fix bbjj api: return err when hash fails while sign/verify

PID-676: support hash interface for poseidon; support golang crypto interfaces…

.github/workflows/lint.yml

@@ -1,16 +1,18 @@
 name: Lint
-on: [ push, pull_request ]
+on:
+  push:
+    branches:
+      - main
+  pull_request:
+
 jobs:
   lint:
     runs-on: ubuntu-latest
     steps:
-      - name: Install Go
-        uses: actions/setup-go@v1
+      - uses: actions/checkout@v3
+      - uses: actions/setup-go@v3
         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
+          go-version: 1.20.x
+      - uses: golangci/golangci-lint-action@v3
+        with:
+          version: v1.51.1

.github/workflows/test.yml

@@ -4,7 +4,7 @@ jobs:
   test:
     strategy:
       matrix:
-        go-version: [ 1.13.x, 1.14.x ]
+        go-version: [ 1.18.x, 1.19.x, 1.20.x ]
         goarch: [ "amd64", "386" ]
     runs-on: ubuntu-latest
     steps:

.golangci.yml

@@ -1,17 +1,77 @@
-issues:
-        max-same-issues: 0
-        exclude-use-default: false
-linters:
-        enable:
-        - whitespace
-        - gosec
-        - gci
-        - misspell
-        - gomnd
-        - gofmt
-        - goimports
-        - lll
-        - golint
+service:
+  golangci-lint-version: 1.51.x
+
+run:
+  timeout: 2m
+  skip-dirs:
+    - vendor
+
 linters-settings:
-        lll:
-                line-length: 100
+  govet:
+    check-shadowing: true
+  revive:
+    min-confidence: 0.1
+    rules:
+      - name: package-comments
+        disabled: true
+  maligned:
+    suggest-new: true
+  goconst:
+    min-len: 2
+    min-occurrences: 2
+  misspell:
+    locale: US
+  lll:
+    line-length: 140
+  gocritic:
+    enabled-tags:
+      - performance
+      - style
+      - experimental
+    disabled-checks:
+      - hugeParam
+
+linters:
+  enable:
+    - bodyclose
+    - megacheck
+    - revive
+    - govet
+    - unconvert
+    - megacheck
+    - gas
+    - gocyclo
+    - dupl
+    - misspell
+    - unparam
+    - typecheck
+    - ineffassign
+    - stylecheck
+    - exportloopref
+    - nakedret
+    - gosimple
+    - prealloc
+    - unused
+
+    ## format - fill free to fix
+#    - errcheck
+#    - gofmt
+#    - goimports
+  fast: false
+  disable-all: true
+
+issues:
+  exclude-rules:
+#    - Fix and remove
+    - text: "at least one file in a package should have a package comment"
+      linters:
+        - stylecheck
+  #    - Fix and remove
+    - text: "should have a package comment, unless it's in another file for this package"
+      linters:
+        - revive
+    - path: _test\.go
+      linters:
+        - gosec
+        - dupl
+  exclude-use-default: false

LICENSE

@@ -1,674 +0,0 @@
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LICENSE-APACHE

@@ -0,0 +1,201 @@
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+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
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+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
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+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
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+   9. Accepting Warranty or Additional Liability. While redistributing
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+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
+   APPENDIX: How to apply the Apache License to your work.
+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
+      replaced with your own identifying information. (Don't include
+      the brackets!)  The text should be enclosed in the appropriate
+      comment syntax for the file format. We also recommend that a
+      file or class name and description of purpose be included on the
+      same "printed page" as the copyright notice for easier
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+
+   Copyright 2023 0kims Association
+
+   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.

LICENSE-MIT

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright 2023 0kims Association.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

@@ -1,4 +1,25 @@
 # 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
+Go implementation of some cryptographic primitives (that fit inside the SNARK field) used in iden3:
+* BabyJubJub curve arithmetics & EdDSA on it
+* Goldilocks curve arithmetics
+* Poseidon hash for BN254
+* Poseidon hash for Goldilocks
+* MIMC7
 
+## Contributing
+
+Unless you explicitly state otherwise, any contribution intentionally submitted
+for inclusion in the work by you, as defined in the Apache-2.0 license, shall be
+dual licensed as below, without any additional terms or conditions.
+
+## License
+
+© 2023 0kims Association
+
+This project is licensed under either of
+
+- [Apache License, Version 2.0](https://www.apache.org/licenses/LICENSE-2.0) ([`LICENSE-APACHE`](LICENSE-APACHE))
+- [MIT license](https://opensource.org/licenses/MIT) ([`LICENSE-MIT`](LICENSE-MIT))
+
+at your option.

babyjub/babyjub.go

@@ -41,7 +41,7 @@ func init() {
 
 	Order = utils.NewIntFromString(
 		"21888242871839275222246405745257275088614511777268538073601725287587578984328")
-	SubOrder = new(big.Int).Rsh(Order, 3)
+	SubOrder = new(big.Int).Rsh(Order, 3) //nolint:gomnd
 
 	B8 = NewPoint()
 	B8.X = utils.NewIntFromString(
@@ -87,7 +87,7 @@ func (p *PointProjective) Affine() *Point {
 
 // Add computes the addition of two points in projective coordinates
 // representation
-func (p *PointProjective) Add(q *PointProjective, o *PointProjective) *PointProjective {
+func (p *PointProjective) Add(q, 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)
@@ -95,20 +95,20 @@ func (p *PointProjective) Add(q *PointProjective, o *PointProjective) *PointProj
 	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)
+	e.Mul(e, 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)
+	x3.Sub(x3, c)
+	x3.Sub(x3, d)
+	x3.Mul(x3, a)
+	x3.Mul(x3, f)
 	ac := ff.NewElement().Mul(Aff, c)
 	y3 := ff.NewElement().Sub(d, ac)
-	y3.MulAssign(a)
-	y3.MulAssign(g)
+	y3.Mul(y3, a)
+	y3.Mul(y3, g)
 	z3 := ff.NewElement().Mul(f, g)
 
 	p.X = x3
@@ -203,31 +203,46 @@ func PointCoordSign(c *big.Int) bool {
 	return c.Cmp(new(big.Int).Rsh(constants.Q, 1)) == 1
 }
 
