Update Poseidon last changes of the reference impl

Update Poseidon to last changes of the reference implementation from
26ddaa91db

Compatible with update at circomlib
(cf853c1cc9)

.github/workflows/lint.yml

@@ -0,0 +1,16 @@
+name: Lint
+on: [ push, pull_request ]
+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 v1.30.0
+          $(go env GOPATH)/bin/golangci-lint run --timeout=5m -c .golangci.yml

.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 ./...

.golangci.yml

@@ -0,0 +1,17 @@
+issues:
+        max-same-issues: 0
+        exclude-use-default: false
+linters:
+        enable:
+        - whitespace
+        - gosec
+        - gci
+        - misspell
+        - gomnd
+        - gofmt
+        - goimports
+        - lll
+        - golint
+linters-settings:
+        lll:
+                line-length: 100

.travis.yml

@@ -1,8 +0,0 @@
-dist: xenial
-language: go
-
-go:
-  - "1.12"
-
-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

@@ -5,15 +5,22 @@ import (
 	"math/big"
 
 	"github.com/iden3/go-iden3-crypto/constants"
+	"github.com/iden3/go-iden3-crypto/ff"
 	"github.com/iden3/go-iden3-crypto/utils"
 )
 
 // A is one of the babyjub constants.
 var A *big.Int
 
+// Aff is A value in *ff.Element representation
+var Aff *ff.Element
+
 // D is one of the babyjub constants.
 var D *big.Int
 
+// Dff is D value in *ff.Element representation
+var Dff *ff.Element
+
 // Order of the babyjub curve.
 var Order *big.Int
 
@@ -29,6 +36,8 @@ var B8 *Point
 func init() {
 	A = utils.NewIntFromString("168700")
 	D = utils.NewIntFromString("168696")
+	Aff = ff.NewElement().SetBigInt(A)
+	Dff = ff.NewElement().SetBigInt(D)
 
 	Order = utils.NewIntFromString(
 		"21888242871839275222246405745257275088614511777268538073601725287587578984328")
@@ -41,6 +50,73 @@ func init() {
 		"16950150798460657717958625567821834550301663161624707787222815936182638968203")
 }
 
+// PointProjective is the Point representation in projective coordinates
+type PointProjective struct {
+	X *ff.Element
+	Y *ff.Element
+	Z *ff.Element
+}
+
+// NewPointProjective creates a new Point in projective coordinates.
+func NewPointProjective() *PointProjective {
+	return &PointProjective{X: ff.NewElement().SetZero(),
+		Y: ff.NewElement().SetOne(), Z: ff.NewElement().SetOne()}
+}
+
+// Affine returns the Point from the projective representation
+func (p *PointProjective) Affine() *Point {
+	if p.Z.Equal(ff.NewElement().SetZero()) {
+		return &Point{
+			X: big.NewInt(0),
+			Y: big.NewInt(0),
+		}
+	}
+	zinv := ff.NewElement().Inverse(p.Z)
+	x := ff.NewElement().Mul(p.X, zinv)
+
+	y := ff.NewElement().Mul(p.Y, zinv)
+	xBig := big.NewInt(0)
+	x.ToBigIntRegular(xBig)
+	yBig := big.NewInt(0)
+	y.ToBigIntRegular(yBig)
+	return &Point{
+		X: xBig,
+		Y: yBig,
+	}
+}
+
+// Add computes the addition of two points in projective coordinates
+// representation
+func (p *PointProjective) Add(q *PointProjective, o *PointProjective) *PointProjective {
+	// add-2008-bbjlp
+	// https://hyperelliptic.org/EFD/g1p/auto-twisted-projective.html#doubling-dbl-2008-bbjlp
+	a := ff.NewElement().Mul(q.Z, o.Z)
+	b := ff.NewElement().Square(a)
+	c := ff.NewElement().Mul(q.X, o.X)
+	d := ff.NewElement().Mul(q.Y, o.Y)
+	e := ff.NewElement().Mul(Dff, c)
+	e.MulAssign(d)
+	f := ff.NewElement().Sub(b, e)
+	g := ff.NewElement().Add(b, e)
+	x1y1 := ff.NewElement().Add(q.X, q.Y)
+	x2y2 := ff.NewElement().Add(o.X, o.Y)
+	x3 := ff.NewElement().Mul(x1y1, x2y2)
+	x3.SubAssign(c)
+	x3.SubAssign(d)
+	x3.MulAssign(a)
+	x3.MulAssign(f)
+	ac := ff.NewElement().Mul(Aff, c)
+	y3 := ff.NewElement().Sub(d, ac)
+	y3.MulAssign(a)
+	y3.MulAssign(g)
+	z3 := ff.NewElement().Mul(f, g)
+
+	p.X = x3
+	p.Y = y3
+	p.Z = z3
+	return p
+}
+
 // Point represents a point of the babyjub curve.
 type Point struct {
 	X *big.Int
@@ -59,63 +135,33 @@ func (p *Point) Set(c *Point) *Point {
 	return p
 }
 
-// Add adds Point a and b into res
-func (res *Point) Add(a *Point, b *Point) *Point {
-	// x = (a.x * b.y + b.x * a.y) * (1 + D * a.x * b.x * a.y * b.y)^-1 mod q
-	x1a := new(big.Int).Mul(a.X, b.Y)
-	x1b := new(big.Int).Mul(b.X, a.Y)
-	x1a.Add(x1a, x1b) // x1a = a.x * b.y + b.x * a.y
-
-	x2 := new(big.Int).Set(D)
-	x2.Mul(x2, a.X)
-	x2.Mul(x2, b.X)
-	x2.Mul(x2, a.Y)
-	x2.Mul(x2, b.Y)
-	x2.Add(constants.One, x2)
-	x2.Mod(x2, constants.Q)
-	x2.ModInverse(x2, constants.Q) // x2 = (1 + D * a.x * b.x * a.y * b.y)^-1
-
-	// y = (a.y * b.y - A * a.x * b.x) * (1 - D * a.x * b.x * a.y * b.y)^-1 mod q
-	y1a := new(big.Int).Mul(a.Y, b.Y)
-	y1b := new(big.Int).Set(A)
-	y1b.Mul(y1b, a.X)
-	y1b.Mul(y1b, b.X)
-
-	y1a.Sub(y1a, y1b) // y1a = a.y * b.y - A * a.x * b.x
-
-	y2 := new(big.Int).Set(D)
-	y2.Mul(y2, a.X)
-	y2.Mul(y2, b.X)
-	y2.Mul(y2, a.Y)
-	y2.Mul(y2, b.Y)
-	y2.Sub(constants.One, y2)
-	y2.Mod(y2, constants.Q)
-	y2.ModInverse(y2, constants.Q) // y2 = (1 - D * a.x * b.x * a.y * b.y)^-1
-
-	res.X = x1a.Mul(x1a, x2)
-	res.X = res.X.Mod(res.X, constants.Q)
-
-	res.Y = y1a.Mul(y1a, y2)
-	res.Y = res.Y.Mod(res.Y, constants.Q)
-
-	return res
+// Projective returns a PointProjective from the Point
+func (p *Point) Projective() *PointProjective {
+	return &PointProjective{
+		X: ff.NewElement().SetBigInt(p.X),
+		Y: ff.NewElement().SetBigInt(p.Y),
+		Z: ff.NewElement().SetOne(),
+	}
 }
 
