&t)
-			ge--
-		}
-
-		g.Square(&t)
-		y.MulAssign(&t)
-		b.MulAssign(&g)
-		r = m
 	}
+	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_mul.go

@@ -1,170 +0,0 @@
-// +build !amd64
-
-// 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 (v0.2.0) DO NOT EDIT
-
-// Package ff contains field arithmetic operations
-package ff
-
-// /!\ WARNING /!\
-// this code has not been audited and is provided as-is. In particular,
-// there is no security guarantees such as constant time implementation
-// or side-channel attack resistance
-// /!\ WARNING /!\
-
-import "math/bits"
-
-// Mul z = x * y mod q
-// see https://hackmd.io/@zkteam/modular_multiplication
-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
-	// note: this is NOT constant time
-	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
-// see https://hackmd.io/@zkteam/modular_multiplication
-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
-	// note: this is NOT constant time
-	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_mul_amd64.go

@@ -1,39 +0,0 @@
-// 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 (v0.2.0) DO NOT EDIT
-
-// Package ff contains field arithmetic operations
-package ff
-
-// MulAssignElement z = z * x mod q (constant time)
-// calling this instead of z.MulAssign(x) is prefered for performance critical path
-//go:noescape
-func MulAssignElement(res, y *Element)
-
-// Mul z = x * y mod q (constant time)
-// see https://hackmd.io/@zkteam/modular_multiplication
-func (z *Element) Mul(x, y *Element) *Element {
-	res := *x
-	MulAssignElement(&res, y)
-	z.Set(&res)
-	return z
-}
-
-// MulAssign z = z * x mod q (constant time)
-// see https://hackmd.io/@zkteam/modular_multiplication
-func (z *Element) MulAssign(x *Element) *Element {
-	MulAssignElement(z, x)
-	return z
-}

