Add goff to BabyJubJub point addition

```
Benchmarks (On a Intel(R) Core(TM) i7-8705G CPU @ 3.10GHz, with 32 GB of RAM):

- Old (commit: e04ca5764a):
BenchmarkBabyjub/AddConst-8              1000000              1072 ns/op
BenchmarkBabyjub/AddRnd-8                  93417             12943 ns/op
BenchmarkBabyjub/MulRnd-8                    252           4797810 ns/op
BenchmarkBabyjub/Compress-8              7291580               166 ns/op
BenchmarkBabyjub/InCurve-8                611137              1999 ns/op
BenchmarkBabyjub/InSubGroup-8             615792              2021 ns/op
BenchmarkBabyjubEddsa/SignMimc7-8            126           9358542 ns/op
BenchmarkBabyjubEddsa/VerifyMimc7-8          124           9484005 ns/op
BenchmarkBabyjubEddsa/SignPoseidon-8                 126           9486484 ns/op
BenchmarkBabyjubEddsa/VerifyPoseidon-8               126           9622807 ns/op

- With new point addition algorithm (commit: aab1a681dd):
BenchmarkBabyjub/AddConst-8              1356836               881 ns/op
BenchmarkBabyjub/AddRnd-8                 274112              4220 ns/op
BenchmarkBabyjub/MulRnd-8                    492           2474412 ns/op
BenchmarkBabyjub/Compress-8              6964855               197 ns/op
BenchmarkBabyjub/InCurve-8                608169              2008 ns/op
BenchmarkBabyjub/InSubGroup-8             618772              1954 ns/op
BenchmarkBabyjubEddsa/SignMimc7-8            238           4962397 ns/op
BenchmarkBabyjubEddsa/VerifyMimc7-8          235           5234883 ns/op
BenchmarkBabyjubEddsa/SignPoseidon-8                 240           5028720 ns/op
BenchmarkBabyjubEddsa/VerifyPoseidon-8               243           5226654 ns/op

Point Addition: ~3x
Point scalar Mul: ~1.9x
Signature (poseidon): ~1.88x
Verification (poseidon): ~1.84x

- With new point addition algorithm & goff (current commit):
BenchmarkBabyjub/AddConst-8              3000531               400 ns/op
BenchmarkBabyjub/AddRnd-8                2770335               428 ns/op
BenchmarkBabyjub/MulRnd-8                   6636            175522 ns/op
BenchmarkBabyjub/Compress-8              7358768               180 ns/op
BenchmarkBabyjub/InCurve-8                539193              1950 ns/op
BenchmarkBabyjub/InSubGroup-8             601402              1958 ns/op
BenchmarkBabyjubEddsa/SignMimc7-8           2940            409487 ns/op
BenchmarkBabyjubEddsa/VerifyMimc7-8         2908            414407 ns/op
BenchmarkBabyjubEddsa/SignPoseidon-8                2395            493165 ns/op
BenchmarkBabyjubEddsa/VerifyPoseidon-8              2491            494849 ns/op

Point Addition: ~9.86x
Point scalar Mul: ~14x
Signature (poseidon): ~10.2x
Verification (poseidon): ~10.56x

---

Total improvement (from old to current):
Point Addition: ~30.24x
Point scalar Mul: ~27.33x
Signature (poseidon): ~19.24x
Verification (poseidon): ~19.44x
```

.github/workflows/lint.yml

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

.github/workflows/test.yml

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

.travis.yml

@@ -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

@@ -10,10 +10,16 @@ import (
 )
 
 // A is one of the babyjub constants.
-var A *ff.Element
+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 *ff.Element
+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
@@ -28,52 +34,95 @@ var B8 *Point
 
 // init initializes global numbers and the subgroup base.
 func init() {
-	A = ff.NewElement().SetString("168700")
+	A = utils.NewIntFromString("168700")
-	D = ff.NewElement().SetString("168696")
+	D = utils.NewIntFromString("168696")
+	Aff = ff.NewElement().SetBigInt(A)
+	Dff = ff.NewElement().SetBigInt(D)
 
 	Order = utils.NewIntFromString(
 		"21888242871839275222246405745257275088614511777268538073601725287587578984328")
 	SubOrder = new(big.Int).Rsh(Order, 3)
 
 	B8 = NewPoint()
-	B8.X = ff.NewElement().SetString(
+	B8.X = utils.NewIntFromString(
 		"5299619240641551281634865583518297030282874472190772894086521144482721001553")
-	B8.Y = ff.NewElement().SetString(
+	B8.Y = utils.NewIntFromString(
 		"16950150798460657717958625567821834550301663161624707787222815936182638968203")
 }
 
-// PointBI represents a point of the babyjub curve.
+// PointProjective is the Point representation in projective coordinates
-type PointBI struct {
+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 (res *PointProjective) Add(p *PointProjective, q *PointProjective) *PointProjective {
+	// add-2008-bbjlp https://hyperelliptic.org/EFD/g1p/auto-twisted-projective.html#doubling-dbl-2008-bbjlp
+	a := ff.NewElement().Mul(p.Z, q.Z)
+	b := ff.NewElement().Square(a)
+	c := ff.NewElement().Mul(p.X, q.X)
+	d := ff.NewElement().Mul(p.Y, q.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(p.X, p.Y)
+	x2y2 := ff.NewElement().Add(q.X, q.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)
+
+	res.X = x3
+	res.Y = y3
+	res.Z = z3
+	return res
+}
+
+// Point represents a point of the babyjub curve.
+type Point struct {
 	X *big.Int
 	Y *big.Int
 }
 