-// Mul multiplies the Point p by the scalar s and stores the result in res,
+// Mul multiplies the Point q by the scalar s and stores the result in p,
 // which is also returned.
-func (res *Point) Mul(s *big.Int, p *Point) *Point {
-	res.X = big.NewInt(0)
-	res.Y = big.NewInt(1)
-	exp := NewPoint().Set(p)
+func (p *Point) Mul(s *big.Int, q *Point) *Point {
+	resProj := &PointProjective{
+		X: ff.NewElement().SetZero(),
+		Y: ff.NewElement().SetOne(),
+		Z: ff.NewElement().SetOne(),
+	}
+	exp := q.Projective()
 
 	for i := 0; i < s.BitLen(); i++ {
 		if s.Bit(i) == 1 {
-			res.Add(res, exp)
+			resProj.Add(resProj, exp)
 		}
-		exp.Add(exp, exp)
+		exp = exp.Add(exp, exp)
 	}
-
-	return res
+	p = resProj.Affine()
+	return p
 }
 
 // InCurve returns true when the Point p is in the babyjub curve.
@@ -154,36 +200,57 @@ 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 true
-	}
-	return false
+	return c.Cmp(new(big.Int).Rsh(constants.Q, 1)) == 1
 }
 
-func PackPoint(ay *big.Int, sign bool) [32]byte {
-	leBuf := utils.BigIntLEBytes(ay)
+// PackSignY packs the given sign and the coordinate Y of a point into a 32
+// byte array. This method does not check that the values belong to a valid
+// Point in the curve.
+func PackSignY(sign bool, y *big.Int) [32]byte {
+	leBuf := utils.BigIntLEBytes(y)
 	if sign {
-		leBuf[31] = leBuf[31] | 0x80
+		leBuf[31] = leBuf[31] | 0x80 //nolint:gomnd
 	}
 	return leBuf
 }
 
+// UnpackSignY returns the sign and coordinate Y from a given compressed point.
+// This method does not check that the Point belongs to the BabyJubJub curve,
+// thus does not return error in such case. This method is intended to obtain
+// the sign and the Y coordinate without checking if the point belongs to the
+// curve, if the objective is to uncompress a point, Decompress method should
+// be used instead.
+func UnpackSignY(leBuf [32]byte) (bool, *big.Int) {
+	sign := false
+	y := big.NewInt(0)
+	if (leBuf[31] & 0x80) != 0x00 { //nolint:gomnd
+		sign = true
+		leBuf[31] = leBuf[31] & 0x7F //nolint:gomnd
+	}
+	utils.SetBigIntFromLEBytes(y, leBuf[:])
+	return sign, y
+}
+
 // Compress the point into a 32 byte array that contains the y coordinate in
 // little endian and the sign of the x coordinate.
 func (p *Point) Compress() [32]byte {
 	sign := PointCoordSign(p.X)
-	return PackPoint(p.Y, sign)
+	return PackSignY(sign, p.Y)
 }
 
 // Decompress a compressed Point into p, and also returns the decompressed
 // Point.  Returns error if the compressed Point is invalid.
 func (p *Point) Decompress(leBuf [32]byte) (*Point, error) {
-	sign := false
-	if (leBuf[31] & 0x80) != 0x00 {
-		sign = true
-		leBuf[31] = leBuf[31] & 0x7F
-	}
-	utils.SetBigIntFromLEBytes(p.Y, leBuf[:])
+	var sign bool
+	sign, p.Y = UnpackSignY(leBuf)
+	return PointFromSignAndY(sign, p.Y)
+}
+
+// PointFromSignAndY returns a Point from a Sign and the Y coordinate
+func PointFromSignAndY(sign bool, y *big.Int) (*Point, error) {
+	var p Point
+	p.X = big.NewInt(0)
+	p.Y = y
 	if p.Y.Cmp(constants.Q) >= 0 {
 		return nil, fmt.Errorf("p.y >= Q")
 	}
@@ -212,5 +279,5 @@ func (p *Point) Decompress(leBuf [32]byte) (*Point, error) {
 	}
 	p.X.Mod(p.X, constants.Q)
 
-	return p, nil
+	return &p, nil
 }

babyjub/babyjub_test.go

@@ -15,7 +15,7 @@ func TestAdd1(t *testing.T) {
 	a := &Point{X: big.NewInt(0), Y: big.NewInt(1)}
 	b := &Point{X: big.NewInt(0), Y: big.NewInt(1)}
 
-	c := NewPoint().Add(a, b)
+	c := NewPoint().Projective().Add(a.Projective(), b.Projective())
 	// fmt.Printf("%v = 2 * %v", *c, *a)
 	assert.Equal(t, "0", c.X.String())
 	assert.Equal(t, "1", c.Y.String())
@@ -34,7 +34,7 @@ func TestAdd2(t *testing.T) {
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	b := &Point{X: bX, Y: bY}
 
-	c := NewPoint().Add(a, b)
+	c := NewPoint().Projective().Add(a.Projective(), b.Projective()).Affine()
 	// fmt.Printf("%v = 2 * %v", *c, *a)
 	assert.Equal(t,
 		"6890855772600357754907169075114257697580319025794532037257385534741338397365",
@@ -42,6 +42,18 @@ func TestAdd2(t *testing.T) {
 	assert.Equal(t,
 		"4338620300185947561074059802482547481416142213883829469920100239455078257889",
 		c.Y.String())
+
+	d := NewPointProjective().Add(c.Projective(), c.Projective()).Affine()
+	assert.Equal(t,
+		"2f6458832049e917c95867185a96621336df33e13c98e81d1ef4928cdbb77772",
+		hex.EncodeToString(d.X.Bytes()))
+
+	// Projective
+	aP := a.Projective()
+	bP := b.Projective()
+	cP := NewPointProjective().Add(aP, bP)
+	c2 := cP.Affine()
+	assert.Equal(t, c, c2)
 }
 
 func TestAdd3(t *testing.T) {
@@ -57,7 +69,7 @@ func TestAdd3(t *testing.T) {
 		"20819045374670962167435360035096875258406992893633759881276124905556507972311")
 	b := &Point{X: bX, Y: bY}
 
-	c := NewPoint().Add(a, b)
+	c := NewPoint().Projective().Add(a.Projective(), b.Projective()).Affine()
 	// fmt.Printf("%v = 2 * %v", *c, *a)
 	assert.Equal(t,
 		"7916061937171219682591368294088513039687205273691143098332585753343424131937",
@@ -80,7 +92,7 @@ func TestAdd4(t *testing.T) {
 		"20819045374670962167435360035096875258406992893633759881276124905556507972311")
 	b := &Point{X: bX, Y: bY}
 
-	c := NewPoint().Add(a, b)
+	c := NewPoint().Projective().Add(a.Projective(), b.Projective()).Affine()
 	// fmt.Printf("%v = 2 * %v", *c, *a)
 	assert.Equal(t,
 		"16540640123574156134436876038791482806971768689494387082833631921987005038935",
@@ -108,8 +120,8 @@ func TestMul0(t *testing.T) {
 	p := &Point{X: x, Y: y}
 	s := utils.NewIntFromString("3")
 
-	r2 := NewPoint().Add(p, p)
-	r2 = NewPoint().Add(r2, p)
+	r2 := NewPoint().Projective().Add(p.Projective(), p.Projective()).Affine()
+	r2 = NewPoint().Projective().Add(r2.Projective(), p.Projective()).Affine()
 	r := NewPoint().Mul(s, p)
 	assert.Equal(t, r2.X.String(), r.X.String())
 	assert.Equal(t, r2.Y.String(), r.Y.String())
@@ -192,6 +204,40 @@ func TestInSubGroup2(t *testing.T) {
 	assert.Equal(t, true, p.InSubGroup())
 }
 