-// PackPoint packs a point into a 32 byte array
-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 //nolint:gomnd
+		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] &= 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 { //nolint:gomnd
-		sign = true
-		leBuf[31] = leBuf[31] & 0x7F //nolint:gomnd
-	}
-	utils.SetBigIntFromLEBytes(p.Y, leBuf[:])
+	var sign bool
+	sign, p.Y = UnpackSignY(leBuf)
 	return PointFromSignAndY(sign, p.Y)
 }
 

babyjub/babyjub_test.go

@@ -218,6 +218,26 @@ func TestPointFromSignAndy(t *testing.T) {
 	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")

babyjub/babyjub_wrapper.go

@@ -0,0 +1,84 @@
+package babyjub
+
+import (
+	"bytes"
+	"crypto"
+	"io"
+	"math/big"
+)
+
+// BjjWrappedPublicKey is a wrapper for PublicKey.
+type BjjWrappedPublicKey struct {
+	pubKey *PublicKey
+}
+
+// Equal returns true if the public keys are equal.
+func (pub *BjjWrappedPublicKey) Equal(x crypto.PublicKey) bool {
+	var xk *BjjWrappedPublicKey
+	switch x := x.(type) {
+	case BjjWrappedPublicKey:
+		xk = &x
+	case *BjjWrappedPublicKey:
+		xk = x
+	default:
+		return false
+	}
+	return pub.pubKey.X.Cmp(xk.pubKey.X) == 0 &&
+		pub.pubKey.Y.Cmp(xk.pubKey.Y) == 0
+}
+
+// BjjWrappedPrivateKey is a wrapper for PrivateKey.
+type BjjWrappedPrivateKey struct {
+	privKey *PrivateKey
+}
+
+// NewBjjWrappedKey creates a new BjjWrappedPrivateKey.
+func NewBjjWrappedKey(privKey *PrivateKey) *BjjWrappedPrivateKey {
+	return &BjjWrappedPrivateKey{privKey}
+}
+
+// RandomBjjWrappedKey creates a new BjjWrappedPrivateKey with a random private key.
+func RandomBjjWrappedKey() *BjjWrappedPrivateKey {
+	privKey := NewRandPrivKey()
+	return NewBjjWrappedKey(&privKey)
+}
+
+// Public returns the public key of the private key.
+func (w *BjjWrappedPrivateKey) Public() crypto.PublicKey {
+	return &BjjWrappedPublicKey{w.privKey.Public()}
+}
+
+// Sign signs the digest with the private key.
+func (w *BjjWrappedPrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) {
+	hash := opts.HashFunc()
+
+	switch hash {
+	// alredy hashed
+	case crypto.Hash(0):
+	default:
+		hasher := hash.New()
+		hasher.Write(digest)
+		digest = hasher.Sum(nil)
+	}
+
+	digestBI := big.NewInt(0).SetBytes(digest)
+	sig, err := w.privKey.SignPoseidon(digestBI)
+	if err != nil {
+		return nil, err
+	}
+	return sig.Compress().MarshalText()
+}
+
+// Equal returns true if the private keys are equal.
+func (w *BjjWrappedPrivateKey) Equal(x crypto.PrivateKey) bool {
+	var xk *BjjWrappedPrivateKey
+	switch x := x.(type) {
+	case BjjWrappedPrivateKey:
+		xk = &x
+	case *BjjWrappedPrivateKey:
+		xk = x
+	default:
+		return false
+	}
+	return bytes.Equal(w.privKey[:], xk.privKey[:])
+}

babyjub/babyjub_wrapper_test.go

@@ -0,0 +1,65 @@
+package babyjub
+
+import (
+	"crypto"
+	"crypto/rand"
+	"math/big"
+	"testing"
+
+	"github.com/iden3/go-iden3-crypto/poseidon"
+	"github.com/stretchr/testify/require"
+)
+
+// https://pkg.go.dev/crypto#PrivateKey
+type shadowPrivateKey interface {
+	Public() crypto.PublicKey
+	Equal(x crypto.PrivateKey) bool
+}
+
+// https://pkg.go.dev/crypto#PublicKey
+type shadowPublicKey interface {
+	Equal(x crypto.PublicKey) bool
+}
+
+func TestBjjWrappedPrivateKeyInterfaceImpl(t *testing.T) {
+	require.Implements(t, (*crypto.Signer)(nil), new(BjjWrappedPrivateKey))
+	require.Implements(t, (*shadowPrivateKey)(nil), new(BjjWrappedPrivateKey))
+}
+
+func TestBjjWrappedPrivateKey(t *testing.T) {
+	pk := RandomBjjWrappedKey()
+
+	hasher, err := poseidon.New(16)
+	require.NoError(t, err)
+	hasher.Write([]byte("test"))
+	digest := hasher.Sum(nil)
+
+	sig, err := pk.Sign(rand.Reader, digest, crypto.Hash(0))
+	require.NoError(t, err)
+	pub, ok := pk.Public().(*BjjWrappedPublicKey)
+	require.True(t, ok)
+
+	decomrpessSig, err := DecompressSig(sig)
+	require.NoError(t, err)
+
+	digestBI := big.NewInt(0).SetBytes(digest)
+	pub.pubKey.VerifyPoseidon(digestBI, decomrpessSig)
+}
+
+func TestBjjWrappedPrivateKeyEqual(t *testing.T) {
+	x1 := RandomBjjWrappedKey()
+	require.True(t, x1.Equal(x1))
+	x2 := RandomBjjWrappedKey()
+	require.False(t, x1.Equal(x2))
+}
+
+func TestBjjWrappedPublicKeyInterfaceImpl(t *testing.T) {
+	require.Implements(t, (*shadowPublicKey)(nil), new(BjjWrappedPublicKey))
+}
+
+func TestBjjWrappedPublicKeyEqual(t *testing.T) {
+	x1 := RandomBjjWrappedKey().Public().(*BjjWrappedPublicKey)
+	require.True(t, x1.Equal(x1))
+	x2 := RandomBjjWrappedKey().Public()
+	require.False(t, x1.Equal(x2))
+}

babyjub/eddsa.go

@@ -1,4 +1,5 @@
 // Package babyjub eddsa implements the EdDSA over the BabyJubJub curve
+//
 //nolint:gomnd
 package babyjub
 
@@ -16,9 +17,9 @@ import (
 // pruneBuffer prunes the buffer during key generation according to RFC 8032.
 // https://tools.ietf.org/html/rfc8032#page-13
 func pruneBuffer(buf *[32]byte) *[32]byte {
-	buf[0] = buf[0] & 0xF8
-	buf[31] = buf[31] & 0x7F
-	buf[31] = buf[31] | 0x40
+	buf[0] &= 0xF8
+	buf[31] &= 0x7F
+	buf[31] |= 0x40
 	return buf
 }
 
@@ -210,7 +211,7 @@ func (sComp *SignatureComp) Scan(src interface{}) error {
 	if len(srcB) != 64 {
 		return fmt.Errorf("can't scan []byte of len %d into Signature, want %d", len(srcB), 64)
 	}
-	copy(sComp[:], srcB[:])
+	copy(sComp[:], srcB)
 	return nil
 }
 
@@ -229,7 +230,7 @@ func (s *Signature) Scan(src interface{}) error {
 		return fmt.Errorf("can't scan []byte of len %d into Signature, want %d", len(srcB), 64)
 	}
 	buf := [64]byte{}
-	copy(buf[:], srcB[:])
+	copy(buf[:], srcB)
 	_, err := s.Decompress(buf)
 	return err
 }
@@ -242,7 +243,7 @@ func (s Signature) Value() (driver.Value, error) {
 
 // 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 {
+func (k *PrivateKey) SignMimc7(msg *big.Int) (*Signature, error) {
 	h1 := Blake512(k[:])
 	msgBuf := utils.BigIntLEBytes(msg)
 	msgBuf32 := [32]byte{}
@@ -255,23 +256,23 @@ func (k *PrivateKey) SignMimc7(msg *big.Int) *Signature {
 	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)
+		return nil, err
 	}
 	S := new(big.Int).Lsh(k.Scalar().BigInt(), 3)
 	S = S.Mul(hm, S)
 	S.Add(r, S)
 	S.Mod(S, SubOrder) // S = r + hm * 8 * s
 