-type Point struct {
+// NewPoint creates a new Point.
-	X *ff.Element
-	Y *ff.Element
-}
-
-func PointBIToPoint(p *PointBI) *Point {
-	return &Point{
-		X: ff.NewElement().SetBigInt(p.X),
-		Y: ff.NewElement().SetBigInt(p.Y),
-	}
-}
-
-func PointToPointBI(p *Point) *PointBI {
-	return &PointBI{
-		X: p.X.BigInt(),
-		Y: p.Y.BigInt(),
-	}
-}
-
-// NewPoint creates a new PointBI.
-func NewPointBI() *PointBI {
-	return &PointBI{X: big.NewInt(0), Y: big.NewInt(1)}
-}
-
 func NewPoint() *Point {
-	return &Point{X: ff.NewElement().SetZero(), Y: ff.NewElement().SetOne()}
+	return &Point{X: big.NewInt(0), Y: big.NewInt(1)}
 }
 
 // Set copies a Point c into the Point p
@@ -83,83 +132,56 @@ func (p *Point) Set(c *Point) *Point {
 	return p
 }
 
-func (p *Point) Equal(q *Point) bool {
+// Projective returns a PointProjective from the Point
-	// return p.X.Cmp(q.X) == 0 && p.Y.Cmp(q.Y) == 0
+func (p *Point) Projective() *PointProjective {
-	return p.X.Equal(q.X) && p.Y.Equal(q.Y)
+	return &PointProjective{
-}
+		X: ff.NewElement().SetBigInt(p.X),
-
+		Y: ff.NewElement().SetBigInt(p.Y),
-// Add adds Point a and b into res
+		Z: ff.NewElement().SetOne(),
-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 := ff.NewElement().Mul(a.X, b.Y)
-	x1b := ff.NewElement().Mul(b.X, a.Y)
-	x1a.Add(x1a, x1b) // x1a = a.x * b.y + b.x * a.y
-
-	x2 := ff.NewElement().Set(D)
-	x2.Mul(x2, a.X)
-	x2.Mul(x2, b.X)
-	x2.Mul(x2, a.Y)
-	x2.Mul(x2, b.Y)
-	x2.Add(ff.NewElement().SetOne(), x2)
-	x2.Inverse(x2) // 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 := ff.NewElement().Mul(a.Y, b.Y)
-	y1b := ff.NewElement().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 := ff.NewElement().Set(D)
-	y2.Mul(y2, a.X)
-	y2.Mul(y2, b.X)
-	y2.Mul(y2, a.Y)
-	y2.Mul(y2, b.Y)
-	y2.Sub(ff.NewElement().SetOne(), y2)
-	y2.Inverse(y2) // y2 = (1 - D * a.x * b.x * a.y * b.y)^-1
-
-	res.X = x1a.Mul(x1a, x2)
-
-	res.Y = y1a.Mul(y1a, y2)
-
-	return res
 }
 
 // Mul multiplies the Point p by the scalar s and stores the result in res,
 // which is also returned.
 func (res *Point) Mul(s *big.Int, p *Point) *Point {
-	res.X = ff.NewElement().SetZero()
+	resProj := &PointProjective{
-	res.Y = ff.NewElement().SetOne()
+		X: ff.NewElement().SetZero(),
-	exp := NewPoint().Set(p)
+		Y: ff.NewElement().SetOne(),
+		Z: ff.NewElement().SetOne(),
+	}
+	exp := p.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)
 	}
-
+	res = resProj.Affine()
 	return res
 }
 
 // InCurve returns true when the Point p is in the babyjub curve.
 func (p *Point) InCurve() bool {
-	x2 := ff.NewElement().Set(p.X)
+	x2 := new(big.Int).Set(p.X)
 	x2.Mul(x2, x2)
+	x2.Mod(x2, constants.Q)
 
-	y2 := ff.NewElement().Set(p.Y)
+	y2 := new(big.Int).Set(p.Y)
 	y2.Mul(y2, y2)
+	y2.Mod(y2, constants.Q)
 
-	a := ff.NewElement().Mul(A, x2)
+	a := new(big.Int).Mul(A, x2)
 	a.Add(a, y2)
+	a.Mod(a, constants.Q)
 
-	b := ff.NewElement().Set(D)
+	b := new(big.Int).Set(D)
 	b.Mul(b, x2)
 	b.Mul(b, y2)
-	b.Add(ff.NewElement().SetOne(), b)
+	b.Add(constants.One, b)
+	b.Mod(b, constants.Q)
 
-	return a.Equal(b)
+	return a.Cmp(b) == 0
 }
 
 // InSubGroup returns true when the Point p is in the subgroup of the babyjub
@@ -169,16 +191,13 @@ func (p *Point) InSubGroup() bool {
 		return false
 	}
 	res := NewPoint().Mul(SubOrder, p)
-	return res.X.Equal(ff.NewElement().SetZero()) && res.Y.Equal(ff.NewElement().SetOne())
+	return (res.X.Cmp(constants.Zero) == 0) && (res.Y.Cmp(constants.One) == 0)
 }
 
 // PointCoordSign returns the sign of the curve point coordinate.  It returns
 // false if the sign is positive and false if the sign is negative.
 func PointCoordSign(c *big.Int) bool {
-	if c.Cmp(new(big.Int).Rsh(constants.Q, 1)) == 1 {
+	return c.Cmp(new(big.Int).Rsh(constants.Q, 1)) == 1
-		return true
-	}
-	return false
 }
 
 func PackPoint(ay *big.Int, sign bool) [32]byte {
@@ -192,9 +211,8 @@ func PackPoint(ay *big.Int, sign bool) [32]byte {
 // 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 {
-	pBI := PointToPointBI(p)
+	sign := PointCoordSign(p.X)
-	sign := PointCoordSign(pBI.X)
+	return PackPoint(p.Y, sign)
-	return PackPoint(pBI.Y, sign)
 }
 