ff/element_mul_amd64.s

@@ -1,695 +0,0 @@
-// Code generated by goff (v0.2.0) DO NOT EDIT
-
-#include "textflag.h"
-
-// func MulAssignElement(res,y *Element)
-// montgomery multiplication of res by y
-// stores the result in res
-TEXT ·MulAssignElement(SB), NOSPLIT, $0-16
-    
-    // dereference our parameters
-    MOVQ res+0(FP), DI
-    MOVQ y+8(FP), R8
-    
-    // check if we support adx and mulx
-    CMPB ·supportAdx(SB), $1
-    JNE no_adx
-    
-    // the algorithm is described here
-    // https://hackmd.io/@zkteam/modular_multiplication
-    // however, to benefit from the ADCX and ADOX carry chains
-    // we split the inner loops in 2:
-    // for i=0 to N-1
-    // 		for j=0 to N-1
-    // 		    (A,t[j])  := t[j] + a[j]*b[i] + A
-    // 		m := t[0]*q'[0] mod W
-    // 		C,_ := t[0] + m*q[0]
-    // 		for j=1 to N-1
-    // 		    (C,t[j-1]) := t[j] + m*q[j] + C
-    // 		t[N-1] = C + A
-    
-    // ---------------------------------------------------------------------------------------------
-    // outter loop 0
-    
-    // clear up the carry flags
-    XORQ R9 , R9
-    
-    // R12 = y[0]
-    MOVQ 0(R8), R12
-    
-    // for j=0 to N-1
-    //    (A,t[j])  := t[j] + x[j]*y[i] + A
-    
-    // DX = res[0]
-    MOVQ 0(DI), DX
-    MULXQ R12, CX ,  R9
-    
-    // DX = res[1]
-    MOVQ 8(DI), DX
-    MOVQ R9, BX
-    MULXQ R12, AX,  R9
-    ADOXQ AX, BX
-    
-    // DX = res[2]
-    MOVQ 16(DI), DX
-    MOVQ R9, BP
-    MULXQ R12, AX,  R9
-    ADOXQ AX, BP
-    
-    // DX = res[3]
-    MOVQ 24(DI), DX
-    MOVQ R9, SI
-    MULXQ R12, AX,  R9
-    ADOXQ AX, SI
-    
-    // add the last carries to R9
-    MOVQ $0, DX
-    ADCXQ DX, R9
-    ADOXQ DX, R9
-    
-    // m := t[0]*q'[0] mod W
-    MOVQ $0xc2e1f593efffffff, DX
-    MULXQ CX,R11, DX
-    
-    // clear the carry flags
-    XORQ DX, DX
-    
-    // C,_ := t[0] + m*q[0]
-    MOVQ $0x43e1f593f0000001, DX
-    MULXQ R11, AX, R10
-    ADCXQ CX ,AX
-    
-    // for j=1 to N-1
-    //    (C,t[j-1]) := t[j] + m*q[j] + C
-    
-    MOVQ $0x2833e84879b97091, DX
-    MULXQ R11, AX, DX
-    ADCXQ  BX, R10
-    ADOXQ AX, R10
-    MOVQ R10, CX
-    MOVQ DX, R10
-    
-    MOVQ $0xb85045b68181585d, DX
-    MULXQ R11, AX, DX
-    ADCXQ  BP, R10
-    ADOXQ AX, R10
-    MOVQ R10, BX
-    MOVQ DX, R10
-    
-    MOVQ $0x30644e72e131a029, DX
-    MULXQ R11, AX, DX
-    ADCXQ  SI, R10
-    ADOXQ AX, R10
-    MOVQ R10, BP
-    MOVQ $0, AX
-    ADCXQ AX, DX
-    ADOXQ DX, R9
-    MOVQ R9, SI
-    
-    // ---------------------------------------------------------------------------------------------
-    // outter loop 1
-    
-    // clear up the carry flags
-    XORQ R9 , R9
-    
-    // R12 = y[1]
-    MOVQ 8(R8), R12
-    
-    // for j=0 to N-1
-    //    (A,t[j])  := t[j] + x[j]*y[i] + A
-    
-    // DX = res[0]
-    MOVQ 0(DI), DX
-    MULXQ R12, AX,  R9
-    ADOXQ AX, CX
-    
-    // DX = res[1]
-    MOVQ 8(DI), DX
-    ADCXQ R9, BX
-    MULXQ R12, AX,  R9
-    ADOXQ AX, BX
-    
-    // DX = res[2]
-    MOVQ 16(DI), DX
-    ADCXQ R9, BP
-    MULXQ R12, AX,  R9
-    ADOXQ AX, BP
-    
-    // DX = res[3]
-    MOVQ 24(DI), DX
-    ADCXQ R9, SI
-    MULXQ R12, AX,  R9
-    ADOXQ AX, SI
-    
-    // add the last carries to R9
-    MOVQ $0, DX
-    ADCXQ DX, R9
-    ADOXQ DX, R9
-    
-    // m := t[0]*q'[0] mod W
-    MOVQ $0xc2e1f593efffffff, DX
-    MULXQ CX,R11, DX
-    
-    // clear the carry flags
-    XORQ DX, DX
-    
-    // C,_ := t[0] + m*q[0]
-    MOVQ $0x43e1f593f0000001, DX
-    MULXQ R11, AX, R10