-	return &Signature{R8: R8, S: S}
+	return &Signature{R8: R8, S: S}, nil
 }
 
 // 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 (pk *PublicKey) VerifyMimc7(msg *big.Int, sig *Signature) bool {
+func (pk *PublicKey) VerifyMimc7(msg *big.Int, sig *Signature) error {
 	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 {
-		return false
+		return err
 	}
 
 	left := NewPoint().Mul(sig.S, B8) // left = s * 8 * B
@@ -281,12 +282,15 @@ func (pk *PublicKey) VerifyMimc7(msg *big.Int, sig *Signature) bool {
 	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)
+	if (left.X.Cmp(right.X) == 0) && (left.Y.Cmp(right.Y) == 0) {
+		return nil
+	}
+	return fmt.Errorf("verifyMimc7 failed")
 }
 
 // SignPoseidon signs a message encoded as a big.Int in Zq using blake-512 hash
 // for buffer hashing and Poseidon for big.Int hashing.
-func (k *PrivateKey) SignPoseidon(msg *big.Int) *Signature {
+func (k *PrivateKey) SignPoseidon(msg *big.Int) (*Signature, error) {
 	h1 := Blake512(k[:])
 	msgBuf := utils.BigIntLEBytes(msg)
 	msgBuf32 := [32]byte{}
@@ -300,7 +304,7 @@ func (k *PrivateKey) SignPoseidon(msg *big.Int) *Signature {
 	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)
+		return nil, err
 	}
 
 	S := new(big.Int).Lsh(k.Scalar().BigInt(), 3)
@@ -308,16 +312,16 @@ func (k *PrivateKey) SignPoseidon(msg *big.Int) *Signature {
 	S.Add(r, S)
 	S.Mod(S, SubOrder) // S = r + hm * 8 * s
 
-	return &Signature{R8: R8, S: S}
+	return &Signature{R8: R8, S: S}, nil
 }
 
 // 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 (pk *PublicKey) VerifyPoseidon(msg *big.Int, sig *Signature) bool {
+func (pk *PublicKey) VerifyPoseidon(msg *big.Int, sig *Signature) error {
 	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 {
-		return false
+		return err
 	}
 
 	left := NewPoint().Mul(sig.S, B8) // left = s * 8 * B
@@ -327,7 +331,10 @@ func (pk *PublicKey) VerifyPoseidon(msg *big.Int, sig *Signature) bool {
 	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)
+	if (left.X.Cmp(right.X) == 0) && (left.Y.Cmp(right.Y) == 0) {
+		return nil
+	}
+	return fmt.Errorf("verifyPoseidon failed")
 }
 
 // Scan implements Scanner for database/sql.

babyjub/eddsa_test.go

@@ -43,7 +43,8 @@ func TestSignVerifyMimc7(t *testing.T) {
 		"13622229784656158136036771217484571176836296686641868549125388198837476602820",
 		pk.Y.String())
 
-	sig := k.SignMimc7(msg)
+	sig, err := k.SignMimc7(msg)
+	assert.NoError(t, err)
 	assert.Equal(t,
 		"11384336176656855268977457483345535180380036354188103142384839473266348197733",
 		sig.R8.X.String())
@@ -54,20 +55,20 @@ func TestSignVerifyMimc7(t *testing.T) {
 		"2523202440825208709475937830811065542425109372212752003460238913256192595070",
 		sig.S.String())
 
-	ok := pk.VerifyMimc7(msg, sig)
-	assert.Equal(t, true, ok)
+	err = pk.VerifyMimc7(msg, sig)
+	assert.NoError(t, err)
 
 	sigBuf := sig.Compress()
 	sig2, err := new(Signature).Decompress(sigBuf)
-	assert.Equal(t, nil, err)
+	assert.NoError(t, err)
 
 	assert.Equal(t, ""+
 		"dfedb4315d3f2eb4de2d3c510d7a987dcab67089c8ace06308827bf5bcbe02a2"+
 		"7ed40dab29bf993c928e789d007387998901a24913d44fddb64b1f21fc149405",
 		hex.EncodeToString(sigBuf[:]))
 
-	ok = pk.VerifyMimc7(msg, sig2)
-	assert.Equal(t, true, ok)
+	err = pk.VerifyMimc7(msg, sig2)
+	assert.NoError(t, err)
 }
 
 func TestSignVerifyPoseidon(t *testing.T) {
@@ -89,7 +90,8 @@ func TestSignVerifyPoseidon(t *testing.T) {
 		"13622229784656158136036771217484571176836296686641868549125388198837476602820",
 		pk.Y.String())
 
-	sig := k.SignPoseidon(msg)
+	sig, err := k.SignPoseidon(msg)
+	assert.NoError(t, err)
 	assert.Equal(t,
 		"11384336176656855268977457483345535180380036354188103142384839473266348197733",
 		sig.R8.X.String())
@@ -97,23 +99,23 @@ func TestSignVerifyPoseidon(t *testing.T) {
 		"15383486972088797283337779941324724402501462225528836549661220478783371668959",
 		sig.R8.Y.String())
 	assert.Equal(t,
-		"1398758333392199195742243841591064350253744445503462896781493968760929513778",
+		"1672775540645840396591609181675628451599263765380031905495115170613215233181",
 		sig.S.String())
 
-	ok := pk.VerifyPoseidon(msg, sig)
-	assert.Equal(t, true, ok)
+	err = pk.VerifyPoseidon(msg, sig)
+	assert.NoError(t, err)
 
 	sigBuf := sig.Compress()
 	sig2, err := new(Signature).Decompress(sigBuf)
-	assert.Equal(t, nil, err)
+	assert.NoError(t, err)
 
 	assert.Equal(t, ""+
 		"dfedb4315d3f2eb4de2d3c510d7a987dcab67089c8ace06308827bf5bcbe02a2"+
-		"32f16b0f2f4c4e1169aa59685637e1429b6581a9531d058d65f4ab224eab1703",
+		"9d043ece562a8f82bfc0adb640c0107a7d3a27c1c7c1a6179a0da73de5c1b203",
 		hex.EncodeToString(sigBuf[:]))
 
-	ok = pk.VerifyPoseidon(msg, sig2)
-	assert.Equal(t, true, ok)
+	err = pk.VerifyPoseidon(msg, sig2)
+	assert.NoError(t, err)
 }
 
 func TestCompressDecompress(t *testing.T) {
@@ -128,22 +130,28 @@ func TestCompressDecompress(t *testing.T) {
 			panic(err)
 		}
 		msg := utils.SetBigIntFromLEBytes(new(big.Int), msgBuf)
-		sig := k.SignMimc7(msg)
+		sig, err := k.SignMimc7(msg)
+		assert.NoError(t, err)
 		sigBuf := sig.Compress()
 		sig2, err := new(Signature).Decompress(sigBuf)
-		assert.Equal(t, nil, err)
-		ok := pk.VerifyMimc7(msg, sig2)
-		assert.Equal(t, true, ok)
+		assert.NoError(t, err)
+		err = pk.VerifyMimc7(msg, sig2)
+		assert.NoError(t, err)
 	}
 }
 