 // Decompress a compressed Point into p, and also returns the decompressed
@@ -205,37 +223,42 @@ func (p *Point) Decompress(leBuf [32]byte) (*Point, error) {
 		sign = true
 		leBuf[31] = leBuf[31] & 0x7F
 	}
-	y := big.NewInt(0)
+	utils.SetBigIntFromLEBytes(p.Y, leBuf[:])
-	utils.SetBigIntFromLEBytes(y, leBuf[:])
+	return PointFromSignAndY(sign, p.Y)
-	if y.Cmp(constants.Q) >= 0 {
+}
+
+// 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")
 	}
-	p.Y = ff.NewElement().SetBigInt(y)
 
-	y2 := ff.NewElement().Mul(p.Y, p.Y)
+	y2 := new(big.Int).Mul(p.Y, p.Y)
-	xa := ff.NewElement().SetOne()
+	y2.Mod(y2, constants.Q)
+	xa := big.NewInt(1)
 	xa.Sub(xa, y2) // xa == 1 - y^2
 
-	xb := ff.NewElement().Mul(D, y2)
+	xb := new(big.Int).Mul(D, y2)
+	xb.Mod(xb, constants.Q)
 	xb.Sub(A, xb) // xb = A - d * y^2
 
-	if xb.Equal(ff.NewElement().SetZero()) {
+	if xb.Cmp(big.NewInt(0)) == 0 {
 		return nil, fmt.Errorf("division by 0")
 	}
-	xb.Inverse(xb)
+	xb.ModInverse(xb, constants.Q)
 	p.X.Mul(xa, xb) // xa / xb
-
+	p.X.Mod(p.X, constants.Q)
-	q := PointToPointBI(p)
+	noSqrt := p.X.ModSqrt(p.X, constants.Q)
-	noSqrt := q.X.ModSqrt(q.X, constants.Q)
 	if noSqrt == nil {
 		return nil, fmt.Errorf("x is not a square mod q")
 	}
-	if (sign && !PointCoordSign(q.X)) || (!sign && PointCoordSign(q.X)) {
+	if (sign && !PointCoordSign(p.X)) || (!sign && PointCoordSign(p.X)) {
-		q.X.Mul(q.X, constants.MinusOne)
+		p.X.Mul(p.X, constants.MinusOne)
 	}
-	q.X.Mod(q.X, constants.Q)
+	p.X.Mod(p.X, constants.Q)
 
-	p = PointBIToPoint(q)
+	return &p, nil
-
-	return p, nil
 }

babyjub/babyjub_test.go

@@ -7,42 +7,34 @@ import (
 	"testing"
 
 	"github.com/iden3/go-iden3-crypto/constants"
-	"github.com/iden3/go-iden3-crypto/ff"
 	"github.com/iden3/go-iden3-crypto/utils"
 	"github.com/stretchr/testify/assert"
 )
 
-func zero() *ff.Element {
-	return ff.NewElement().SetZero()
-}
-func one() *ff.Element {
-	return ff.NewElement().SetOne()
-}
-
 func TestAdd1(t *testing.T) {
-	a := &Point{X: zero(), Y: one()}
+	a := &Point{X: big.NewInt(0), Y: big.NewInt(1)}
-	b := &Point{X: zero(), Y: one()}
+	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())
 }
 
 func TestAdd2(t *testing.T) {
-	aX := ff.NewElement().SetString(
+	aX := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	aY := ff.NewElement().SetString(
+	aY := utils.NewIntFromString(
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	a := &Point{X: aX, Y: aY}
 
-	bX := ff.NewElement().SetString(
+	bX := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	bY := ff.NewElement().SetString(
+	bY := utils.NewIntFromString(
 		"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",
@@ -50,22 +42,33 @@ 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) {
-	aX := ff.NewElement().SetString(
+	aX := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	aY := ff.NewElement().SetString(
+	aY := utils.NewIntFromString(
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	a := &Point{X: aX, Y: aY}
 
-	bX := ff.NewElement().SetString(
+	bX := utils.NewIntFromString(
 		"16540640123574156134436876038791482806971768689494387082833631921987005038935")
-	bY := ff.NewElement().SetString(
+	bY := utils.NewIntFromString(
 		"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",
@@ -76,19 +79,19 @@ func TestAdd3(t *testing.T) {
 }
 
 func TestAdd4(t *testing.T) {
-	aX := ff.NewElement().SetString(
+	aX := utils.NewIntFromString(
 		"0")
-	aY := ff.NewElement().SetString(
+	aY := utils.NewIntFromString(
 		"1")
 	a := &Point{X: aX, Y: aY}
 
-	bX := ff.NewElement().SetString(
+	bX := utils.NewIntFromString(
 		"16540640123574156134436876038791482806971768689494387082833631921987005038935")
-	bY := ff.NewElement().SetString(
+	bY := utils.NewIntFromString(
 		"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",
@@ -99,25 +102,25 @@ func TestAdd4(t *testing.T) {
 }
 
 func TestInCurve1(t *testing.T) {
-	p := &Point{X: zero(), Y: one()}
+	p := &Point{X: big.NewInt(0), Y: big.NewInt(1)}
 	assert.Equal(t, true, p.InCurve())
 }
 
 func TestInCurve2(t *testing.T) {
-	p := &Point{X: one(), Y: zero()}
+	p := &Point{X: big.NewInt(1), Y: big.NewInt(0)}
 	assert.Equal(t, false, p.InCurve())
 }
 
 func TestMul0(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	y := ff.NewElement().SetString(
+	y := utils.NewIntFromString(
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	p := &Point{X: x, Y: y}
 	s := utils.NewIntFromString("3")
 