-    ADCXQ CX ,AX
-    
-    // for j=1 to N-1
-    //    (C,t[j-1]) := t[j] + m*q[j] + C
-    
-    MOVQ $0x2833e84879b97091, DX
-    MULXQ R11, AX, DX
-    ADCXQ  BX, R10
-    ADOXQ AX, R10
-    MOVQ R10, CX
-    MOVQ DX, R10
-    
-    MOVQ $0xb85045b68181585d, DX
-    MULXQ R11, AX, DX
-    ADCXQ  BP, R10
-    ADOXQ AX, R10
-    MOVQ R10, BX
-    MOVQ DX, R10
-    
-    MOVQ $0x30644e72e131a029, DX
-    MULXQ R11, AX, DX
-    ADCXQ  SI, R10
-    ADOXQ AX, R10
-    MOVQ R10, BP
-    MOVQ $0, AX
-    ADCXQ AX, DX
-    ADOXQ DX, R9
-    MOVQ R9, SI
-    
-    // ---------------------------------------------------------------------------------------------
-    // outter loop 2
-    
-    // clear up the carry flags
-    XORQ R9 , R9
-    
-    // R12 = y[2]
-    MOVQ 16(R8), R12
-    
-    // for j=0 to N-1
-    //    (A,t[j])  := t[j] + x[j]*y[i] + A
-    
-    // DX = res[0]
-    MOVQ 0(DI), DX
-    MULXQ R12, AX,  R9
-    ADOXQ AX, CX
-    
-    // DX = res[1]
-    MOVQ 8(DI), DX
-    ADCXQ R9, BX
-    MULXQ R12, AX,  R9
-    ADOXQ AX, BX
-    
-    // DX = res[2]
-    MOVQ 16(DI), DX
-    ADCXQ R9, BP
-    MULXQ R12, AX,  R9
-    ADOXQ AX, BP
-    
-    // DX = res[3]
-    MOVQ 24(DI), DX
-    ADCXQ R9, SI
-    MULXQ R12, AX,  R9
-    ADOXQ AX, SI
-    
-    // add the last carries to R9
-    MOVQ $0, DX
-    ADCXQ DX, R9
-    ADOXQ DX, R9
-    
-    // m := t[0]*q'[0] mod W
-    MOVQ $0xc2e1f593efffffff, DX
-    MULXQ CX,R11, DX
-    
-    // clear the carry flags
-    XORQ DX, DX
-    
-    // C,_ := t[0] + m*q[0]
-    MOVQ $0x43e1f593f0000001, DX
-    MULXQ R11, AX, R10
-    ADCXQ CX ,AX
-    
-    // for j=1 to N-1
-    //    (C,t[j-1]) := t[j] + m*q[j] + C
-    
-    MOVQ $0x2833e84879b97091, DX
-    MULXQ R11, AX, DX
-    ADCXQ  BX, R10
-    ADOXQ AX, R10
-    MOVQ R10, CX
-    MOVQ DX, R10
-    
-    MOVQ $0xb85045b68181585d, DX
-    MULXQ R11, AX, DX
-    ADCXQ  BP, R10
-    ADOXQ AX, R10
-    MOVQ R10, BX
-    MOVQ DX, R10
-    
-    MOVQ $0x30644e72e131a029, DX
-    MULXQ R11, AX, DX
-    ADCXQ  SI, R10
-    ADOXQ AX, R10
-    MOVQ R10, BP
-    MOVQ $0, AX
-    ADCXQ AX, DX
-    ADOXQ DX, R9
-    MOVQ R9, SI
-    
-    // ---------------------------------------------------------------------------------------------
-    // outter loop 3
-    
-    // clear up the carry flags
-    XORQ R9 , R9
-    
-    // R12 = y[3]
-    MOVQ 24(R8), R12
-    
-    // for j=0 to N-1
-    //    (A,t[j])  := t[j] + x[j]*y[i] + A
-    
-    // DX = res[0]
-    MOVQ 0(DI), DX
-    MULXQ R12, AX,  R9
-    ADOXQ AX, CX
-    
-    // DX = res[1]
-    MOVQ 8(DI), DX
-    ADCXQ R9, BX
-    MULXQ R12, AX,  R9
-    ADOXQ AX, BX
-    
-    // DX = res[2]
-    MOVQ 16(DI), DX
-    ADCXQ R9, BP
-    MULXQ R12, AX,  R9
-    ADOXQ AX, BP
-    
-    // DX = res[3]
-    MOVQ 24(DI), DX
-    ADCXQ R9, SI
-    MULXQ R12, AX,  R9
-    ADOXQ AX, SI
-    
-    // add the last carries to R9
-    MOVQ $0, DX
-    ADCXQ DX, R9
-    ADOXQ DX, R9
-    
-    // m := t[0]*q'[0] mod W
-    MOVQ $0xc2e1f593efffffff, DX
-    MULXQ CX,R11, DX
-    
-    // clear the carry flags
-    XORQ DX, DX
-    
-    // C,_ := t[0] + m*q[0]
-    MOVQ $0x43e1f593f0000001, DX
-    MULXQ R11, AX, R10
-    ADCXQ CX ,AX
-    
-    // for j=1 to N-1
-    //    (C,t[j-1]) := t[j] + m*q[j] + C
-    
-    MOVQ $0x2833e84879b97091, DX
-    MULXQ R11, AX, DX
-    ADCXQ  BX, R10
-    ADOXQ AX, R10
-    MOVQ R10, CX
-    MOVQ DX, R10
-    
-    MOVQ $0xb85045b68181585d, DX
-    MULXQ R11, AX, DX
-    ADCXQ  BP, R10
-    ADOXQ AX, R10
-    MOVQ R10, BX