+func TestPointFromSignAndy(t *testing.T) {
+	x := utils.NewIntFromString(
+		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
+	y := utils.NewIntFromString(
+		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
+	p := &Point{X: x, Y: y}
+
+	sign := PointCoordSign(p.X)
+	p2, err := PointFromSignAndY(sign, p.Y)
+	assert.Equal(t, nil, err)
+	assert.Equal(t, p.X.String(), p2.X.String())
+	assert.Equal(t, p.Y.String(), p2.Y.String())
+}
+
+func TestPackAndUnpackSignY(t *testing.T) {
+	x := utils.NewIntFromString(
+		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
+	y := utils.NewIntFromString(
+		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
+	p := &Point{X: x, Y: y}
+	pComp := p.Compress()
+
+	s, y := UnpackSignY(pComp)
+
+	pComp2 := PackSignY(s, y)
+	assert.Equal(t, pComp, pComp2)
+
+	emptyPointComp := [32]byte{}
+	s, y = UnpackSignY(emptyPointComp)
+
+	pComp2 = PackSignY(s, y)
+	assert.Equal(t, emptyPointComp, pComp2)
+}
+
 func TestCompressDecompress1(t *testing.T) {
 	x := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
@@ -200,7 +246,9 @@ func TestCompressDecompress1(t *testing.T) {
 	p := &Point{X: x, Y: y}
 
 	buf := p.Compress()
-	assert.Equal(t, "53b81ed5bffe9545b54016234682e7b2f699bd42a5e9eae27ff4051bc698ce85", hex.EncodeToString(buf[:]))
+	assert.Equal(t,
+		"53b81ed5bffe9545b54016234682e7b2f699bd42a5e9eae27ff4051bc698ce85",
+		hex.EncodeToString(buf[:]))
 
 	p2, err := NewPoint().Decompress(buf)
 	assert.Equal(t, nil, err)
@@ -216,7 +264,9 @@ func TestCompressDecompress2(t *testing.T) {
 	p := &Point{X: x, Y: y}
 
 	buf := p.Compress()
-	assert.Equal(t, "e114eb17eddf794f063a68fecac515e3620e131976108555735c8b0773929709", hex.EncodeToString(buf[:]))
+	assert.Equal(t,
+		"e114eb17eddf794f063a68fecac515e3620e131976108555735c8b0773929709",
+		hex.EncodeToString(buf[:]))
 
 	p2, err := NewPoint().Decompress(buf)
 	assert.Equal(t, nil, err)
@@ -230,14 +280,15 @@ func TestCompressDecompressRnd(t *testing.T) {
 		buf := p1.Compress()
 		p2, err := NewPoint().Decompress(buf)
 		assert.Equal(t, nil, err)
-		assert.Equal(t, p1, p2)
+		assert.Equal(t, p1.X.Bytes(), p2.X.Bytes())
+		assert.Equal(t, p1.Y.Bytes(), p2.Y.Bytes())
 	}
 }
 
 func BenchmarkBabyjub(b *testing.B) {
 	const n = 256
 
-	rnd := rand.New(rand.NewSource(42))
+	rnd := rand.New(rand.NewSource(42)) //nolint:gosec
 
 	var badpoints [n]*Point
 	for i := 0; i < n; i++ {
@@ -247,6 +298,7 @@ func BenchmarkBabyjub(b *testing.B) {
 	}
 
 	var points [n]*Point
+	var pointsProj [n]*PointProjective
 	baseX := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
 	baseY := utils.NewIntFromString(
@@ -255,6 +307,7 @@ func BenchmarkBabyjub(b *testing.B) {
 	for i := 0; i < n; i++ {
 		s := new(big.Int).Rand(rnd, constants.Q)
 		points[i] = NewPoint().Mul(s, base)
+		pointsProj[i] = NewPoint().Mul(s, base).Projective()
 	}
 
 	var scalars [n]*big.Int
@@ -265,17 +318,19 @@ func BenchmarkBabyjub(b *testing.B) {
 	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)}
+		p0Proj := p0.Projective()
+		p1Proj := p1.Projective()
 
-		p2 := NewPoint()
+		p2 := NewPoint().Projective()
 		for i := 0; i < b.N; i++ {
-			p2.Add(p0, p1)
+			p2.Add(p0Proj, p1Proj)
 		}
 	})
 
 	b.Run("AddRnd", func(b *testing.B) {
-		res := NewPoint()
+		res := NewPoint().Projective()
 		for i := 0; i < b.N; i++ {
-			res.Add(points[i%(n/2)], points[i%(n/2)+1])
+			res.Add(pointsProj[i%(n/2)], pointsProj[i%(n/2)+1])
 		}
 	})
 

babyjub/eddsa.go

@@ -1,13 +1,16 @@
+// Package babyjub eddsa implements the EdDSA over the BabyJubJub curve
+//nolint:gomnd
 package babyjub
 
 import (
 	"crypto/rand"
+	"database/sql/driver"
+	"fmt"
+	"math/big"
 
 	"github.com/iden3/go-iden3-crypto/mimc7"
 	"github.com/iden3/go-iden3-crypto/poseidon"
 	"github.com/iden3/go-iden3-crypto/utils"
-
-	"math/big"
 )
 
 // pruneBuffer prunes the buffer during key generation according to RFC 8032.
@@ -36,6 +39,13 @@ 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])
@@ -43,10 +53,10 @@ 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.
+// Public returns the public key corresponding to a private key.
 func (k *PrivateKey) Public() *PublicKey {
 	return k.Scalar().Public()
 }
@@ -60,8 +70,8 @@ func NewPrivKeyScalar(s *big.Int) *PrivKeyScalar {
 	return &sk
 }
 
-// Pub returns the public key corresponding to the scalar value s of a private
-// key.
+// Public returns the public key corresponding to the scalar value s of a
+// private key.
 func (s *PrivKeyScalar) Public() *PublicKey {
 	p := NewPoint().Mul((*big.Int)(s), B8)
 	pk := PublicKey(*p)
@@ -76,16 +86,19 @@ func (s *PrivKeyScalar) BigInt() *big.Int {
 // PublicKey represents an EdDSA public key, which is a curve point.
 type PublicKey Point
 
+// MarshalText implements the marshaler for PublicKey
 func (pk PublicKey) MarshalText() ([]byte, error) {
 	pkc := pk.Compress()
 	return utils.Hex(pkc[:]).MarshalText()
 }
 
+// String returns the string representation of the PublicKey
 func (pk PublicKey) String() string {
 	pkc := pk.Compress()
 	return utils.Hex(pkc[:]).String()
 }
 
+// UnmarshalText implements the unmarshaler for the PublicKey
 func (pk *PublicKey) UnmarshalText(h []byte) error {
 	var pkc PublicKeyComp
 	if err := utils.HexDecodeInto(pkc[:], h); err != nil {
@@ -100,24 +113,35 @@ func (pk *PublicKey) UnmarshalText(h []byte) error {
 }
 
 // Point returns the Point corresponding to a PublicKey.
-func (p *PublicKey) Point() *Point {
-	return (*Point)(p)
+func (pk *PublicKey) Point() *Point {
+	return (*Point)(pk)
 }
 
 // PublicKeyComp represents a compressed EdDSA Public key; it's a compressed curve
 // point.
 type PublicKeyComp [32]byte
 
-func (buf PublicKeyComp) MarshalText() ([]byte, error)  { return utils.Hex(buf[:]).MarshalText() }
-func (buf PublicKeyComp) String() string                { return utils.Hex(buf[:]).String() }
-func (buf *PublicKeyComp) UnmarshalText(h []byte) error { return utils.HexDecodeInto(buf[:], h) }
-
-func (p *PublicKey) Compress() PublicKeyComp {
-	return PublicKeyComp((*Point)(p).Compress())
+// MarshalText implements the marshaler for the PublicKeyComp
+func (pkComp PublicKeyComp) MarshalText() ([]byte, error) {
+	return utils.Hex(pkComp[:]).MarshalText()
 }
 