-	r2 := NewPoint().Add(p, p)
+	r2 := NewPoint().Projective().Add(p.Projective(), p.Projective()).Affine()
-	r2 = NewPoint().Add(r2, p)
+	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())
@@ -131,9 +134,9 @@ func TestMul0(t *testing.T) {
 }
 
 func TestMul1(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	y := ff.NewElement().SetString(
+	y := utils.NewIntFromString(
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	p := &Point{X: x, Y: y}
 	s := utils.NewIntFromString(
@@ -148,9 +151,9 @@ func TestMul1(t *testing.T) {
 }
 
 func TestMul2(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"6890855772600357754907169075114257697580319025794532037257385534741338397365")
-	y := ff.NewElement().SetString(
+	y := utils.NewIntFromString(
 		"4338620300185947561074059802482547481416142213883829469920100239455078257889")
 	p := &Point{X: x, Y: y}
 	s := utils.NewIntFromString(
@@ -165,45 +168,59 @@ func TestMul2(t *testing.T) {
 }
 
 func TestInCurve3(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	y := ff.NewElement().SetString(
+	y := utils.NewIntFromString(
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	p := &Point{X: x, Y: y}
 	assert.Equal(t, true, p.InCurve())
 }
 
 func TestInCurve4(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"6890855772600357754907169075114257697580319025794532037257385534741338397365")
-	y := ff.NewElement().SetString(
+	y := utils.NewIntFromString(
 		"4338620300185947561074059802482547481416142213883829469920100239455078257889")
 	p := &Point{X: x, Y: y}
 	assert.Equal(t, true, p.InCurve())
 }
 
 func TestInSubGroup1(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	y := ff.NewElement().SetString(
+	y := utils.NewIntFromString(
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	p := &Point{X: x, Y: y}
 	assert.Equal(t, true, p.InSubGroup())
 }
 
 func TestInSubGroup2(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"6890855772600357754907169075114257697580319025794532037257385534741338397365")
-	y := ff.NewElement().SetString(
+	y := utils.NewIntFromString(
 		"4338620300185947561074059802482547481416142213883829469920100239455078257889")
 	p := &Point{X: x, Y: y}
 	assert.Equal(t, true, p.InSubGroup())
 }
 
-func TestCompressDecompress1(t *testing.T) {
+func TestPointFromSignAndy(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	y := ff.NewElement().SetString(
+	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 TestCompressDecompress1(t *testing.T) {
+	x := utils.NewIntFromString(
+		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
+	y := utils.NewIntFromString(
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	p := &Point{X: x, Y: y}
 
@@ -217,9 +234,9 @@ func TestCompressDecompress1(t *testing.T) {
 }
 
 func TestCompressDecompress2(t *testing.T) {
-	x := ff.NewElement().SetString(
+	x := utils.NewIntFromString(
 		"6890855772600357754907169075114257697580319025794532037257385534741338397365")
-	y := ff.NewElement().SetString(
+	y := utils.NewIntFromString(
 		"4338620300185947561074059802482547481416142213883829469920100239455078257889")
 	p := &Point{X: x, Y: y}
 
@@ -238,8 +255,8 @@ 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.True(t, p1.Equal(p2))
+		assert.Equal(t, p1.Y.Bytes(), p2.Y.Bytes())
 	}
 }
 
@@ -250,20 +267,22 @@ func BenchmarkBabyjub(b *testing.B) {
 
 	var badpoints [n]*Point
 	for i := 0; i < n; i++ {
-		x := ff.NewElement().SetRandom()
+		x := new(big.Int).Rand(rnd, constants.Q)
-		y := ff.NewElement().SetRandom()
+		y := new(big.Int).Rand(rnd, constants.Q)
 		badpoints[i] = &Point{X: x, Y: y}
 	}
 
 	var points [n]*Point
-	baseX := ff.NewElement().SetString(
+	var pointsProj [n]*PointProjective
+	baseX := utils.NewIntFromString(
 		"17777552123799933955779906779655732241715742912184938656739573121738514868268")
-	baseY := ff.NewElement().SetString(
+	baseY := utils.NewIntFromString(
 		"2626589144620713026669568689430873010625803728049924121243784502389097019475")
 	base := &Point{X: baseX, Y: baseY}
 	for i := 0; i < n; i++ {
 		s := new(big.Int).Rand(rnd, constants.Q)
 		points[i] = NewPoint().Mul(s, base)
+		pointsProj[i] = NewPoint().Mul(s, base).Projective()
 	}
 
 	var scalars [n]*big.Int
@@ -272,19 +291,21 @@ func BenchmarkBabyjub(b *testing.B) {
 	}
 
 	b.Run("AddConst", func(b *testing.B) {
-		p0 := &Point{X: zero(), Y: one()}
+		p0 := &Point{X: big.NewInt(0), Y: big.NewInt(1)}
-		p1 := &Point{X: zero(), Y: one()}
+		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

@@ -2,6 +2,8 @@ package babyjub
 
 import (
 	"crypto/rand"
+	"database/sql/driver"
+	"fmt"
 
 	"github.com/iden3/go-iden3-crypto/mimc7"
 	"github.com/iden3/go-iden3-crypto/poseidon"
@@ -36,6 +38,13 @@ func NewRandPrivKey() PrivateKey {
 // Scalar converts a private key into the scalar value s following the EdDSA
 // standard, and using blake-512 hash.
 func (k *PrivateKey) Scalar() *PrivKeyScalar {
+	s := SkToBigInt(k)
+	return NewPrivKeyScalar(s)
+}
+
+// SkToBigInt converts a private key into the *big.Int value following the
+// EdDSA standard, and using blake-512 hash
+func SkToBigInt(k *PrivateKey) *big.Int {
 	sBuf := Blake512(k[:])
 	sBuf32 := [32]byte{}
 	copy(sBuf32[:], sBuf[:32])
@@ -43,7 +52,7 @@ func (k *PrivateKey) Scalar() *PrivKeyScalar {
 	s := new(big.Int)
 	utils.SetBigIntFromLEBytes(s, sBuf32[:])
 	s.Rsh(s, 3)
-	return NewPrivKeyScalar(s)
+	return s
 }
 
 // Pub returns the public key corresponding to a private key.
@@ -168,6 +177,27 @@ func (s *SignatureComp) Decompress() (*Signature, error) {
 	return new(Signature).Decompress(*s)
 }
 