-    MOVQ DX, R10
-    
-    MOVQ $0x30644e72e131a029, DX
-    MULXQ R11, AX, DX
-    ADCXQ  SI, R10
-    ADOXQ AX, R10
-    MOVQ R10, BP
-    MOVQ $0, AX
-    ADCXQ AX, DX
-    ADOXQ DX, R9
-    MOVQ R9, SI
-    
-    reduce:
-    // reduce, constant time version
-    // first we copy registers storing t in a separate set of registers
-    // as SUBQ modifies the 2nd operand
-    MOVQ CX, DX
-    MOVQ BX, R8
-    MOVQ BP, R9
-    MOVQ SI, R10
-    MOVQ $0x43e1f593f0000001, R11
-    SUBQ  R11, DX
-    MOVQ $0x2833e84879b97091, R11
-    SBBQ  R11, R8
-    MOVQ $0xb85045b68181585d, R11
-    SBBQ  R11, R9
-    MOVQ $0x30644e72e131a029, R11
-    SBBQ  R11, R10
-    JCS t_is_smaller // no borrow, we return t
-    
-    // borrow is set, we return u
-    MOVQ DX, (DI)
-    MOVQ R8, 8(DI)
-    MOVQ R9, 16(DI)
-    MOVQ R10, 24(DI)
-    RET
-    t_is_smaller:
-    MOVQ CX, 0(DI)
-    MOVQ BX, 8(DI)
-    MOVQ BP, 16(DI)
-    MOVQ SI, 24(DI)
-    RET
-    
-    no_adx:
-    
-    // ---------------------------------------------------------------------------------------------
-    // outter loop 0
-    
-    // (A,t[0]) := t[0] + x[0]*y[0]
-    MOVQ (DI), AX // x[0]
-    MOVQ 0(R8), R12
-    MULQ R12 // x[0] * y[0]
-    MOVQ DX, R9
-    MOVQ AX, CX
-    
-    // m := t[0]*q'[0] mod W
-    MOVQ $0xc2e1f593efffffff, R11
-    IMULQ CX , R11
-    
-    // C,_ := t[0] + m*q[0]
-    MOVQ $0x43e1f593f0000001, AX
-    MULQ R11
-    ADDQ CX ,AX
-    ADCQ $0, DX
-    MOVQ  DX, R10
-    
-    // for j=1 to N-1
-    //    (A,t[j])  := t[j] + x[j]*y[i] + A
-    //    (C,t[j-1]) := t[j] + m*q[j] + C
-    MOVQ 8(DI), AX
-    MULQ R12 // x[1] * y[0]
-    MOVQ R9, BX
-    ADDQ AX, BX
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0x2833e84879b97091, AX
-    MULQ R11
-    ADDQ  BX, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, CX
-    MOVQ DX, R10
-    MOVQ 16(DI), AX
-    MULQ R12 // x[2] * y[0]
-    MOVQ R9, BP
-    ADDQ AX, BP
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0xb85045b68181585d, AX
-    MULQ R11
-    ADDQ  BP, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, BX
-    MOVQ DX, R10
-    MOVQ 24(DI), AX
-    MULQ R12 // x[3] * y[0]
-    MOVQ R9, SI
-    ADDQ AX, SI
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0x30644e72e131a029, AX
-    MULQ R11
-    ADDQ  SI, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, BP
-    MOVQ DX, R10
-    
-    ADDQ R10, R9
-    MOVQ R9, SI
-    
-    // ---------------------------------------------------------------------------------------------
-    // outter loop 1
-    
-    // (A,t[0]) := t[0] + x[0]*y[1]
-    MOVQ (DI), AX // x[0]
-    MOVQ 8(R8), R12
-    MULQ R12 // x[0] * y[1]
-    ADDQ AX, CX
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    // m := t[0]*q'[0] mod W
-    MOVQ $0xc2e1f593efffffff, R11
-    IMULQ CX , R11
-    
-    // C,_ := t[0] + m*q[0]
-    MOVQ $0x43e1f593f0000001, AX
-    MULQ R11
-    ADDQ CX ,AX
-    ADCQ $0, DX
-    MOVQ  DX, R10
-    
-    // for j=1 to N-1
-    //    (A,t[j])  := t[j] + x[j]*y[i] + A
-    //    (C,t[j-1]) := t[j] + m*q[j] + C
-    MOVQ 8(DI), AX
-    MULQ R12 // x[1] * y[1]
-    ADDQ R9, BX
-    ADCQ $0, DX
-    ADDQ AX, BX
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0x2833e84879b97091, AX
-    MULQ R11
-    ADDQ  BX, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, CX
-    MOVQ DX, R10
-    MOVQ 16(DI), AX
-    MULQ R12 // x[2] * y[1]
-    ADDQ R9, BP
-    ADCQ $0, DX
-    ADDQ AX, BP
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0xb85045b68181585d, AX