-func (p *PublicKeyComp) Decompress() (*PublicKey, error) {
-	point, err := NewPoint().Decompress(*p)
+// String returns the string representation of the PublicKeyComp
+func (pkComp PublicKeyComp) String() string { return utils.Hex(pkComp[:]).String() }
+
+// UnmarshalText implements the unmarshaler for the PublicKeyComp
+func (pkComp *PublicKeyComp) UnmarshalText(h []byte) error {
+	return utils.HexDecodeInto(pkComp[:], h)
+}
+
+// Compress returns the PublicKeyCompr for the given PublicKey
+func (pk *PublicKey) Compress() PublicKeyComp {
+	return PublicKeyComp((*Point)(pk).Compress())
+}
+
+// Decompress returns the PublicKey for the given PublicKeyComp
+func (pkComp *PublicKeyComp) Decompress() (*PublicKey, error) {
+	point, err := NewPoint().Decompress(*pkComp)
 	if err != nil {
 		return nil, err
 	}
@@ -134,9 +158,18 @@ type Signature struct {
 // SignatureComp represents a compressed EdDSA signature.
 type SignatureComp [64]byte
 
-func (buf SignatureComp) MarshalText() ([]byte, error)  { return utils.Hex(buf[:]).MarshalText() }
-func (buf SignatureComp) String() string                { return utils.Hex(buf[:]).String() }
-func (buf *SignatureComp) UnmarshalText(h []byte) error { return utils.HexDecodeInto(buf[:], h) }
+// MarshalText implements the marshaler for the SignatureComp
+func (sComp SignatureComp) MarshalText() ([]byte, error) {
+	return utils.Hex(sComp[:]).MarshalText()
+}
+
+// String returns the string representation of the SignatureComp
+func (sComp SignatureComp) String() string { return utils.Hex(sComp[:]).String() }
+
+// UnmarshalText implements the unmarshaler for the SignatureComp
+func (sComp *SignatureComp) UnmarshalText(h []byte) error {
+	return utils.HexDecodeInto(sComp[:], h)
+}
 
 // Compress an EdDSA signature by concatenating the compression of
 // the point R8 and the Little-Endian encoding of S.
@@ -164,8 +197,47 @@ func (s *Signature) Decompress(buf [64]byte) (*Signature, error) {
 
 // Decompress a compressed signature.  Returns error if the Point decompression
 // fails.
-func (s *SignatureComp) Decompress() (*Signature, error) {
-	return new(Signature).Decompress(*s)
+func (sComp *SignatureComp) Decompress() (*Signature, error) {
+	return new(Signature).Decompress(*sComp)
+}
+
+// Scan implements Scanner for database/sql.
+func (sComp *SignatureComp) Scan(src interface{}) error {
+	srcB, ok := src.([]byte)
+	if !ok {
+		return fmt.Errorf("can't scan %T into Signature", src)
+	}
+	if len(srcB) != 64 {
+		return fmt.Errorf("can't scan []byte of len %d into Signature, want %d", len(srcB), 64)
+	}
+	copy(sComp[:], srcB[:])
+	return nil
+}
+
+// Value implements valuer for database/sql.
+func (sComp SignatureComp) Value() (driver.Value, error) {
+	return sComp[:], nil
+}
+
+// Scan implements Scanner for database/sql.
+func (s *Signature) Scan(src interface{}) error {
+	srcB, ok := src.([]byte)
+	if !ok {
+		return fmt.Errorf("can't scan %T into Signature", src)
+	}
+	if len(srcB) != 64 {
+		return fmt.Errorf("can't scan []byte of len %d into Signature, want %d", len(srcB), 64)
+	}
+	buf := [64]byte{}
+	copy(buf[:], srcB[:])
+	_, err := s.Decompress(buf)
+	return err
+}
+
+// Value implements valuer for database/sql.
+func (s Signature) Value() (driver.Value, error) {
+	comp := s.Compress()
+	return comp[:], nil
 }
 
 // SignMimc7 signs a message encoded as a big.Int in Zq using blake-512 hash
@@ -195,18 +267,20 @@ func (k *PrivateKey) SignMimc7(msg *big.Int) *Signature {
 
 // VerifyMimc7 verifies the signature of a message encoded as a big.Int in Zq
 // using blake-512 hash for buffer hashing and mimc7 for big.Int hashing.
-func (p *PublicKey) VerifyMimc7(msg *big.Int, sig *Signature) bool {
-	hmInput := []*big.Int{sig.R8.X, sig.R8.Y, p.X, p.Y, msg}
+func (pk *PublicKey) VerifyMimc7(msg *big.Int, sig *Signature) bool {
+	hmInput := []*big.Int{sig.R8.X, sig.R8.Y, pk.X, pk.Y, msg}
 	hm, err := mimc7.Hash(hmInput, nil) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
 	if err != nil {
-		panic(err)
+		return false
 	}
 
 	left := NewPoint().Mul(sig.S, B8) // left = s * 8 * B
 	r1 := big.NewInt(8)
 	r1.Mul(r1, hm)
-	right := NewPoint().Mul(r1, p.Point())
-	right.Add(sig.R8, right) // right = 8 * R + 8 * hm * A
+	right := NewPoint().Mul(r1, pk.Point())
+	rightProj := right.Projective()
+	rightProj.Add(sig.R8.Projective(), rightProj) // right = 8 * R + 8 * hm * A
+	right = rightProj.Affine()
 	return (left.X.Cmp(right.X) == 0) && (left.Y.Cmp(right.Y) == 0)
 }
 
@@ -222,11 +296,13 @@ 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 := [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)
+
+	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)
 	if err != nil {
 		panic(err)
 	}
+
 	S := new(big.Int).Lsh(k.Scalar().BigInt(), 3)
 	S = S.Mul(hm, S)
 	S.Add(r, S)
@@ -237,17 +313,62 @@ 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 := [poseidon.T]*big.Int{sig.R8.X, sig.R8.Y, p.X, p.Y, msg, big.NewInt(int64(0))}
-	hm, err := poseidon.PoseidonHash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
+func (pk *PublicKey) VerifyPoseidon(msg *big.Int, sig *Signature) bool {
+	hmInput := []*big.Int{sig.R8.X, sig.R8.Y, pk.X, pk.Y, msg}
+	hm, err := poseidon.Hash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
 	if err != nil {
-		panic(err)
+		return false
 	}
 
 	left := NewPoint().Mul(sig.S, B8) // left = s * 8 * B
 	r1 := big.NewInt(8)
 	r1.Mul(r1, hm)
-	right := NewPoint().Mul(r1, p.Point())
-	right.Add(sig.R8, right) // right = 8 * R + 8 * hm * A
+	right := NewPoint().Mul(r1, pk.Point())
+	rightProj := right.Projective()
+	rightProj.Add(sig.R8.Projective(), rightProj) // right = 8 * R + 8 * hm * A
+	right = rightProj.Affine()
 	return (left.X.Cmp(right.X) == 0) && (left.Y.Cmp(right.Y) == 0)
 }
+
+// Scan implements Scanner for database/sql.
+func (pk *PublicKey) Scan(src interface{}) error {
+	srcB, ok := src.([]byte)
+	if !ok {
+		return fmt.Errorf("can't scan %T into PublicKey", src)
+	}
+	if len(srcB) != 32 {
+		return fmt.Errorf("can't scan []byte of len %d into PublicKey, want %d", len(srcB), 32)
+	}
+	var comp PublicKeyComp
+	copy(comp[:], srcB)
+	decomp, err := comp.Decompress()
+	if err != nil {
+		return err
+	}
+	*pk = *decomp
+	return nil
+}
+
+// Value implements valuer for database/sql.
+func (pk PublicKey) Value() (driver.Value, error) {
+	comp := pk.Compress()
+	return comp[:], nil
+}
+
+// Scan implements Scanner for database/sql.
+func (pkComp *PublicKeyComp) Scan(src interface{}) error {
+	srcB, ok := src.([]byte)
+	if !ok {
+		return fmt.Errorf("can't scan %T into PublicKeyComp", src)
+	}
+	if len(srcB) != 32 {
+		return fmt.Errorf("can't scan []byte of len %d into PublicKeyComp, want %d", len(srcB), 32)
+	}
+	copy(pkComp[:], srcB)
+	return nil
+}
+
+// Value implements valuer for database/sql.
+func (pkComp PublicKeyComp) Value() (driver.Value, error) {
+	return pkComp[:], nil
+}