 func TestSignatureCompScannerValuer(t *testing.T) {
 	privK := NewRandPrivKey()
-	var value driver.Valuer //nolint:gosimple this is done to ensure interface compability
-	value = privK.SignPoseidon(big.NewInt(674238462)).Compress()
-	scan := privK.SignPoseidon(big.NewInt(1)).Compress()
+	var err error
+	sig, err := privK.SignPoseidon(big.NewInt(674238462))
+	assert.NoError(t, err)
+	var value driver.Valuer //nolint:gosimple // this is done to ensure interface compatibility
+	value = sig.Compress()
+	sig, err = privK.SignPoseidon(big.NewInt(1))
+	assert.NoError(t, err)
+	scan := sig.Compress()
 	fromDB, err := value.Value()
-	assert.Nil(t, err)
+	assert.NoError(t, err)
 	assert.Nil(t, scan.Scan(fromDB))
 	assert.Equal(t, value, scan)
 }
@@ -152,10 +160,13 @@ 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))
+	var err error
+	value, err = privK.SignPoseidon(big.NewInt(674238462))
+	assert.NoError(t, err)
+	scan, err = privK.SignPoseidon(big.NewInt(1))
+	assert.NoError(t, err)
 	fromDB, err := value.Value()
-	assert.Nil(t, err)
+	assert.NoError(t, err)
 	assert.Nil(t, scan.Scan(fromDB))
 	assert.Equal(t, value, scan)
 }
@@ -217,12 +228,12 @@ func BenchmarkBabyjubEddsa(b *testing.B) {
 	})
 
 	for i := 0; i < n; i++ {
-		sigs[i%n] = k.SignMimc7(msgs[i%n])
+		sigs[i%n], _ = k.SignMimc7(msgs[i%n])
 	}
 
 	b.Run("VerifyMimc7", func(b *testing.B) {
 		for i := 0; i < b.N; i++ {
-			pk.VerifyMimc7(msgs[i%n], sigs[i%n])
+			_ = pk.VerifyMimc7(msgs[i%n], sigs[i%n])
 		}
 	})
 
@@ -233,12 +244,12 @@ func BenchmarkBabyjubEddsa(b *testing.B) {
 	})
 
 	for i := 0; i < n; i++ {
-		sigs[i%n] = k.SignPoseidon(msgs[i%n])
+		sigs[i%n], _ = k.SignPoseidon(msgs[i%n])
 	}
 
 	b.Run("VerifyPoseidon", func(b *testing.B) {
 		for i := 0; i < b.N; i++ {
-			pk.VerifyPoseidon(msgs[i%n], sigs[i%n])
+			_ = pk.VerifyPoseidon(msgs[i%n], sigs[i%n])
 		}
 	})
 }

babyjub/helpers.go

@@ -12,9 +12,22 @@ import (
 // the original blake from the SHA3 competition and not the new blake2 version.
 func Blake512(m []byte) []byte {
 	h := blake512.New()
-	_, err := h.Write(m[:])
+	_, err := h.Write(m)
 	if err != nil {
 		panic(err)
 	}
 	return h.Sum(nil)
 }
+
+// DecompressSig decompresses a compressed signature.
+func DecompressSig(commpresedSig []byte) (*Signature, error) {
+	poseidonComSig := &SignatureComp{}
+	if err := poseidonComSig.UnmarshalText(commpresedSig); err != nil {
+		return nil, err
+	}
+	poseidonDecSig, err := poseidonComSig.Decompress()
+	if err != nil {
+		return nil, err
+	}
+	return poseidonDecSig, nil
+}

constants/constants.go

@@ -1,31 +1,19 @@
 package constants
 
 import (
-	"fmt"
 	"math/big"
 )
 
+const qString = "21888242871839275222246405745257275088548364400416034343698204186575808495617"
+
 // Q is the order of the integer field (Zq) that fits inside the SNARK.
-var Q *big.Int
+var Q, _ = new(big.Int).SetString(qString, 10)
 
 // Zero is 0.
-var Zero *big.Int
+var Zero = big.NewInt(0)
 
 // One is 1.
-var One *big.Int
+var One = big.NewInt(1)
 
 // MinusOne is -1.
-var MinusOne *big.Int
-
-func init() {
-	Zero = big.NewInt(0)
-	One = big.NewInt(1)
-	MinusOne = big.NewInt(-1)
-
-	qString := "21888242871839275222246405745257275088548364400416034343698204186575808495617"
-	var ok bool
-	Q, ok = new(big.Int).SetString(qString, 10)
-	if !ok {
-		panic(fmt.Sprintf("Bad base 10 string %s", qString))
-	}
-}
+var MinusOne = big.NewInt(-1)

ff/arith.go

@@ -1,4 +1,4 @@
-// Copyright 2020 ConsenSys AG
+// Copyright 2020 ConsenSys Software Inc.
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
@@ -12,7 +12,7 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// Code generated by goff DO NOT EDIT
+// Code generated by consensys/gnark-crypto DO NOT EDIT
 
 package ff
 
@@ -20,15 +20,6 @@ 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
@@ -58,59 +49,6 @@ func madd2(a, b, c, d uint64) (hi uint64, lo uint64) {
 	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)

ff/asm.go

@@ -0,0 +1,24 @@
+//go:build !noadx
+// +build !noadx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ff
+
+import "golang.org/x/sys/cpu"
+
+var supportAdx = cpu.X86.HasADX && cpu.X86.HasBMI2

ff/asm_noadx.go

@@ -0,0 +1,25 @@
+//go:build noadx
+// +build noadx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ff
+
+// note: this is needed for test purposes, as dynamically changing supportAdx doesn't flag
+// certain errors (like fatal error: missing stackmap)
+// this ensures we test all asm path.
+var supportAdx = false

ff/doc.go

@@ -0,0 +1,43 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+// Package ff contains field arithmetic operations for modulus = 0x30644e...000001.
+//
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@zkteam/modular_multiplication)
+//
+// The modulus is hardcoded in all the operations.
+//
+// Field elements are represented as an array, and assumed to be in Montgomery form in all methods:
+// 	type Element [4]uint64
+//
+// Example API signature
+// 	// Mul z = x * y mod q
+// 	func (z *Element) Mul(x, y *Element) *Element
+//
+// and can be used like so:
+// 	var a, b Element
+// 	a.SetUint64(2)
+// 	b.SetString("984896738")
+// 	a.Mul(a, b)
+// 	a.Sub(a, a)
+// 	 .Add(a, b)
+// 	 .Inv(a)
+// 	b.Exp(b, new(big.Int).SetUint64(42))
+//
+// Modulus
+// 	0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001 // base 16
+// 	21888242871839275222246405745257275088548364400416034343698204186575808495617 // base 10
+package ff