-    MULQ R11
-    ADDQ  BP, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, BX
-    MOVQ DX, R10
-    MOVQ 24(DI), AX
-    MULQ R12 // x[3] * y[1]
-    ADDQ R9, SI
-    ADCQ $0, DX
-    ADDQ AX, SI
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0x30644e72e131a029, AX
-    MULQ R11
-    ADDQ  SI, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, BP
-    MOVQ DX, R10
-    
-    ADDQ R10, R9
-    MOVQ R9, SI
-    
-    // ---------------------------------------------------------------------------------------------
-    // outter loop 2
-    
-    // (A,t[0]) := t[0] + x[0]*y[2]
-    MOVQ (DI), AX // x[0]
-    MOVQ 16(R8), R12
-    MULQ R12 // x[0] * y[2]
-    ADDQ AX, CX
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    // m := t[0]*q'[0] mod W
-    MOVQ $0xc2e1f593efffffff, R11
-    IMULQ CX , R11
-    
-    // C,_ := t[0] + m*q[0]
-    MOVQ $0x43e1f593f0000001, AX
-    MULQ R11
-    ADDQ CX ,AX
-    ADCQ $0, DX
-    MOVQ  DX, R10
-    
-    // for j=1 to N-1
-    //    (A,t[j])  := t[j] + x[j]*y[i] + A
-    //    (C,t[j-1]) := t[j] + m*q[j] + C
-    MOVQ 8(DI), AX
-    MULQ R12 // x[1] * y[2]
-    ADDQ R9, BX
-    ADCQ $0, DX
-    ADDQ AX, BX
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0x2833e84879b97091, AX
-    MULQ R11
-    ADDQ  BX, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, CX
-    MOVQ DX, R10
-    MOVQ 16(DI), AX
-    MULQ R12 // x[2] * y[2]
-    ADDQ R9, BP
-    ADCQ $0, DX
-    ADDQ AX, BP
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0xb85045b68181585d, AX
-    MULQ R11
-    ADDQ  BP, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, BX
-    MOVQ DX, R10
-    MOVQ 24(DI), AX
-    MULQ R12 // x[3] * y[2]
-    ADDQ R9, SI
-    ADCQ $0, DX
-    ADDQ AX, SI
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0x30644e72e131a029, AX
-    MULQ R11
-    ADDQ  SI, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, BP
-    MOVQ DX, R10
-    
-    ADDQ R10, R9
-    MOVQ R9, SI
-    
-    // ---------------------------------------------------------------------------------------------
-    // outter loop 3
-    
-    // (A,t[0]) := t[0] + x[0]*y[3]
-    MOVQ (DI), AX // x[0]
-    MOVQ 24(R8), R12
-    MULQ R12 // x[0] * y[3]
-    ADDQ AX, CX
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    // m := t[0]*q'[0] mod W
-    MOVQ $0xc2e1f593efffffff, R11
-    IMULQ CX , R11
-    
-    // C,_ := t[0] + m*q[0]
-    MOVQ $0x43e1f593f0000001, AX
-    MULQ R11
-    ADDQ CX ,AX
-    ADCQ $0, DX
-    MOVQ  DX, R10
-    
-    // for j=1 to N-1
-    //    (A,t[j])  := t[j] + x[j]*y[i] + A
-    //    (C,t[j-1]) := t[j] + m*q[j] + C
-    MOVQ 8(DI), AX
-    MULQ R12 // x[1] * y[3]
-    ADDQ R9, BX
-    ADCQ $0, DX
-    ADDQ AX, BX
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0x2833e84879b97091, AX
-    MULQ R11
-    ADDQ  BX, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, CX
-    MOVQ DX, R10
-    MOVQ 16(DI), AX
-    MULQ R12 // x[2] * y[3]
-    ADDQ R9, BP
-    ADCQ $0, DX
-    ADDQ AX, BP
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0xb85045b68181585d, AX
-    MULQ R11
-    ADDQ  BP, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, BX
-    MOVQ DX, R10
-    MOVQ 24(DI), AX
-    MULQ R12 // x[3] * y[3]
-    ADDQ R9, SI
-    ADCQ $0, DX
-    ADDQ AX, SI
-    ADCQ $0, DX
-    MOVQ DX, R9
-    
-    MOVQ $0x30644e72e131a029, AX
-    MULQ R11
-    ADDQ  SI, R10
-    ADCQ $0, DX
-    ADDQ AX, R10
-    ADCQ $0, DX
-    
-    MOVQ R10, BP
-    MOVQ DX, R10
-    
-    ADDQ R10, R9
-    MOVQ R9, SI
-    
-    JMP reduce