babyjub/eddsa_test.go

@@ -1,7 +1,8 @@
 package babyjub
 
 import (
-	"crypto/rand"
+	"database/sql"
+	"database/sql/driver"
 	"encoding/hex"
 	"fmt"
 	"math/big"
@@ -10,25 +11,13 @@ 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++ {
-		hex.Decode(k[:], []byte{byte(i)})
+	for i := 0; i < 32; i++ {
+		k[i] = byte(i)
 	}
 	pk := k.Public()
 	assert.True(t, pk.X.Cmp(constants.Q) == -1)
@@ -37,7 +26,9 @@ 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 +72,9 @@ 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)
@@ -104,7 +97,7 @@ func TestSignVerifyPoseidon(t *testing.T) {
 		"15383486972088797283337779941324724402501462225528836549661220478783371668959",
 		sig.R8.Y.String())
 	assert.Equal(t,
-		"248298168863866362217836334079793350221620631973732197668910946177382043688",
+		"1672775540645840396591609181675628451599263765380031905495115170613215233181",
 		sig.S.String())
 
 	ok := pk.VerifyPoseidon(msg, sig)
@@ -116,7 +109,7 @@ func TestSignVerifyPoseidon(t *testing.T) {
 
 	assert.Equal(t, ""+
 		"dfedb4315d3f2eb4de2d3c510d7a987dcab67089c8ace06308827bf5bcbe02a2"+
-		"28506bce274aa1b3f7e7c2fd7e4fe09bff8f9aa37a42def7994e98f322888c00",
+		"9d043ece562a8f82bfc0adb640c0107a7d3a27c1c7c1a6179a0da73de5c1b203",
 		hex.EncodeToString(sigBuf[:]))
 
 	ok = pk.VerifyPoseidon(msg, sig2)
@@ -125,7 +118,9 @@ 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))
@@ -142,9 +137,64 @@ func TestCompressDecompress(t *testing.T) {
 	}
 }
 
+func TestSignatureCompScannerValuer(t *testing.T) {
+	privK := NewRandPrivKey()
+	var value driver.Valuer //nolint:gosimple this is done to ensure interface compatibility
+	value = privK.SignPoseidon(big.NewInt(674238462)).Compress()
+	scan := privK.SignPoseidon(big.NewInt(1)).Compress()
+	fromDB, err := value.Value()
+	assert.Nil(t, err)
+	assert.Nil(t, scan.Scan(fromDB))
+	assert.Equal(t, value, scan)
+}
+
+func TestSignatureScannerValuer(t *testing.T) {
+	privK := NewRandPrivKey()
+	var value driver.Valuer
+	var scan sql.Scanner
+	value = privK.SignPoseidon(big.NewInt(674238462))
+	scan = privK.SignPoseidon(big.NewInt(1))
+	fromDB, err := value.Value()
+	assert.Nil(t, err)
+	assert.Nil(t, scan.Scan(fromDB))
+	assert.Equal(t, value, scan)
+}
+
+func TestPublicKeyScannerValuer(t *testing.T) {
+	privKValue := NewRandPrivKey()
+	pubKValue := privKValue.Public()
+	privKScan := NewRandPrivKey()
+	pubKScan := privKScan.Public()
+	var value driver.Valuer
+	var scan sql.Scanner
+	value = pubKValue
+	scan = pubKScan
+	fromDB, err := value.Value()
+	assert.Nil(t, err)
+	assert.Nil(t, scan.Scan(fromDB))
+	assert.Equal(t, value, scan)
+}
+
+func TestPublicKeyCompScannerValuer(t *testing.T) {
+	privKValue := NewRandPrivKey()
+	pubKCompValue := privKValue.Public().Compress()
+	privKScan := NewRandPrivKey()
+	pubKCompScan := privKScan.Public().Compress()
+	var value driver.Valuer
+	var scan sql.Scanner
+	value = &pubKCompValue
+	scan = &pubKCompScan
+	fromDB, err := value.Value()
+	assert.Nil(t, err)
+	assert.Nil(t, scan.Scan(fromDB))
+	assert.Equal(t, value, scan)
+}
+
 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

@@ -1,13 +1,20 @@
 package babyjub
 
 import (
-	"github.com/dchest/blake512" // I have personally reviewed that this module doesn't do anything suspicious
+	"github.com/dchest/blake512"
 )
 
+// Note on dchest/blake512: This specific blake512 module is compatible with
+// the version of Blake512 used at circomlib, and this module has been reviewed
+// to don't be doing do anything suspicious.
+
 // Blake512 performs the blake-512 hash over the buffer m.  Note that this is
 // 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

@@ -1,7 +1,7 @@
 package constants
 
 import (
-	"github.com/iden3/go-iden3-crypto/utils"
+	"fmt"
 	"math/big"
 )
 
@@ -21,6 +21,11 @@ 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 +1,6 @@
+package ff
+
+// NewElement returns a new empty *Element
+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 +4,8 @@ go 1.12
 
 require (
 	github.com/dchest/blake512 v1.0.0
-	github.com/ethereum/go-ethereum v1.8.27
-	github.com/stretchr/testify v1.3.0
-	golang.org/x/crypto v0.0.0-20190621222207-cc06ce4a13d4
+	github.com/ethereum/go-ethereum v1.9.12
+	github.com/stretchr/testify v1.4.0
+	golang.org/x/crypto v0.0.0-20200311171314-f7b00557c8c4
+	golang.org/x/sys v0.0.0-20200323222414-85ca7c5b95cd // indirect
 )

go.sum

@@ -1,20 +1,173 @@
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mimc7/mimc7.go

@@ -6,82 +6,84 @@ 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"
 )
 
+// SEED defines the seed used to constants
 const SEED = "mimc"
 
 var constants = generateConstantsData()
 
 type constantsData struct {
-	maxFieldVal *big.Int
 	seedHash *big.Int
 	iv       *big.Int
-	fqR         field.Fq
 	nRounds  int
-	cts         []*big.Int
+	cts      []*ff.Element
 }
 
 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 {
-	cts := make([]*big.Int, nRounds)
-	cts[0] = big.NewInt(int64(0))
+func getConstants(seed string, nRounds int) []*ff.Element {
+	cts := make([]*ff.Element, nRounds)
+	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)
-		cts[i] = n
+		n := new(big.Int).Mod(c, _constants.Q)
+		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 {
-	cts := getConstants(fqR, SEED, nRounds)
-	var r *big.Int
+// 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(xInBI, kBI *big.Int, nRounds int) *big.Int { //nolint:golint
+	xIn := ff.NewElement().SetBigInt(xInBI)
+	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)
-		t4 := fqR.Square(t2)
-		r = fqR.Mul(fqR.Mul(t4, t2), t)
+		t2 := ff.NewElement().Square(t)
+		t4 := ff.NewElement().Square(t2)
+		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) {
-	if !utils.CheckBigIntArrayInField(arr, constants.fqR.Q) {
+// 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, nRounds int) (*big.Int, error) {
+	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
 		}
@@ -89,48 +91,57 @@ func HashGeneric(iv *big.Int, arr []*big.Int, fqR field.Fq, nRounds int) (*big.I
 	return r, nil
 }
 
-// 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 {
-	var r *big.Int
+// 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(xInBI, kBI *big.Int) *big.Int { //nolint:golint
+	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)
-		t4 := constants.fqR.Square(t2)
-		r = constants.fqR.Mul(constants.fqR.Mul(t4, t2), t)
+		t2 := ff.NewElement().Square(t)
+		t4 := ff.NewElement().Square(t2)
+		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(
-			constants.fqR.Add(
+		r = new(big.Int).Add(
+			new(big.Int).Add(
 				r,
 				arr[i],
 			),
 			MIMC7Hash(arr[i], r))
+		r = new(big.Int).Mod(r, _constants.Q)
 	}
 	return r, nil
 }
 