ff/element_fuzz.go

@@ -0,0 +1,136 @@
+//go:build gofuzz
+// +build gofuzz
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ff
+
+import (
+	"bytes"
+	"encoding/binary"
+	"io"
+	"math/big"
+	"math/bits"
+)
+
+const (
+	fuzzInteresting = 1
+	fuzzNormal      = 0
+	fuzzDiscard     = -1
+)
+
+// Fuzz arithmetic operations fuzzer
+func Fuzz(data []byte) int {
+	r := bytes.NewReader(data)
+
+	var e1, e2 Element
+	e1.SetRawBytes(r)
+	e2.SetRawBytes(r)
+
+	{
+		// mul assembly
+
+		var c, _c Element
+		a, _a, b, _b := e1, e1, e2, e2
+		c.Mul(&a, &b)
+		_mulGeneric(&_c, &_a, &_b)
+
+		if !c.Equal(&_c) {
+			panic("mul asm != mul generic on Element")
+		}
+	}
+
+	{
+		// inverse
+		inv := e1
+		inv.Inverse(&inv)
+
+		var bInv, b1, b2 big.Int
+		e1.ToBigIntRegular(&b1)
+		bInv.ModInverse(&b1, Modulus())
+		inv.ToBigIntRegular(&b2)
+
+		if b2.Cmp(&bInv) != 0 {
+			panic("inverse operation doesn't match big int result")
+		}
+	}
+
+	{
+		// a + -a == 0
+		a, b := e1, e1
+		b.Neg(&b)
+		a.Add(&a, &b)
+		if !a.IsZero() {
+			panic("a + -a != 0")
+		}
+	}
+
+	return fuzzNormal
+
+}
+
+// SetRawBytes reads up to Bytes (bytes needed to represent Element) from reader
+// and interpret it as big endian uint64
+// used for fuzzing purposes only
+func (z *Element) SetRawBytes(r io.Reader) {
+
+	buf := make([]byte, 8)
+
+	for i := 0; i < len(z); i++ {
+		if _, err := io.ReadFull(r, buf); err != nil {
+			goto eof
+		}
+		z[i] = binary.BigEndian.Uint64(buf[:])
+	}
+eof:
+	z[3] %= qElement[3]
+
+	if z.BiggerModulus() {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], qElement[0], 0)
+		z[1], b = bits.Sub64(z[1], qElement[1], b)
+		z[2], b = bits.Sub64(z[2], qElement[2], b)
+		z[3], b = bits.Sub64(z[3], qElement[3], b)
+	}
+
+	return
+}
+
+func (z *Element) BiggerModulus() bool {
+	if z[3] > qElement[3] {
+		return true
+	}
+	if z[3] < qElement[3] {
+		return false
+	}
+
+	if z[2] > qElement[2] {
+		return true
+	}
+	if z[2] < qElement[2] {
+		return false
+	}
+
+	if z[1] > qElement[1] {
+		return true
+	}
+	if z[1] < qElement[1] {
+		return false
+	}
+
+	return z[0] >= qElement[0]
+}

ff/element_mul_adx_amd64.s

@@ -0,0 +1,466 @@
+// +build amd64_adx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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.
+
+#include "textflag.h"
+#include "funcdata.h"
+
+// modulus q
+DATA q<>+0(SB)/8, $0x43e1f593f0000001
+DATA q<>+8(SB)/8, $0x2833e84879b97091
+DATA q<>+16(SB)/8, $0xb85045b68181585d
+DATA q<>+24(SB)/8, $0x30644e72e131a029
+GLOBL q<>(SB), (RODATA+NOPTR), $32
+
+// qInv0 q'[0]
+DATA qInv0<>(SB)/8, $0xc2e1f593efffffff
+GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
+
+#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
+	MOVQ    ra0, rb0;        \
+	SUBQ    q<>(SB), ra0;    \
+	MOVQ    ra1, rb1;        \
+	SBBQ    q<>+8(SB), ra1;  \
+	MOVQ    ra2, rb2;        \
+	SBBQ    q<>+16(SB), ra2; \
+	MOVQ    ra3, rb3;        \
+	SBBQ    q<>+24(SB), ra3; \
+	CMOVQCS rb0, ra0;        \
+	CMOVQCS rb1, ra1;        \
+	CMOVQCS rb2, ra2;        \
+	CMOVQCS rb3, ra3;        \
+
+// mul(res, x, y *Element)
+TEXT ·mul(SB), NOSPLIT, $0-24
+
+	// the algorithm is described here
+	// https://hackmd.io/@zkteam/modular_multiplication
+	// however, to benefit from the ADCX and ADOX carry chains
+	// we split the inner loops in 2:
+	// for i=0 to N-1
+	// 		for j=0 to N-1
+	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C + A
+
+	MOVQ x+8(FP), SI
+
+	// x[0] -> DI
+	// x[1] -> R8
+	// x[2] -> R9
+	// x[3] -> R10
+	MOVQ 0(SI), DI
+	MOVQ 8(SI), R8
+	MOVQ 16(SI), R9
+	MOVQ 24(SI), R10
+	MOVQ y+16(FP), R11
+
+	// A -> BP
+	// t[0] -> R14
+	// t[1] -> R15
+	// t[2] -> CX
+	// t[3] -> BX
+	// clear the flags
+	XORQ AX, AX
+	MOVQ 0(R11), DX
+
+	// (A,t[0])  := x[0]*y[0] + A
+	MULXQ DI, R14, R15
+
+	// (A,t[1])  := x[1]*y[0] + A
+	MULXQ R8, AX, CX
+	ADOXQ AX, R15
+
+	// (A,t[2])  := x[2]*y[0] + A
+	MULXQ R9, AX, BX
+	ADOXQ AX, CX
+
+	// (A,t[3])  := x[3]*y[0] + A
+	MULXQ R10, AX, BP
+	ADOXQ AX, BX
+
+	// A += carries from ADCXQ and ADOXQ
+	MOVQ  $0, AX
+	ADOXQ AX, BP
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+
+	// clear the flags
+	XORQ AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, R12
+	ADCXQ R14, AX
+	MOVQ  R12, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// t[3] = C + A
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ BP, BX
+
+	// clear the flags
+	XORQ AX, AX
+	MOVQ 8(R11), DX
+
+	// (A,t[0])  := t[0] + x[0]*y[1] + A
+	MULXQ DI, AX, BP
+	ADOXQ AX, R14
+
+	// (A,t[1])  := t[1] + x[1]*y[1] + A
+	ADCXQ BP, R15
+	MULXQ R8, AX, BP
+	ADOXQ AX, R15
+
+	// (A,t[2])  := t[2] + x[2]*y[1] + A
+	ADCXQ BP, CX
+	MULXQ R9, AX, BP
+	ADOXQ AX, CX
+
+	// (A,t[3])  := t[3] + x[3]*y[1] + A
+	ADCXQ BP, BX
+	MULXQ R10, AX, BP
+	ADOXQ AX, BX
+
+	// A += carries from ADCXQ and ADOXQ
+	MOVQ  $0, AX
+	ADCXQ AX, BP
+	ADOXQ AX, BP
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+
+	// clear the flags
+	XORQ AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, R12
+	ADCXQ R14, AX
+	MOVQ  R12, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// t[3] = C + A
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ BP, BX
+
+	// clear the flags
+	XORQ AX, AX
+	MOVQ 16(R11), DX
+
+	// (A,t[0])  := t[0] + x[0]*y[2] + A
+	MULXQ DI, AX, BP
+	ADOXQ AX, R14
+
+	// (A,t[1])  := t[1] + x[1]*y[2] + A
+	ADCXQ BP, R15
+	MULXQ R8, AX, BP
+	ADOXQ AX, R15
+
+	// (A,t[2])  := t[2] + x[2]*y[2] + A
+	ADCXQ BP, CX
+	MULXQ R9, AX, BP
+	ADOXQ AX, CX
+
+	// (A,t[3])  := t[3] + x[3]*y[2] + A
+	ADCXQ BP, BX
+	MULXQ R10, AX, BP
+	ADOXQ AX, BX
+
+	// A += carries from ADCXQ and ADOXQ
+	MOVQ  $0, AX
+	ADCXQ AX, BP
+	ADOXQ AX, BP
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+
+	// clear the flags
+	XORQ AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, R12
+	ADCXQ R14, AX
+	MOVQ  R12, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// t[3] = C + A
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ BP, BX
+
+	// clear the flags
+	XORQ AX, AX
+	MOVQ 24(R11), DX
+
+	// (A,t[0])  := t[0] + x[0]*y[3] + A
+	MULXQ DI, AX, BP
+	ADOXQ AX, R14
+
+	// (A,t[1])  := t[1] + x[1]*y[3] + A
+	ADCXQ BP, R15
+	MULXQ R8, AX, BP
+	ADOXQ AX, R15
+
+	// (A,t[2])  := t[2] + x[2]*y[3] + A
+	ADCXQ BP, CX
+	MULXQ R9, AX, BP
+	ADOXQ AX, CX
+
+	// (A,t[3])  := t[3] + x[3]*y[3] + A
+	ADCXQ BP, BX
+	MULXQ R10, AX, BP
+	ADOXQ AX, BX
+
+	// A += carries from ADCXQ and ADOXQ
+	MOVQ  $0, AX
+	ADCXQ AX, BP
+	ADOXQ AX, BP
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+
+	// clear the flags
+	XORQ AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, R12
+	ADCXQ R14, AX
+	MOVQ  R12, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// t[3] = C + A
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ BP, BX
+
+	// reduce element(R14,R15,CX,BX) using temp registers (R13,SI,R12,R11)
+	REDUCE(R14,R15,CX,BX,R13,SI,R12,R11)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	RET
+
+TEXT ·fromMont(SB), NOSPLIT, $0-8
+
+	// the algorithm is described here
+	// https://hackmd.io/@zkteam/modular_multiplication
+	// when y = 1 we have:
+	// for i=0 to N-1
+	// 		t[i] = x[i]
+	// for i=0 to N-1
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C
+	MOVQ res+0(FP), DX
+	MOVQ 0(DX), R14
+	MOVQ 8(DX), R15
+	MOVQ 16(DX), CX
+	MOVQ 24(DX), BX
+	XORQ DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+
+	// reduce element(R14,R15,CX,BX) using temp registers (SI,DI,R8,R9)
+	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	RET