ff/element_square.go

@@ -1,93 +0,0 @@
-// +build !amd64
-
-// 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 (v0.2.0) DO NOT EDIT
-
-// Package ff contains field arithmetic operations
-package ff
-
-// /!\ WARNING /!\
-// this code has not been audited and is provided as-is. In particular,
-// there is no security guarantees such as constant time implementation
-// or side-channel attack resistance
-// /!\ WARNING /!\
-
-import "math/bits"
-
-// Square z = x * x mod q
-// see https://hackmd.io/@zkteam/modular_multiplication
-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
-	// note: this is NOT constant time
-	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_square_amd64.go

@@ -1,34 +0,0 @@
-// 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 (v0.2.0) DO NOT EDIT
-
-// Package ff contains field arithmetic operations
-package ff
-
-// SquareElement z = x * x mod q
-// calling this instead of z.Square(x) is prefered for performance critical path
-// go - noescape
-// func SquareElement(res,x *Element)
-
-// Square z = x * x mod q
-// see https://hackmd.io/@zkteam/modular_multiplication
-func (z *Element) Square(x *Element) *Element {
-	if z != x {
-		z.Set(x)
-	}
-	MulAssignElement(z, x)
-	// SquareElement(z, x)
-	return z
-}

ff/element_test.go

@@ -1,26 +1,9 @@
-// Copyright 2020 ConsenSys AG
+// Code generated by goff DO NOT EDIT
-//
-// 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 (v0.2.0) DO NOT EDIT
-
-// Package ff contains field arithmetic operations
 package ff
 
 import (
 	"crypto/rand"
 	"math/big"
-	"math/bits"
 	mrand "math/rand"
 	"testing"
 )
@@ -38,14 +21,7 @@ func TestELEMENTCorrectnessAgainstBigInt(t *testing.T) {
 
 	modulusMinusOne.Sub(modulus, &one)
 
-	var n int
+	for i := 0; i < 1000; i++ {
-	if testing.Short() {
-		n = 10
-	} else {
-		n = 500
-	}
-
-	for i := 0; i < n; i++ {
 
 		// sample 2 random big int
 		b1, _ := rand.Int(rand.Reader, modulus)
@@ -81,7 +57,7 @@ func TestELEMENTCorrectnessAgainstBigInt(t *testing.T) {
 
 		rbExp := new(big.Int).SetUint64(rExp)
 
-		var bMul, bAdd, bSub, bDiv, bNeg, bLsh, bInv, bExp, bExp2, bSquare big.Int
+		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
@@ -130,40 +106,12 @@ func TestELEMENTCorrectnessAgainstBigInt(t *testing.T) {
 		cmpEandB(&eNeg, &bNeg, "Neg")
 		cmpEandB(&eInv, &bInv, "Inv")
 		cmpEandB(&eExp, &bExp, "Exp")
-
 		cmpEandB(&eLsh, &bLsh, "Lsh")
-
-		// legendre symbol
-		if e1.Legendre() != big.Jacobi(b1, modulus) {
-			t.Fatal("legendre symbol computation failed")
-		}
-		if e2.Legendre() != big.Jacobi(b2, modulus) {
-			t.Fatal("legendre symbol computation failed")
-		}
-
-		// these are slow, killing circle ci
-		if n <= 5 {
-			// sqrt
-			var eSqrt, eExp2 Element
-			var bSqrt big.Int
-			bSqrt.ModSqrt(b1, modulus)
-			eSqrt.Sqrt(&e1)
-			cmpEandB(&eSqrt, &bSqrt, "Sqrt")
-
-			bits := b2.Bits()
-			exponent := make([]uint64, len(bits))
-			for k := 0; k < len(bits); k++ {
-				exponent[k] = uint64(bits[k])
-			}
-			eExp2.Exp(e1, exponent...)
-			bExp2.Exp(b1, b2, modulus)
-			cmpEandB(&eExp2, &bExp2, "Exp multi words")
-		}
 	}
 }
 
 func TestELEMENTIsRandom(t *testing.T) {
-	for i := 0; i < 50; i++ {
+	for i := 0; i < 1000; i++ {
 		var x, y Element
 		x.SetRandom()
 		y.SetRandom()
@@ -177,6 +125,7 @@ func TestELEMENTIsRandom(t *testing.T) {
 // 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
 