+// 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
 // for buffer hashing and mimc7 for big.Int hashing.
 func (k *PrivateKey) SignMimc7(msg *big.Int) *Signature {
@@ -180,7 +210,7 @@ func (k *PrivateKey) SignMimc7(msg *big.Int) *Signature {
 	r.Mod(r, SubOrder)
 	R8 := NewPoint().Mul(r, B8) // R8 = r * 8 * B
 	A := k.Public().Point()
-	hmInput := []*big.Int{R8.X.BigInt(), R8.Y.BigInt(), A.X.BigInt(), A.Y.BigInt(), msg}
+	hmInput := []*big.Int{R8.X, R8.Y, A.X, A.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)
@@ -196,7 +226,7 @@ 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.BigInt(), sig.R8.Y.BigInt(), p.X.BigInt(), p.Y.BigInt(), msg}
+	hmInput := []*big.Int{sig.R8.X, sig.R8.Y, p.X, p.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)
@@ -206,8 +236,10 @@ func (p *PublicKey) VerifyMimc7(msg *big.Int, sig *Signature) bool {
 	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
+	rightProj := right.Projective()
-	return left.X.Equal(right.X) && left.Y.Equal(right.Y)
+	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)
 }
 
 // SignPoseidon signs a message encoded as a big.Int in Zq using blake-512 hash
@@ -223,8 +255,8 @@ func (k *PrivateKey) SignPoseidon(msg *big.Int) *Signature {
 	R8 := NewPoint().Mul(r, B8) // R8 = r * 8 * B
 	A := k.Public().Point()
 
-	hmInput := [poseidon.T]*big.Int{R8.X.BigInt(), R8.Y.BigInt(), A.X.BigInt(), A.Y.BigInt(), msg, big.NewInt(int64(0))}
+	hmInput := []*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)
+	hm, err := poseidon.Hash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
 	if err != nil {
 		panic(err)
 	}
@@ -240,8 +272,8 @@ func (k *PrivateKey) SignPoseidon(msg *big.Int) *Signature {
 // VerifyPoseidon verifies the signature of a message encoded as a big.Int in Zq
 // using blake-512 hash for buffer hashing and Poseidon for big.Int hashing.
 func (p *PublicKey) VerifyPoseidon(msg *big.Int, sig *Signature) bool {
-	hmInput := [poseidon.T]*big.Int{sig.R8.X.BigInt(), sig.R8.Y.BigInt(), p.X.BigInt(), p.Y.BigInt(), msg, big.NewInt(int64(0))}
+	hmInput := []*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)
+	hm, err := poseidon.Hash(hmInput) // hm = H1(8*R.x, 8*R.y, A.x, A.y, msg)
 	if err != nil {
 		panic(err)
 	}
@@ -250,6 +282,33 @@ func (p *PublicKey) VerifyPoseidon(msg *big.Int, sig *Signature) bool {
 	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
+	rightProj := right.Projective()
-	return left.X.Equal(right.X) && left.Y.Equal(right.Y)
+	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 (p *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
+	}
+	*p = *decomp
+	return nil
+}
+
+// Value implements valuer for database/sql.
+func (p PublicKey) Value() (driver.Value, error) {
+	comp := p.Compress()
+	return comp[:], nil
 }

babyjub/eddsa_test.go

@@ -1,43 +1,34 @@
 package babyjub
 
 import (
-	"crypto/rand"
 	"encoding/hex"
 	"fmt"
 	"math/big"
 	"testing"
 
+	"database/sql"
+	"database/sql/driver"
+
 	"github.com/iden3/go-iden3-crypto/constants"
 	"github.com/iden3/go-iden3-crypto/utils"
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
 )
 
-func genInputs() (*PrivateKey, *big.Int) {
-	k := NewRandPrivKey()
-	fmt.Println("k", hex.EncodeToString(k[:]))
-
-	msgBuf := [32]byte{}
-	rand.Read(msgBuf[:])
-	msg := utils.SetBigIntFromLEBytes(new(big.Int), msgBuf[:])
-	msg.Mod(msg, constants.Q)
-	fmt.Println("msg", msg)
-
-	return &k, msg
-}
-
 func TestPublicKey(t *testing.T) {
 	var k PrivateKey
-	for i := 0; i < 256; i++ {
+	for i := 0; i < 32; i++ {
-		hex.Decode(k[:], []byte{byte(i)})
+		k[i] = byte(i)
 	}
 	pk := k.Public()
-	assert.True(t, pk.X.BigInt().Cmp(constants.Q) == -1)
+	assert.True(t, pk.X.Cmp(constants.Q) == -1)
-	assert.True(t, pk.Y.BigInt().Cmp(constants.Q) == -1)
+	assert.True(t, pk.Y.Cmp(constants.Q) == -1)
 }
 
 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 +72,8 @@ func TestSignVerifyMimc7(t *testing.T) {
 
 func TestSignVerifyPoseidon(t *testing.T) {
 	var k PrivateKey
-	hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	_, err := hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	require.Nil(t, err)
 	msgBuf, err := hex.DecodeString("00010203040506070809")
 	if err != nil {
 		panic(err)
@@ -104,7 +96,7 @@ func TestSignVerifyPoseidon(t *testing.T) {
 		"15383486972088797283337779941324724402501462225528836549661220478783371668959",
 		sig.R8.Y.String())
 	assert.Equal(t,
-		"248298168863866362217836334079793350221620631973732197668910946177382043688",
+		"1662463587877312619203503803508234533733252768380479199263194005796068211378",
 		sig.S.String())
 
 	ok := pk.VerifyPoseidon(msg, sig)
@@ -116,7 +108,7 @@ func TestSignVerifyPoseidon(t *testing.T) {
 