ff/element_mul_amd64.s

@@ -0,0 +1,488 @@
+// +build !amd64_adx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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.
+
+#include "textflag.h"
+#include "funcdata.h"
+
+// modulus q
+DATA q<>+0(SB)/8, $0x43e1f593f0000001
+DATA q<>+8(SB)/8, $0x2833e84879b97091
+DATA q<>+16(SB)/8, $0xb85045b68181585d
+DATA q<>+24(SB)/8, $0x30644e72e131a029
+GLOBL q<>(SB), (RODATA+NOPTR), $32
+
+// qInv0 q'[0]
+DATA qInv0<>(SB)/8, $0xc2e1f593efffffff
+GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
+
+#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
+	MOVQ    ra0, rb0;        \
+	SUBQ    q<>(SB), ra0;    \
+	MOVQ    ra1, rb1;        \
+	SBBQ    q<>+8(SB), ra1;  \
+	MOVQ    ra2, rb2;        \
+	SBBQ    q<>+16(SB), ra2; \
+	MOVQ    ra3, rb3;        \
+	SBBQ    q<>+24(SB), ra3; \
+	CMOVQCS rb0, ra0;        \
+	CMOVQCS rb1, ra1;        \
+	CMOVQCS rb2, ra2;        \
+	CMOVQCS rb3, ra3;        \
+
+// mul(res, x, y *Element)
+TEXT ·mul(SB), $24-24
+
+	// the algorithm is described here
+	// https://hackmd.io/@zkteam/modular_multiplication
+	// however, to benefit from the ADCX and ADOX carry chains
+	// we split the inner loops in 2:
+	// for i=0 to N-1
+	// 		for j=0 to N-1
+	// 		    (A,t[j])  := t[j] + x[j]*y[i] + A
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C + A
+
+	NO_LOCAL_POINTERS
+	CMPB ·supportAdx(SB), $1
+	JNE  l1
+	MOVQ x+8(FP), SI
+
+	// x[0] -> DI
+	// x[1] -> R8
+	// x[2] -> R9
+	// x[3] -> R10
+	MOVQ 0(SI), DI
+	MOVQ 8(SI), R8
+	MOVQ 16(SI), R9
+	MOVQ 24(SI), R10
+	MOVQ y+16(FP), R11
+
+	// A -> BP
+	// t[0] -> R14
+	// t[1] -> R15
+	// t[2] -> CX
+	// t[3] -> BX
+	// clear the flags
+	XORQ AX, AX
+	MOVQ 0(R11), DX
+
+	// (A,t[0])  := x[0]*y[0] + A
+	MULXQ DI, R14, R15
+
+	// (A,t[1])  := x[1]*y[0] + A
+	MULXQ R8, AX, CX
+	ADOXQ AX, R15
+
+	// (A,t[2])  := x[2]*y[0] + A
+	MULXQ R9, AX, BX
+	ADOXQ AX, CX
+
+	// (A,t[3])  := x[3]*y[0] + A
+	MULXQ R10, AX, BP
+	ADOXQ AX, BX
+
+	// A += carries from ADCXQ and ADOXQ
+	MOVQ  $0, AX
+	ADOXQ AX, BP
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+
+	// clear the flags
+	XORQ AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, R12
+	ADCXQ R14, AX
+	MOVQ  R12, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// t[3] = C + A
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ BP, BX
+
+	// clear the flags
+	XORQ AX, AX
+	MOVQ 8(R11), DX
+
+	// (A,t[0])  := t[0] + x[0]*y[1] + A
+	MULXQ DI, AX, BP
+	ADOXQ AX, R14
+
+	// (A,t[1])  := t[1] + x[1]*y[1] + A
+	ADCXQ BP, R15
+	MULXQ R8, AX, BP
+	ADOXQ AX, R15
+
+	// (A,t[2])  := t[2] + x[2]*y[1] + A
+	ADCXQ BP, CX
+	MULXQ R9, AX, BP
+	ADOXQ AX, CX
+
+	// (A,t[3])  := t[3] + x[3]*y[1] + A
+	ADCXQ BP, BX
+	MULXQ R10, AX, BP
+	ADOXQ AX, BX
+
+	// A += carries from ADCXQ and ADOXQ
+	MOVQ  $0, AX
+	ADCXQ AX, BP
+	ADOXQ AX, BP
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+
+	// clear the flags
+	XORQ AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, R12
+	ADCXQ R14, AX
+	MOVQ  R12, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// t[3] = C + A
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ BP, BX
+
+	// clear the flags
+	XORQ AX, AX
+	MOVQ 16(R11), DX
+
+	// (A,t[0])  := t[0] + x[0]*y[2] + A
+	MULXQ DI, AX, BP
+	ADOXQ AX, R14
+
+	// (A,t[1])  := t[1] + x[1]*y[2] + A
+	ADCXQ BP, R15
+	MULXQ R8, AX, BP
+	ADOXQ AX, R15
+
+	// (A,t[2])  := t[2] + x[2]*y[2] + A
+	ADCXQ BP, CX
+	MULXQ R9, AX, BP
+	ADOXQ AX, CX
+
+	// (A,t[3])  := t[3] + x[3]*y[2] + A
+	ADCXQ BP, BX