 // HashBytes hashes a msg byte slice by blocks of 31 bytes encoded as
 // little-endian
-func HashBytes(b []byte) (*big.Int, error) {
+func HashBytes(b []byte) *big.Int {
 	n := 31
 	bElems := make([]*big.Int, 0, len(b)/n+1)
 	for i := 0; i < len(b)/n; i++ {
@@ -143,5 +154,9 @@ func HashBytes(b []byte) (*big.Int, error) {
 		utils.SetBigIntFromLEBytes(v, b[(len(b)/n)*n:])
 		bElems = append(bElems, v)
 	}
-	return Hash(bElems, nil)
+	h, err := Hash(bElems, nil)
+	if err != nil {
+		panic(err)
+	}
+	return h
 }

mimc7/mimc7_test.go

@@ -6,15 +6,18 @@ import (
 	"testing"
 
 	"github.com/ethereum/go-ethereum/crypto"
-	"github.com/iden3/go-iden3-crypto/field"
 	"github.com/stretchr/testify/assert"
 )
 
 func TestKeccak256(t *testing.T) {
 	res := crypto.Keccak256([]byte(SEED))
-	assert.Equal(t, "b6e489e6b37224a50bebfddbe7d89fa8fdcaa84304a70bd13f79b5d9f7951e9e", hex.EncodeToString(res))
+	assert.Equal(t,
+		"b6e489e6b37224a50bebfddbe7d89fa8fdcaa84304a70bd13f79b5d9f7951e9e",
+		hex.EncodeToString(res))
 	c := new(big.Int).SetBytes(crypto.Keccak256([]byte(SEED)))
-	assert.Equal(t, "82724731331859054037315113496710413141112897654334566532528783843265082629790", c.String())
+	assert.Equal(t,
+		"82724731331859054037315113496710413141112897654334566532528783843265082629790",
+		c.String())
 }
 
 func TestMIMC7Generic(t *testing.T) {
@@ -22,18 +25,18 @@ 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)
-	assert.Equal(t, "10594780656576967754230020536574539122676596303354946869887184401991294982664", mhg.String())
-	hg, err := HashGeneric(fqR.Zero(), bigArray, fqR, 91)
+	mhg := MIMC7HashGeneric(b1, b2, 91)
+	assert.Equal(t,
+		"10594780656576967754230020536574539122676596303354946869887184401991294982664",
+		mhg.String())
+	hg, err := HashGeneric(big.NewInt(0), bigArray, 91)
 	assert.Nil(t, err)
-	assert.Equal(t, "6464402164086696096195815557694604139393321133243036833927490113253119343397", (*big.Int)(hg).String())
+	assert.Equal(t,
+		"6464402164086696096195815557694604139393321133243036833927490113253119343397",
+		(*big.Int)(hg).String())
 }
 
 func TestMIMC7(t *testing.T) {
@@ -48,7 +51,8 @@ func TestMIMC7(t *testing.T) {
 	h1, err := Hash(bigArray1, nil)
 	assert.Nil(t, err)
 	// same hash value than the iden3js and circomlib tests:
-	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h1).Bytes()), "0x237c92644dbddb86d8a259e0e923aaab65a93f1ec5758b8799988894ac0958fd")
+	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h1).Bytes()),
+		"0x237c92644dbddb86d8a259e0e923aaab65a93f1ec5758b8799988894ac0958fd")
 
 	// h2a, hash of 2 elements
 	bigArray2a := []*big.Int{b78, b41}
@@ -56,19 +60,22 @@ func TestMIMC7(t *testing.T) {
 	h2a, err := Hash(bigArray2a, nil)
 	assert.Nil(t, err)
 	// same hash value than the iden3js and circomlib tests:
-	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h2a).Bytes()), "0x067f3202335ea256ae6e6aadcd2d5f7f4b06a00b2d1e0de903980d5ab552dc70")
+	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h2a).Bytes()),
+		"0x067f3202335ea256ae6e6aadcd2d5f7f4b06a00b2d1e0de903980d5ab552dc70")
 
 	// h2b, hash of 2 elements
 	bigArray2b := []*big.Int{b12, b45}
 
 	mh2b := MIMC7Hash(b12, b45)
 	assert.Nil(t, err)
-	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(mh2b).Bytes()), "0x2ba7ebad3c6b6f5a20bdecba2333c63173ca1a5f2f49d958081d9fa7179c44e4")
+	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(mh2b).Bytes()),
+		"0x2ba7ebad3c6b6f5a20bdecba2333c63173ca1a5f2f49d958081d9fa7179c44e4")
 
 	h2b, err := Hash(bigArray2b, nil)
 	assert.Nil(t, err)
 	// same hash value than the iden3js and circomlib tests:
-	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h2b).Bytes()), "0x15ff7fe9793346a17c3150804bcb36d161c8662b110c50f55ccb7113948d8879")
+	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h2b).Bytes()),
+		"0x15ff7fe9793346a17c3150804bcb36d161c8662b110c50f55ccb7113948d8879")
 
 	// h4, hash of 4 elements
 	bigArray4 := []*big.Int{b12, b45, b78, b41}
@@ -76,12 +83,14 @@ func TestMIMC7(t *testing.T) {
 	h4, err := Hash(bigArray4, nil)
 	assert.Nil(t, err)
 	// same hash value than the iden3js and circomlib tests:
-	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h4).Bytes()), "0x284bc1f34f335933a23a433b6ff3ee179d682cd5e5e2fcdd2d964afa85104beb")
+	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h4).Bytes()),
+		"0x284bc1f34f335933a23a433b6ff3ee179d682cd5e5e2fcdd2d964afa85104beb")
 
-	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.")
-	hmsg, err := HashBytes(msg)
-	assert.Nil(t, err)
-	assert.Equal(t, "16855787120419064316734350414336285711017110414939748784029922801367685456065", hmsg.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.") //nolint:lll
+	hmsg := HashBytes(msg)
+	assert.Equal(t,
+		"16855787120419064316734350414336285711017110414939748784029922801367685456065",
+		hmsg.String())
 }
 
 func BenchmarkMIMC7(b *testing.B) {
@@ -92,6 +101,6 @@ 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,gosec
 	}
 }

poseidon/poseidon.go

@@ -1,209 +1,89 @@
 package poseidon
 
 import (
-	"bytes"
 	"errors"
+	"fmt"
 	"math/big"
-	"strconv"
 
-	"github.com/iden3/go-iden3-crypto/constants"
+	"github.com/iden3/go-iden3-crypto/ff"
 	"github.com/iden3/go-iden3-crypto/utils"
-	"golang.org/x/crypto/blake2b"
 )
 
-const SEED = "poseidon"
-const NROUNDSF = 8
-const NROUNDSP = 57
-const T = 6
+const NROUNDSF = 8 //nolint:golint
 
-var constC []*big.Int
-var constM [T][T]*big.Int
+var NROUNDSP = []int{56, 57, 56, 60, 60, 63, 64, 63} //nolint:golint
 