 	assert.Equal(t, ""+
 		"dfedb4315d3f2eb4de2d3c510d7a987dcab67089c8ace06308827bf5bcbe02a2"+
-		"28506bce274aa1b3f7e7c2fd7e4fe09bff8f9aa37a42def7994e98f322888c00",
+		"b23a1f04909fc088dec7e4835d85a326f7c0d0b2a3d0232d84448ca7c9ebac03",
 		hex.EncodeToString(sigBuf[:]))
 
 	ok = pk.VerifyPoseidon(msg, sig2)
@@ -125,7 +117,8 @@ func TestSignVerifyPoseidon(t *testing.T) {
 
 func TestCompressDecompress(t *testing.T) {
 	var k PrivateKey
-	hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	_, err := hex.Decode(k[:], []byte("0001020304050607080900010203040506070809000102030405060708090001"))
+	require.Nil(t, err)
 	pk := k.Public()
 	for i := 0; i < 64; i++ {
 		msgBuf, err := hex.DecodeString(fmt.Sprintf("000102030405060708%02d", i))
@@ -142,9 +135,37 @@ func TestCompressDecompress(t *testing.T) {
 	}
 }
 
+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.NoError(t, err)
+	assert.NoError(t, scan.Scan(fromDB))
+	assert.Equal(t, value, scan)
+}
+
+func TestPubKeyScannerValuer(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.NoError(t, err)
+	assert.NoError(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

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

ff/element.go

@@ -513,15 +513,33 @@ func (z *Element) String() string {
 
 // ToBigInt returns z as a big.Int in Montgomery form
 func (z *Element) ToBigInt(res *big.Int) *big.Int {
-	bits := (*[4]big.Word)(unsafe.Pointer(z))
+	if bits.UintSize == 64 {
-	return res.SetBits(bits[:])
+		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()
-	bits := (*[4]big.Word)(unsafe.Pointer(&z))
+	if bits.UintSize == 64 {
-	return res.SetBits(bits[:])
+		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
@@ -548,8 +566,18 @@ func (z *Element) SetBigInt(v *big.Int) *Element {
 	}
 	// v should
 	vBits := vv.Bits()
-	for i := 0; i < len(vBits); i++ {
+	if bits.UintSize == 64 {
-		z[i] = uint64(vBits[i])
+		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()
 }

ff/util.go

@@ -1,13 +1,5 @@
 package ff
 
-import "math/big"
-
 func NewElement() *Element {
 	return &Element{}
 }
-
-func (e *Element) BigInt() *big.Int {
-	b := big.NewInt(0)
-	e.ToBigIntRegular(b)
-	return b
-}

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/ethereum/go-ethereum v1.9.12
-	github.com/stretchr/testify v1.3.0
+	github.com/stretchr/testify v1.4.0
-	golang.org/x/crypto v0.0.0-20190621222207-cc06ce4a13d4
+	golang.org/x/crypto v0.0.0-20200311171314-f7b00557c8c4
+	golang.org/x/sys v0.0.0-20200323222414-85ca7c5b95cd // indirect
 )

go.sum

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

@@ -137,7 +137,7 @@ func Hash(arr []*big.Int, key *big.Int) (*big.Int, error) {
 
 // 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++ {
@@ -150,5 +150,9 @@ 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

@@ -74,8 +74,7 @@ func TestMIMC7(t *testing.T) {
 	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)
+	hmsg := HashBytes(msg)
-	assert.Nil(t, err)
 	assert.Equal(t, "16855787120419064316734350414336285711017110414939748784029922801367685456065", hmsg.String())
 }
 
@@ -87,6 +86,6 @@ func BenchmarkMIMC7(b *testing.B) {
 	bigArray4 := []*big.Int{b12, b45, b78, b41}
 
 	for i := 0; i < b.N; i++ {
-		Hash(bigArray4, nil)
+		Hash(bigArray4, nil) //nolint:errcheck
 	}
 }

poseidon/poseidon.go

@@ -2,196 +2,90 @@ package poseidon
 
 import (
 	"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
 
-var constC []*ff.Element
+var NROUNDSP = []int{56, 57, 56, 60, 60, 63, 64, 63}
-var constM [T][T]*ff.Element
 
-func Zero() *ff.Element {
+func zero() *ff.Element {
 	return ff.NewElement()
 }
 
-func modQ(v *big.Int) {
-	v.Mod(v, constants.Q)
-}
-
-func init() {
-	constC = getPseudoRandom(SEED+"_constants", NROUNDSF+NROUNDSP)
-	constM = getMDS()
-}
-
-func getPseudoRandom(seed string, n int) []*ff.Element {
-	res := make([]*ff.Element, n)
-	hash := blake2b.Sum256([]byte(seed))
-	for i := 0; i < n; i++ {
-		hashBigInt := big.NewInt(int64(0))
-		res[i] = ff.NewElement().SetBigInt(utils.SetBigIntFromLEBytes(hashBigInt, hash[:]))
-		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]*ff.Element {
-	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]*ff.Element
-	for i := 0; i < T; i++ {
-		for j := 0; j < T; j++ {
-			m[i][j] = ff.NewElement().Sub(cauchyMatrix[i], cauchyMatrix[T+j])
-			m[i][j].Inverse(m[i][j])
-		}
-	}
-	return m
-}
-
-func checkAllDifferent(v []*ff.Element) bool {
-	for i := 0; i < len(v); i++ {
-		if v[i].Equal(ff.NewElement()) {
-			return false
-		}
-		for j := i + 1; j < len(v); j++ {
-			if v[i].Equal(v[j]) {
-				return false
-			}
-		}
-	}
-	return true
-}
-
 // ark computes Add-Round Key, from the paper https://eprint.iacr.org/2019/458.pdf
-func ark(state [T]*ff.Element, c *ff.Element) {
+func ark(state []*ff.Element, c []*ff.Element, it int) {
-	for i := 0; i < T; i++ {
+	for i := 0; i < len(state); i++ {
-		state[i].Add(state[i], c)
+		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
-
+func exp5(a *ff.Element) {
-func cubic(a *ff.Element) {
 	a.Exp(*a, 5)
 }
 