+	MULXQ R10, AX, BP
+	ADOXQ AX, BX
+
+	// A += carries from ADCXQ and ADOXQ
+	MOVQ  $0, AX
+	ADCXQ AX, BP
+	ADOXQ AX, BP
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+
+	// clear the flags
+	XORQ AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, R12
+	ADCXQ R14, AX
+	MOVQ  R12, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// t[3] = C + A
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ BP, BX
+
+	// clear the flags
+	XORQ AX, AX
+	MOVQ 24(R11), DX
+
+	// (A,t[0])  := t[0] + x[0]*y[3] + A
+	MULXQ DI, AX, BP
+	ADOXQ AX, R14
+
+	// (A,t[1])  := t[1] + x[1]*y[3] + A
+	ADCXQ BP, R15
+	MULXQ R8, AX, BP
+	ADOXQ AX, R15
+
+	// (A,t[2])  := t[2] + x[2]*y[3] + A
+	ADCXQ BP, CX
+	MULXQ R9, AX, BP
+	ADOXQ AX, CX
+
+	// (A,t[3])  := t[3] + x[3]*y[3] + A
+	ADCXQ BP, BX
+	MULXQ R10, AX, BP
+	ADOXQ AX, BX
+
+	// A += carries from ADCXQ and ADOXQ
+	MOVQ  $0, AX
+	ADCXQ AX, BP
+	ADOXQ AX, BP
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+
+	// clear the flags
+	XORQ AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, R12
+	ADCXQ R14, AX
+	MOVQ  R12, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+
+	// t[3] = C + A
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ BP, BX
+
+	// reduce element(R14,R15,CX,BX) using temp registers (R13,SI,R12,R11)
+	REDUCE(R14,R15,CX,BX,R13,SI,R12,R11)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	RET
+
+l1:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	MOVQ x+8(FP), AX
+	MOVQ AX, 8(SP)
+	MOVQ y+16(FP), AX
+	MOVQ AX, 16(SP)
+	CALL ·_mulGeneric(SB)
+	RET
+
+TEXT ·fromMont(SB), $8-8
+	NO_LOCAL_POINTERS
+
+	// the algorithm is described here
+	// https://hackmd.io/@zkteam/modular_multiplication
+	// when y = 1 we have:
+	// for i=0 to N-1
+	// 		t[i] = x[i]
+	// for i=0 to N-1
+	// 		m := t[0]*q'[0] mod W
+	// 		C,_ := t[0] + m*q[0]
+	// 		for j=1 to N-1
+	// 		    (C,t[j-1]) := t[j] + m*q[j] + C
+	// 		t[N-1] = C
+	CMPB ·supportAdx(SB), $1
+	JNE  l2
+	MOVQ res+0(FP), DX
+	MOVQ 0(DX), R14
+	MOVQ 8(DX), R15
+	MOVQ 16(DX), CX
+	MOVQ 24(DX), BX
+	XORQ DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+	XORQ  DX, DX
+
+	// m := t[0]*q'[0] mod W
+	MOVQ  qInv0<>(SB), DX
+	IMULQ R14, DX
+	XORQ  AX, AX
+
+	// C,_ := t[0] + m*q[0]
+	MULXQ q<>+0(SB), AX, BP
+	ADCXQ R14, AX
+	MOVQ  BP, R14
+
+	// (C,t[0]) := t[1] + m*q[1] + C
+	ADCXQ R15, R14
+	MULXQ q<>+8(SB), AX, R15
+	ADOXQ AX, R14
+
+	// (C,t[1]) := t[2] + m*q[2] + C
+	ADCXQ CX, R15
+	MULXQ q<>+16(SB), AX, CX
+	ADOXQ AX, R15
+
+	// (C,t[2]) := t[3] + m*q[3] + C
+	ADCXQ BX, CX
+	MULXQ q<>+24(SB), AX, BX
+	ADOXQ AX, CX
+	MOVQ  $0, AX
+	ADCXQ AX, BX
+	ADOXQ AX, BX
+
+	// reduce element(R14,R15,CX,BX) using temp registers (SI,DI,R8,R9)
+	REDUCE(R14,R15,CX,BX,SI,DI,R8,R9)
+
+	MOVQ res+0(FP), AX
+	MOVQ R14, 0(AX)
+	MOVQ R15, 8(AX)
+	MOVQ CX, 16(AX)
+	MOVQ BX, 24(AX)
+	RET
+
+l2:
+	MOVQ res+0(FP), AX
+	MOVQ AX, (SP)
+	CALL ·_fromMontGeneric(SB)
+	RET

ff/element_ops_amd64.go

@@ -0,0 +1,50 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ff
+
+//go:noescape
+func MulBy3(x *Element)
+
+//go:noescape
+func MulBy5(x *Element)
+
+//go:noescape
+func MulBy13(x *Element)
+
+//go:noescape
+func add(res, x, y *Element)
+
+//go:noescape
+func sub(res, x, y *Element)
+
+//go:noescape
+func neg(res, x *Element)
+
+//go:noescape
+func double(res, x *Element)
+
+//go:noescape
+func mul(res, x, y *Element)
+
+//go:noescape
+func fromMont(res *Element)
+
+//go:noescape
+func reduce(res *Element)
+
+//go:noescape
+func Butterfly(a, b *Element)