-func Zero() *big.Int {
-	return new(big.Int)
-}
-
-func modQ(v *big.Int) {
-	v.Mod(v, constants.Q)
-}
-
-func init() {
-	constC = getPseudoRandom(SEED+"_constants", NROUNDSF+NROUNDSP)
-	constM = getMDS()
-}
-
-func leByteArrayToBigInt(b []byte) *big.Int {
-	res := big.NewInt(0)
-	for i := 0; i < len(b); i++ {
-		n := big.NewInt(int64(b[i]))
-		res = new(big.Int).Add(res, new(big.Int).Lsh(n, uint(i*8)))
-	}
-	return res
-}
-
-func getPseudoRandom(seed string, n int) []*big.Int {
-	res := make([]*big.Int, n)
-	hash := blake2b.Sum256([]byte(seed))
-	for i := 0; i < n; i++ {
-		hashBigInt := Zero()
-		res[i] = utils.SetBigIntFromLEBytes(hashBigInt, hash[:])
-		modQ(res[i])
-		hash = blake2b.Sum256(hash[:])
-	}
-	return res
-}
-
-func nonceToString(n int) string {
-	r := strconv.Itoa(n)
-	for len(r) < 4 {
-		r = "0" + r
-	}
-	return r
-}
-
-// https://eprint.iacr.org/2019/458.pdf pag.8
-func getMDS() [T][T]*big.Int {
-	nonce := 0
-	cauchyMatrix := getPseudoRandom(SEED+"_matrix_"+nonceToString(nonce), T*2)
-	for !checkAllDifferent(cauchyMatrix) {
-		nonce += 1
-		cauchyMatrix = getPseudoRandom(SEED+"_matrix_"+nonceToString(nonce), T*2)
-	}
-	var m [T][T]*big.Int
-	for i := 0; i < T; i++ {
-		// var mi []*big.Int
-		for j := 0; j < T; j++ {
-			m[i][j] = new(big.Int).Sub(cauchyMatrix[i], cauchyMatrix[T+j])
-			m[i][j].ModInverse(m[i][j], constants.Q)
-		}
-	}
-	return m
-}
-
-func checkAllDifferent(v []*big.Int) bool {
-	for i := 0; i < len(v); i++ {
-		if bytes.Equal(v[i].Bytes(), big.NewInt(int64(0)).Bytes()) {
-			return false
-		}
-		for j := i + 1; j < len(v); j++ {
-			if bytes.Equal(v[i].Bytes(), v[j].Bytes()) {
-				return false
-			}
-		}
-	}
-	return true
+func zero() *ff.Element {
+	return ff.NewElement()
 }
 
 // ark computes Add-Round Key, from the paper https://eprint.iacr.org/2019/458.pdf
-func ark(state [T]*big.Int, c *big.Int) {
-	for i := 0; i < T; i++ {
-		modQ(state[i].Add(state[i], c))
+func ark(state []*ff.Element, c []*ff.Element, it int) {
+	for i := 0; i < len(state); i++ {
+		state[i].Add(state[i], c[it+i])
 	}
 }
 
-// cubic performs x^5 mod p
+// exp5 performs x^5 mod p
 // https://eprint.iacr.org/2019/458.pdf page 8
-var five = big.NewInt(5)
-
-func cubic(a *big.Int) {
-	a.Exp(a, five, constants.Q)
+func exp5(a *ff.Element) {
+	a.Exp(*a, 5)
 }
 
 // sbox https://eprint.iacr.org/2019/458.pdf page 6
-func sbox(state [T]*big.Int, i int) {
-	if (i < NROUNDSF/2) || (i >= NROUNDSF/2+NROUNDSP) {
-		for j := 0; j < T; j++ {
-			cubic(state[j])
+func sbox(nRoundsF, nRoundsP int, state []*ff.Element, i int) {
+	if (i < nRoundsF/2) || (i >= nRoundsF/2+nRoundsP) {
+		for j := 0; j < len(state); j++ {
+			exp5(state[j])
 		}
 	} else {
-		cubic(state[0])
+		exp5(state[0])
 	}
 }
 
 // mix returns [[matrix]] * [vector]
-func mix(state [T]*big.Int, newState [T]*big.Int, m [T][T]*big.Int) {
-	mul := Zero()
-	for i := 0; i < T; i++ {
-		newState[i].SetInt64(0)
-		for j := 0; j < T; j++ {
-			modQ(mul.Mul(m[i][j], state[j]))
+func mix(state []*ff.Element, newState []*ff.Element, m [][]*ff.Element) {
+	mul := zero()
+	for i := 0; i < len(state); i++ {
+		newState[i].SetUint64(0)
+		for j := 0; j < len(state); j++ {
+			mul.Mul(m[i][j], state[j])
 			newState[i].Add(newState[i], mul)
 		}
-		modQ(newState[i])
 	}
 }
 
-// PoseidonHash computes the Poseidon hash for the given inputs
-func PoseidonHash(inp [T]*big.Int) (*big.Int, error) {
-	if !utils.CheckBigIntArrayInField(inp[:], constants.Q) {
+// Hash computes the Poseidon hash for the given inputs
+func Hash(inpBI []*big.Int) (*big.Int, error) {
+	t := len(inpBI) + 1
+	if len(inpBI) == 0 || len(inpBI) >= len(NROUNDSP)-1 {
+		return nil, fmt.Errorf("invalid inputs length %d, max %d", len(inpBI), len(NROUNDSP)-1)
+	}
+	if !utils.CheckBigIntArrayInField(inpBI[:]) {
 		return nil, errors.New("inputs values not inside Finite Field")
 	}
-	state := [T]*big.Int{}
-	for i := 0; i < T; i++ {
-		state[i] = new(big.Int).Set(inp[i])
+	inp := utils.BigIntArrayToElementArray(inpBI[:])
+	state := make([]*ff.Element, t)
+	state[0] = zero()
+	copy(state[1:], inp[:])
+
+	nRoundsF := NROUNDSF
+	nRoundsP := NROUNDSP[t-2]
+
+	newState := make([]*ff.Element, t)
+	for i := 0; i < t; i++ {
+		newState[i] = zero()
 	}
 
 	// ARK --> SBox --> M, https://eprint.iacr.org/2019/458.pdf pag.5
-	var newState [T]*big.Int
-	for i := 0; i < T; i++ {
-		newState[i] = Zero()
-	}
-	for i := 0; i < NROUNDSF+NROUNDSP; i++ {
-		ark(state, constC[i])
-		sbox(state, i)
-		mix(state, newState, constM)
+	for i := 0; i < nRoundsF+nRoundsP; i++ {
+		ark(state, c.c[t-2], i*t)
+		sbox(nRoundsF, nRoundsP, state, i)
+		mix(state, newState, c.m[t-2])
 		state, newState = newState, state
 	}
-	return state[0], nil
-}
-
-// Hash performs the Poseidon hash over a *big.Int array
-// in chunks of 5 elements
-func Hash(arr []*big.Int) (*big.Int, error) {
-	if !utils.CheckBigIntArrayInField(arr, constants.Q) {
-		return nil, errors.New("inputs values not inside Finite Field")
-	}
-
-	r := big.NewInt(1)
-	for i := 0; i < len(arr); i = i + T - 1 {
-		var toHash [T]*big.Int
-		j := 0
-		for ; j < T-1; j++ {
-			if i+j >= len(arr) {
-				break
-			}
-			toHash[j] = arr[i+j]
-		}
-		toHash[j] = r
-		j++
-		for ; j < T; j++ {
-			toHash[j] = constants.Zero
-		}
-
-		ph, err := PoseidonHash(toHash)
-		if err != nil {
-			return nil, err
-		}
-		modQ(r.Add(r, ph))
-	}
-
+	rE := state[0]
+	r := big.NewInt(0)
+	rE.ToBigIntRegular(r)
 	return r, nil
 }
-
-// HashBytes hashes a msg byte slice by blocks of 31 bytes encoded as
-// little-endian
-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 := Zero()
-		utils.SetBigIntFromLEBytes(v, b[n*i:n*(i+1)])
-		bElems = append(bElems, v)
-	}
-	if len(b)%n != 0 {
-		v := Zero()
-		utils.SetBigIntFromLEBytes(v, b[(len(b)/n)*n:])
-		bElems = append(bElems, v)
-	}
-	return Hash(bElems)
-}

poseidon/poseidon_test.go

@@ -12,86 +12,86 @@ import (
 
 func TestBlake2bVersion(t *testing.T) {
 	h := blake2b.Sum256([]byte("poseidon_constants"))
-	assert.Equal(t, "e57ba154fb2c47811dc1a2369b27e25a44915b4e4ece4eb8ec74850cb78e01b1", hex.EncodeToString(h[:]))
+	assert.Equal(t,
+		"e57ba154fb2c47811dc1a2369b27e25a44915b4e4ece4eb8ec74850cb78e01b1",
+		hex.EncodeToString(h[:]))
 }
 