@@ -270,15 +219,6 @@ func BenchmarkSquareELEMENT(b *testing.B) {
 	}
 }
 
-func BenchmarkSqrtELEMENT(b *testing.B) {
-	var a Element
-	a.SetRandom()
-	b.ResetTimer()
-	for i := 0; i < b.N; i++ {
-		benchResElement.Sqrt(&a)
-	}
-}
-
 func BenchmarkMulAssignELEMENT(b *testing.B) {
 	x := Element{
 		1997599621687373223,
@@ -292,183 +232,3 @@ func BenchmarkMulAssignELEMENT(b *testing.B) {
 		benchResElement.MulAssign(&x)
 	}
 }
-
-func BenchmarkMulAssignASMELEMENT(b *testing.B) {
-	x := Element{
-		1997599621687373223,
-		6052339484930628067,
-		10108755138030829701,
-		150537098327114917,
-	}
-	benchResElement.SetOne()
-	b.ResetTimer()
-	for i := 0; i < b.N; i++ {
-		MulAssignElement(&benchResElement, &x)
-	}
-}
-
-func TestELEMENTAsm(t *testing.T) {
-	// ensure ASM implementations matches the ones using math/bits
-	modulus, _ := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
-	for i := 0; i < 500; i++ {
-		// sample 2 random big int
-		b1, _ := rand.Int(rand.Reader, modulus)
-		b2, _ := rand.Int(rand.Reader, modulus)
-
-		// e1 = mont(b1), e2 = mont(b2)
-		var e1, e2, eTestMul, eMulAssign, eSquare, eTestSquare Element
-		e1.SetBigInt(b1)
-		e2.SetBigInt(b2)
-
-		eTestMul = e1
-		eTestMul.testMulAssign(&e2)
-		eMulAssign = e1
-		eMulAssign.MulAssign(&e2)
-
-		if !eTestMul.Equal(&eMulAssign) {
-			t.Fatal("inconsisntencies between MulAssign and testMulAssign --> check if MulAssign is calling ASM implementaiton on amd64")
-		}
-
-		// square
-		eSquare.Square(&e1)
-		eTestSquare.testSquare(&e1)
-
-		if !eTestSquare.Equal(&eSquare) {
-			t.Fatal("inconsisntencies between Square and testSquare --> check if Square is calling ASM implementaiton on amd64")
-		}
-	}
-}
-
-// this is here for consistency purposes, to ensure MulAssign on AMD64 using asm implementation gives consistent results
-func (z *Element) testMulAssign(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
-	// note: this is NOT constant time
-	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
-}
-
-// this is here for consistency purposes, to ensure Square on AMD64 using asm implementation gives consistent results
-func (z *Element) testSquare(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
-	// note: this is NOT constant time
-	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
-
-}

go.mod

@@ -4,8 +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
-	golang.org/x/sys v0.0.0-20190412213103-97732733099d
 )