 // sbox https://eprint.iacr.org/2019/458.pdf page 6
-func sbox(state [T]*ff.Element, i int) {
+func sbox(nRoundsF, nRoundsP int, state []*ff.Element, i int) {
-	if (i < NROUNDSF/2) || (i >= NROUNDSF/2+NROUNDSP) {
+	if (i < nRoundsF/2) || (i >= nRoundsF/2+nRoundsP) {
-		for j := 0; j < T; j++ {
+		for j := 0; j < len(state); j++ {
-			cubic(state[j])
+			exp5(state[j])
 		}
 	} else {
-		cubic(state[0])
+		exp5(state[0])
 	}
 }
 
 // mix returns [[matrix]] * [vector]
-func mix(state [T]*ff.Element, newState [T]*ff.Element, m [T][T]*ff.Element) {
+func mix(state []*ff.Element, newState []*ff.Element, m [][]*ff.Element) {
-	mul := Zero()
+	mul := zero()
-	for i := 0; i < T; i++ {
+	for i := 0; i < len(state); i++ {
 		newState[i].SetUint64(0)
-		for j := 0; j < T; j++ {
+		for j := 0; j < len(state); j++ {
-			mul.Mul(m[i][j], state[j])
+			mul.Mul(m[j][i], state[j])
 			newState[i].Add(newState[i], mul)
 		}
 	}
 }
 
-// PoseidonHash computes the Poseidon hash for the given inputs
+// Hash computes the Poseidon hash for the given inputs
-func PoseidonHash(inpBI [T]*big.Int) (*big.Int, error) {
+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")
 	}
 	inp := utils.BigIntArrayToElementArray(inpBI[:])
-	state := [T]*ff.Element{}
+	state := make([]*ff.Element, t)
-	for i := 0; i < T; i++ {
+	copy(state[:], inp[:])
-		state[i] = ff.NewElement().Set(inp[i])
+	state[len(state)-1] = zero()
+
+	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]*ff.Element
+	for i := 0; i < nRoundsF+nRoundsP; i++ {
-	for i := 0; i < T; i++ {
+		ark(state, c.c[t-2], i*t)
-		newState[i] = Zero()
+		sbox(nRoundsF, nRoundsP, state, i)
-	}
+		if i < nRoundsF+nRoundsP-1 {
-	for i := 0; i < NROUNDSF+NROUNDSP; i++ {
+			mix(state, newState, c.m[t-2])
-		ark(state, constC[i])
+			state, newState = newState, state
-		sbox(state, i)
+		}
-		mix(state, newState, constM)
-		state, newState = newState, state
 	}
 	rE := state[0]
 	r := big.NewInt(0)
 	rE.ToBigIntRegular(r)
 	return r, nil
 }
-
-// Hash performs the Poseidon hash over a ff.Element array
-// in chunks of 5 elements
-func Hash(arr []*big.Int) (*big.Int, error) {
-	r := big.NewInt(int64(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] = big.NewInt(0)
-		}
-
-		ph, err := PoseidonHash(toHash)
-		if err != nil {
-			return nil, err
-		}
-		modQ(r.Add(r, ph))
-	}
-
-	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 := big.NewInt(int64(0))
-		utils.SetBigIntFromLEBytes(v, b[n*i:n*(i+1)])
-		bElems = append(bElems, v)
-
-	}
-	if len(b)%n != 0 {
-		v := big.NewInt(int64(0))
-		utils.SetBigIntFromLEBytes(v, b[(len(b)/n)*n:])
-		bElems = append(bElems, v)
-	}
-	return Hash(bElems)
-}

poseidon/poseidon_test.go

@@ -15,108 +15,67 @@ func TestBlake2bVersion(t *testing.T) {
 	assert.Equal(t, "e57ba154fb2c47811dc1a2369b27e25a44915b4e4ece4eb8ec74850cb78e01b1", hex.EncodeToString(h[:]))
 }
 
-func TestPoseidon(t *testing.T) {
+func TestPoseidonHash(t *testing.T) {
+	b0 := big.NewInt(0)
 	b1 := big.NewInt(1)
 	b2 := big.NewInt(2)
-	h, err := Hash([]*big.Int{b1, b2})
+
+	h, err := Hash([]*big.Int{b1})
 	assert.Nil(t, err)
-	assert.Equal(t, "4932297968297298434239270129193057052722409868268166443802652458940273154855", h.String())
+	assert.Equal(t, "11043376183861534927536506085090418075369306574649619885724436265926427398571", h.String())
+
+	h, err = Hash([]*big.Int{b1, b2})
+	assert.Nil(t, err)
+	assert.Equal(t, "17117985411748610629288516079940078114952304104811071254131751175361957805920", h.String())
+
+	h, err = Hash([]*big.Int{b1, b2, b0, b0, b0})
+	assert.Nil(t, err)
+	assert.Equal(t, "3975478831357328722254985704342968745327876719981393787143845259590563829094", h.String())
+	h, err = Hash([]*big.Int{b1, b2, b0, b0, b0, b0})
+	assert.Nil(t, err)
+	assert.Equal(t, "19772360636270345724087386688434825760738403416279047262510528378903625000110", h.String())
 
 	b3 := big.NewInt(3)
 	b4 := big.NewInt(4)
-	h, err = Hash([]*big.Int{b3, b4})
+	h, err = Hash([]*big.Int{b3, b4, b0, b0, b0})
 	assert.Nil(t, err)
-	assert.Equal(t, "4635491972858758537477743930622086396911540895966845494943021655521913507504", h.String())
+	assert.Equal(t, "3181200837746671699652342497997860344148947482942465819251904554707352676086", h.String())
+	h, err = Hash([]*big.Int{b3, b4, b0, b0, b0, b0})
+	assert.Nil(t, err)
+	assert.Equal(t, "8386348873272147968934270337233829407378789978142456170950021426339096575008", h.String())
 