-func TestPoseidon(t *testing.T) {
-	b1 := big.NewInt(int64(1))
-	b2 := big.NewInt(int64(2))
-	h, err := Hash([]*big.Int{b1, b2})
-	assert.Nil(t, err)
-	assert.Equal(t, "4932297968297298434239270129193057052722409868268166443802652458940273154855", h.String())
+func TestPoseidonHash(t *testing.T) {
+	b0 := big.NewInt(0)
+	b1 := big.NewInt(1)
+	b2 := big.NewInt(2)
 
-	b3 := big.NewInt(int64(3))
-	b4 := big.NewInt(int64(4))
-	h, err = Hash([]*big.Int{b3, b4})
+	h, err := Hash([]*big.Int{b1})
 	assert.Nil(t, err)
-	assert.Equal(t, "4635491972858758537477743930622086396911540895966845494943021655521913507504", h.String())
+	assert.Equal(t,
+		"18586133768512220936620570745912940619677854269274689475585506675881198879027",
+		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
-	msgElems := make([]*big.Int, 0, len(msg)/n+1)
-	for i := 0; i < len(msg)/n; i++ {
-		v := new(big.Int)
-		utils.SetBigIntFromLEBytes(v, msg[n*i:n*(i+1)])
-		msgElems = append(msgElems, v)
-	}
-	if len(msg)%n != 0 {
-		v := new(big.Int)
-		utils.SetBigIntFromLEBytes(v, msg[(len(msg)/n)*n:])
-		msgElems = append(msgElems, v)
-	}
-	hmsg, err := Hash(msgElems)
+	h, err = Hash([]*big.Int{b1, b2})
 	assert.Nil(t, err)
-	assert.Equal(t, "16019700159595764790637132363672701294192939959594423814006267756172551741065", hmsg.String())
+	assert.Equal(t,
+		"7853200120776062878684798364095072458815029376092732009249414926327459813530",
+		h.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)
-	for i := 0; i < len(msg2)/n; i++ {
-		v := new(big.Int)
-		utils.SetBigIntFromLEBytes(v, msg2[n*i:n*(i+1)])
-		msg2Elems = append(msg2Elems, v)
-	}
-	if len(msg2)%n != 0 {
-		v := new(big.Int)
-		utils.SetBigIntFromLEBytes(v, msg2[(len(msg2)/n)*n:])
-		msg2Elems = append(msg2Elems, v)
-	}
-	hmsg2, err := Hash(msg2Elems)
+	h, err = Hash([]*big.Int{b1, b2, b0, b0, b0})
 	assert.Nil(t, err)
-	assert.Equal(t, "2978613163687734485261639854325792381691890647104372645321246092227111432722", hmsg2.String())
+	assert.Equal(t,
+		"1018317224307729531995786483840663576608797660851238720571059489595066344487",
+		h.String())
+	h, err = Hash([]*big.Int{b1, b2, b0, b0, b0, b0})
+	assert.Nil(t, err)
+	assert.Equal(t,
+		"15336558801450556532856248569924170992202208561737609669134139141992924267169",
+		h.String())
 
-	hmsg2, err = HashBytes(msg2)
+	b3 := big.NewInt(3)
+	b4 := big.NewInt(4)
+	h, err = Hash([]*big.Int{b3, b4, b0, b0, b0})
 	assert.Nil(t, err)
-	assert.Equal(t, "2978613163687734485261639854325792381691890647104372645321246092227111432722", hmsg2.String())
+	assert.Equal(t,
+		"5811595552068139067952687508729883632420015185677766880877743348592482390548",
+		h.String())
+	h, err = Hash([]*big.Int{b3, b4, b0, b0, b0, b0})
+	assert.Nil(t, err)
+	assert.Equal(t,
+		"12263118664590987767234828103155242843640892839966517009184493198782366909018",
+		h.String())
+
+	b5 := big.NewInt(5)
+	b6 := big.NewInt(6)
+	h, err = Hash([]*big.Int{b1, b2, b3, b4, b5, b6})
+	assert.Nil(t, err)
+	assert.Equal(t,
+		"20400040500897583745843009878988256314335038853985262692600694741116813247201",
+		h.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)})
+func TestErrorInputs(t *testing.T) {
+	b0 := big.NewInt(0)
+	b1 := big.NewInt(1)
+	b2 := big.NewInt(2)
+
+	_, err := Hash([]*big.Int{b1, b2, b0, b0, b0, b0})
 	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)
+
+	_, err = Hash([]*big.Int{b1, b2, b0, b0, b0, b0, b0})
+	assert.NotNil(t, err)
+	assert.Equal(t, "invalid inputs length 7, max 7", err.Error())
+
+	_, err = Hash([]*big.Int{b1, b2, b0, b0, b0, b0, b0, b0})
+	assert.NotNil(t, err)
+	assert.Equal(t, "invalid inputs length 8, max 7", err.Error())
 }
 
-func TestPoseidonBrokenPadding(t *testing.T) {
-	h1, err := Hash([]*big.Int{big.NewInt(1)})
-	assert.Nil(t, err)
-	h2, err := Hash([]*big.Int{big.NewInt(1), big.NewInt(0)})
-	assert.Nil(t, err)
-	assert.NotEqual(t, h1, h2)
-}
+func BenchmarkPoseidonHash(b *testing.B) {
+	b0 := big.NewInt(0)
+	b1 := utils.NewIntFromString("12242166908188651009877250812424843524687801523336557272219921456462821518061") //nolint:lll
+	b2 := utils.NewIntFromString("12242166908188651009877250812424843524687801523336557272219921456462821518061") //nolint:lll
 
-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}
+	bigArray4 := []*big.Int{b1, b2, b0, b0, b0, b0}
 
 	for i := 0; i < b.N; i++ {
-		Hash(bigArray4)
+		Hash(bigArray4) //nolint:errcheck,gosec
 	}
 }

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 = h[2:]
-	}
+	h = strings.TrimPrefix(h, "0x")
 	return hex.DecodeString(h)
 }
 
@@ -76,7 +77,7 @@ func HexDecodeInto(dst []byte, h []byte) error {
 		h = h[2:]
 	}
 	if len(h)/2 != len(dst) {
-		return fmt.Errorf("expected %v bytes in hex string, got %v", len(dst), len(h)/2)
+		return fmt.Errorf("expected %v bytes in hex string, got %v", len(dst), len(h)/2) //nolint:gomnd
 	}
 	n, err := hex.Decode(dst, h)
 	if err != nil {
@@ -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
-func CheckBigIntInField(a *big.Int, q *big.Int) bool {
-	if a.Cmp(q) != -1 {
+// CheckBigIntInField checks if given *big.Int fits in a Field Q element
+func CheckBigIntInField(a *big.Int) bool {
+	return a.Cmp(constants.Q) == -1
+}
+
+// CheckBigIntArrayInField checks if given *big.Int fits in a Field Q element
+func CheckBigIntArrayInField(arr []*big.Int) bool {
+	for _, a := range arr {
+		if !CheckBigIntInField(a) {
 			return false
 		}
+	}
 	return true
 }
 
-// CheckBigIntArrayInField checks if given big.Int fits in a Field Q element
-func CheckBigIntArrayInField(arr []*big.Int, q *big.Int) bool {
-	for _, a := range arr {
-		if !CheckBigIntInField(a, q) {
-			return false
+// 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 true
+	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
 }