go.sum

@@ -1,20 +1,172 @@
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+github.com/Azure/go-autorest/autorest/adal v0.8.0/go.mod h1:Z6vX6WXXuyieHAXwMj0S6HY6e6wcHn37qQMBQlvY3lc=
+github.com/Azure/go-autorest/autorest/date v0.1.0/go.mod h1:plvfp3oPSKwf2DNjlBjWF/7vwR+cUD/ELuzDCXwHUVA=
+github.com/Azure/go-autorest/autorest/date v0.2.0/go.mod h1:vcORJHLJEh643/Ioh9+vPmf1Ij9AEBM5FuBIXLmIy0g=
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+github.com/Azure/go-autorest/autorest/mocks v0.2.0/go.mod h1:OTyCOPRA2IgIlWxVYxBee2F5Gr4kF2zd2J5cFRaIDN0=
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+golang.org/x/sys v0.0.0-20200302150141-5c8b2ff67527/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
+golang.org/x/text v0.3.2/go.mod h1:bEr9sfX3Q8Zfm5fL9x+3itogRgK3+ptLWKqgva+5dAk=
+golang.org/x/time v0.0.0-20190308202827-9d24e82272b4/go.mod h1:tRJNPiyCQ0inRvYxbN9jk5I+vvW/OXSQhTDSoE431IQ=
+golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
+gopkg.in/alecthomas/kingpin.v2 v2.2.6/go.mod h1:FMv+mEhP44yOT+4EoQTLFTRgOQ1FBLkstjWtayDeSgw=
+gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
+gopkg.in/check.v1 v1.0.0-20180628173108-788fd7840127/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
+gopkg.in/fsnotify.v1 v1.4.7/go.mod h1:Tz8NjZHkW78fSQdbUxIjBTcgA1z1m8ZHf0WmKUhAMys=
+gopkg.in/natefinch/npipe.v2 v2.0.0-20160621034901-c1b8fa8bdcce/go.mod h1:5AcXVHNjg+BDxry382+8OKon8SEWiKktQR07RKPsv1c=
+gopkg.in/olebedev/go-duktape.v3 v3.0.0-20190213234257-ec84240a7772/go.mod h1:uAJfkITjFhyEEuUfm7bsmCZRbW5WRq8s9EY8HZ6hCns=
+gopkg.in/tomb.v1 v1.0.0-20141024135613-dd632973f1e7/go.mod h1:dt/ZhP58zS4L8KSrWDmTeBkI65Dw0HsyUHuEVlX15mw=
+gopkg.in/urfave/cli.v1 v1.20.0/go.mod h1:vuBzUtMdQeixQj8LVd+/98pzhxNGQoyuPBlsXHOQNO0=
+gopkg.in/yaml.v2 v2.2.1/go.mod h1:hI93XBmqTisBFMUTm0b8Fm+jr3Dg1NNxqwp+5A1VGuI=
+gopkg.in/yaml.v2 v2.2.2 h1:ZCJp+EgiOT7lHqUV2J862kp8Qj64Jo6az82+3Td9dZw=
+gopkg.in/yaml.v2 v2.2.2/go.mod h1:hI93XBmqTisBFMUTm0b8Fm+jr3Dg1NNxqwp+5A1VGuI=
+gotest.tools v2.2.0+incompatible/go.mod h1:DsYFclhRJ6vuDpmuTbkuFWG+y2sxOXAzmJt81HFBacw=

mimc7/mimc7_test.go

@@ -87,6 +87,6 @@ func BenchmarkMIMC7(b *testing.B) {
 	bigArray4 := []*big.Int{b12, b45, b78, b41}
 
 	for i := 0; i < b.N; i++ {
-		Hash(bigArray4, nil)
+		Hash(bigArray4, nil) //nolint:errcheck
 	}
 }

poseidon/poseidon_test.go

@@ -104,7 +104,7 @@ func BenchmarkPoseidon(b *testing.B) {
 	bigArray4 := []*big.Int{b12, b45, b78, b41}
 
 	for i := 0; i < b.N; i++ {
-		Hash(bigArray4)
+		Hash(bigArray4) //nolint:errcheck
 	}
 }
 
@@ -117,6 +117,6 @@ func BenchmarkPoseidonLarge(b *testing.B) {
 	bigArray4 := []*big.Int{b12, b45, b78, b41}
 
 	for i := 0; i < b.N; i++ {
-		Hash(bigArray4)
+		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

@@ -66,9 +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)
 }
 
@@ -92,10 +90,7 @@ func HexDecodeInto(dst []byte, h []byte) error {
 
 // CheckBigIntInField checks if given *big.Int fits in a Field Q element
 func CheckBigIntInField(a *big.Int) bool {
-	if a.Cmp(constants.Q) != -1 {
+	return a.Cmp(constants.Q) == -1
-		return false
-	}
-	return true
 }
 
 // CheckBigIntArrayInField checks if given *big.Int fits in a Field Q element
@@ -108,6 +103,7 @@ func CheckBigIntArrayInField(arr []*big.Int) bool {
 	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 {
@@ -115,3 +111,15 @@ func BigIntArrayToElementArray(bi []*big.Int) []*ff.Element {
 	}
 	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
+}