 	b5 := big.NewInt(5)
 	b6 := big.NewInt(6)
-	b7 := big.NewInt(7)
+	h, err = Hash([]*big.Int{b1, b2, b3, b4, b5, b6})
-	b8 := big.NewInt(8)
-	b9 := big.NewInt(9)
-	b10 := big.NewInt(10)
-	b11 := big.NewInt(11)
-	b12 := big.NewInt(12)
-	h, err = Hash([]*big.Int{b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12})
 	assert.Nil(t, err)
-	assert.Equal(t, "15278801138972282646981503374384603641625274360649669926363020545395022098027", h.String())
+	assert.Equal(t, "5202465217520500374834597824465244016759843635092906214933648999760272616044", 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)
-	assert.Nil(t, err)
-	assert.Equal(t, "16019700159595764790637132363672701294192939959594423814006267756172551741065", hmsg.String())
-
-	msg2 := []byte("Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet.")
-	msg2Elems := make([]*big.Int, 0, len(msg2)/n+1)
-	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)
-	assert.Nil(t, err)
-	assert.Equal(t, "2978613163687734485261639854325792381691890647104372645321246092227111432722", hmsg2.String())
-
-	hmsg2, err = HashBytes(msg2)
-	assert.Nil(t, err)
-	assert.Equal(t, "2978613163687734485261639854325792381691890647104372645321246092227111432722", hmsg2.String())
 }
 
-func TestPoseidonBrokenChunks(t *testing.T) {
+func TestErrorInputs(t *testing.T) {
-	h1, err := Hash([]*big.Int{big.NewInt(0), big.NewInt(1), big.NewInt(2), big.NewInt(3), big.NewInt(4),
+	b0 := big.NewInt(0)
-		big.NewInt(5), big.NewInt(6), big.NewInt(7), big.NewInt(8), big.NewInt(9)})
+	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)})
+	_, err = Hash([]*big.Int{b1, b2, b0, b0, b0, b0, b0})
-	assert.Nil(t, err)
+	assert.NotNil(t, err)
-	assert.NotEqual(t, h1, h2)
+	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) {
+func BenchmarkPoseidonHash(b *testing.B) {
-	h1, err := Hash([]*big.Int{big.NewInt(int64(1))})
+	b0 := big.NewInt(0)
-	assert.Nil(t, err)
+	b1 := utils.NewIntFromString("12242166908188651009877250812424843524687801523336557272219921456462821518061")
-	h2, err := Hash([]*big.Int{big.NewInt(int64(1)), big.NewInt(int64(0))})
+	b2 := utils.NewIntFromString("12242166908188651009877250812424843524687801523336557272219921456462821518061")
-	assert.Nil(t, err)
-	assert.NotEqual(t, h1, h2)
-}
 
-func BenchmarkPoseidon(b *testing.B) {
+	bigArray4 := []*big.Int{b1, b2, b0, b0, b0, b0}
-	b12 := big.NewInt(int64(12))
-	b45 := big.NewInt(int64(45))
-	b78 := big.NewInt(int64(78))
-	b41 := big.NewInt(int64(41))
-	bigArray4 := []*big.Int{b12, b45, b78, b41}
 
 	for i := 0; i < b.N; i++ {
-		Hash(bigArray4)
+		Hash(bigArray4) //nolint:errcheck
-	}
-}
-
-func BenchmarkPoseidonLarge(b *testing.B) {
-	b12 := utils.NewIntFromString("11384336176656855268977457483345535180380036354188103142384839473266348197733")
-	b45 := utils.NewIntFromString("11384336176656855268977457483345535180380036354188103142384839473266348197733")
-	b78 := utils.NewIntFromString("11384336176656855268977457483345535180380036354188103142384839473266348197733")
-	b41 := utils.NewIntFromString("11384336176656855268977457483345535180380036354188103142384839473266348197733")
-
-	bigArray4 := []*big.Int{b12, b45, b78, b41}
-
-	for i := 0; i < b.N; i++ {
-		Hash(bigArray4)
 	}
 }

utils/showarchbits_test.go

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

utils/utils.go

@@ -66,9 +66,7 @@ func HexEncode(bs []byte) string {
 
 // HexDecode decodes a hex string into an array of bytes.
 func HexDecode(h string) ([]byte, error) {
-	if strings.HasPrefix(h, "0x") {
+	h = strings.TrimPrefix(h, "0x")
-		h = h[2:]
-	}
 	return hex.DecodeString(h)
 }
 
@@ -92,10 +90,7 @@ func HexDecodeInto(dst []byte, h []byte) error {
 
 // CheckBigIntInField checks if given *big.Int fits in a Field Q element
 func CheckBigIntInField(a *big.Int) bool {
-	if a.Cmp(constants.Q) != -1 {
+	return a.Cmp(constants.Q) == -1
-		return false
-	}
-	return true
 }
 
 // CheckBigIntArrayInField checks if given *big.Int fits in a Field Q element
@@ -108,6 +103,7 @@ func CheckBigIntArrayInField(arr []*big.Int) bool {
 	return true
 }
 
+// BigIntArrayToElementArray converts an array of *big.Int into an array of *ff.Element
 func BigIntArrayToElementArray(bi []*big.Int) []*ff.Element {
 	var o []*ff.Element
 	for i := range bi {
@@ -115,3 +111,15 @@ func BigIntArrayToElementArray(bi []*big.Int) []*ff.Element {
 	}
 	return o
 }
+
+// ElementArrayToBigIntArray converts an array of *ff.Element into an array of *big.Int
+func ElementArrayToBigIntArray(e []*ff.Element) []*big.Int {
+	var o []*big.Int
+	for i := range e {
+		ei := e[i]
+		bi := big.NewInt(0)
+		ei.ToBigIntRegular(bi)
+		o = append(o, bi)
+	}
+	return o
+}