ff/element_ops_amd64.s

@@ -0,0 +1,340 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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.
+
+#include "textflag.h"
+#include "funcdata.h"
+
+// modulus q
+DATA q<>+0(SB)/8, $0x43e1f593f0000001
+DATA q<>+8(SB)/8, $0x2833e84879b97091
+DATA q<>+16(SB)/8, $0xb85045b68181585d
+DATA q<>+24(SB)/8, $0x30644e72e131a029
+GLOBL q<>(SB), (RODATA+NOPTR), $32
+
+// qInv0 q'[0]
+DATA qInv0<>(SB)/8, $0xc2e1f593efffffff
+GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
+
+#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
+	MOVQ    ra0, rb0;        \
+	SUBQ    q<>(SB), ra0;    \
+	MOVQ    ra1, rb1;        \
+	SBBQ    q<>+8(SB), ra1;  \
+	MOVQ    ra2, rb2;        \
+	SBBQ    q<>+16(SB), ra2; \
+	MOVQ    ra3, rb3;        \
+	SBBQ    q<>+24(SB), ra3; \
+	CMOVQCS rb0, ra0;        \
+	CMOVQCS rb1, ra1;        \
+	CMOVQCS rb2, ra2;        \
+	CMOVQCS rb3, ra3;        \
+
+// add(res, x, y *Element)
+TEXT ·add(SB), NOSPLIT, $0-24
+	MOVQ x+8(FP), AX
+	MOVQ 0(AX), CX
+	MOVQ 8(AX), BX
+	MOVQ 16(AX), SI
+	MOVQ 24(AX), DI
+	MOVQ y+16(FP), DX
+	ADDQ 0(DX), CX
+	ADCQ 8(DX), BX
+	ADCQ 16(DX), SI
+	ADCQ 24(DX), DI
+
+	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
+	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
+
+	MOVQ res+0(FP), R12
+	MOVQ CX, 0(R12)
+	MOVQ BX, 8(R12)
+	MOVQ SI, 16(R12)
+	MOVQ DI, 24(R12)
+	RET
+
+// sub(res, x, y *Element)
+TEXT ·sub(SB), NOSPLIT, $0-24
+	XORQ    DI, DI
+	MOVQ    x+8(FP), SI
+	MOVQ    0(SI), AX
+	MOVQ    8(SI), DX
+	MOVQ    16(SI), CX
+	MOVQ    24(SI), BX
+	MOVQ    y+16(FP), SI
+	SUBQ    0(SI), AX
+	SBBQ    8(SI), DX
+	SBBQ    16(SI), CX
+	SBBQ    24(SI), BX
+	MOVQ    $0x43e1f593f0000001, R8
+	MOVQ    $0x2833e84879b97091, R9
+	MOVQ    $0xb85045b68181585d, R10
+	MOVQ    $0x30644e72e131a029, R11
+	CMOVQCC DI, R8
+	CMOVQCC DI, R9
+	CMOVQCC DI, R10
+	CMOVQCC DI, R11
+	ADDQ    R8, AX
+	ADCQ    R9, DX
+	ADCQ    R10, CX
+	ADCQ    R11, BX
+	MOVQ    res+0(FP), R12
+	MOVQ    AX, 0(R12)
+	MOVQ    DX, 8(R12)
+	MOVQ    CX, 16(R12)
+	MOVQ    BX, 24(R12)
+	RET
+
+// double(res, x *Element)
+TEXT ·double(SB), NOSPLIT, $0-16
+	MOVQ x+8(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	MOVQ res+0(FP), R11
+	MOVQ DX, 0(R11)
+	MOVQ CX, 8(R11)
+	MOVQ BX, 16(R11)
+	MOVQ SI, 24(R11)
+	RET
+
+// neg(res, x *Element)
+TEXT ·neg(SB), NOSPLIT, $0-16
+	MOVQ  res+0(FP), DI
+	MOVQ  x+8(FP), AX
+	MOVQ  0(AX), DX
+	MOVQ  8(AX), CX
+	MOVQ  16(AX), BX
+	MOVQ  24(AX), SI
+	MOVQ  DX, AX
+	ORQ   CX, AX
+	ORQ   BX, AX
+	ORQ   SI, AX
+	TESTQ AX, AX
+	JEQ   l1
+	MOVQ  $0x43e1f593f0000001, R8
+	SUBQ  DX, R8
+	MOVQ  R8, 0(DI)
+	MOVQ  $0x2833e84879b97091, R8
+	SBBQ  CX, R8
+	MOVQ  R8, 8(DI)
+	MOVQ  $0xb85045b68181585d, R8
+	SBBQ  BX, R8
+	MOVQ  R8, 16(DI)
+	MOVQ  $0x30644e72e131a029, R8
+	SBBQ  SI, R8
+	MOVQ  R8, 24(DI)
+	RET
+
+l1:
+	MOVQ AX, 0(DI)
+	MOVQ AX, 8(DI)
+	MOVQ AX, 16(DI)
+	MOVQ AX, 24(DI)
+	RET
+
+TEXT ·reduce(SB), NOSPLIT, $0-8
+	MOVQ res+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	RET
+
+// MulBy3(x *Element)
+TEXT ·MulBy3(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	RET
+
+// MulBy5(x *Element)
+TEXT ·MulBy5(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (R15,DI,R8,R9)
+	REDUCE(DX,CX,BX,SI,R15,DI,R8,R9)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	RET
+
+// MulBy13(x *Element)
+TEXT ·MulBy13(SB), NOSPLIT, $0-8
+	MOVQ x+0(FP), AX
+	MOVQ 0(AX), DX
+	MOVQ 8(AX), CX
+	MOVQ 16(AX), BX
+	MOVQ 24(AX), SI
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (R11,R12,R13,R14)
+	REDUCE(DX,CX,BX,SI,R11,R12,R13,R14)
+
+	MOVQ DX, R11
+	MOVQ CX, R12
+	MOVQ BX, R13
+	MOVQ SI, R14
+	ADDQ DX, DX
+	ADCQ CX, CX
+	ADCQ BX, BX
+	ADCQ SI, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ R11, DX
+	ADCQ R12, CX
+	ADCQ R13, BX
+	ADCQ R14, SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	ADDQ 0(AX), DX
+	ADCQ 8(AX), CX
+	ADCQ 16(AX), BX
+	ADCQ 24(AX), SI
+
+	// reduce element(DX,CX,BX,SI) using temp registers (DI,R8,R9,R10)
+	REDUCE(DX,CX,BX,SI,DI,R8,R9,R10)
+
+	MOVQ DX, 0(AX)
+	MOVQ CX, 8(AX)
+	MOVQ BX, 16(AX)
+	MOVQ SI, 24(AX)
+	RET
+
+// Butterfly(a, b *Element) sets a = a + b; b = a - b
+TEXT ·Butterfly(SB), NOSPLIT, $0-16
+	MOVQ    a+0(FP), AX
+	MOVQ    0(AX), CX
+	MOVQ    8(AX), BX
+	MOVQ    16(AX), SI
+	MOVQ    24(AX), DI
+	MOVQ    CX, R8
+	MOVQ    BX, R9
+	MOVQ    SI, R10
+	MOVQ    DI, R11
+	XORQ    AX, AX
+	MOVQ    b+8(FP), DX
+	ADDQ    0(DX), CX
+	ADCQ    8(DX), BX
+	ADCQ    16(DX), SI
+	ADCQ    24(DX), DI
+	SUBQ    0(DX), R8
+	SBBQ    8(DX), R9
+	SBBQ    16(DX), R10
+	SBBQ    24(DX), R11
+	MOVQ    $0x43e1f593f0000001, R12
+	MOVQ    $0x2833e84879b97091, R13
+	MOVQ    $0xb85045b68181585d, R14
+	MOVQ    $0x30644e72e131a029, R15
+	CMOVQCC AX, R12
+	CMOVQCC AX, R13
+	CMOVQCC AX, R14
+	CMOVQCC AX, R15
+	ADDQ    R12, R8
+	ADCQ    R13, R9
+	ADCQ    R14, R10
+	ADCQ    R15, R11
+	MOVQ    R8, 0(DX)
+	MOVQ    R9, 8(DX)
+	MOVQ    R10, 16(DX)
+	MOVQ    R11, 24(DX)
+
+	// reduce element(CX,BX,SI,DI) using temp registers (R8,R9,R10,R11)
+	REDUCE(CX,BX,SI,DI,R8,R9,R10,R11)
+
+	MOVQ a+0(FP), AX
+	MOVQ CX, 0(AX)
+	MOVQ BX, 8(AX)
+	MOVQ SI, 16(AX)
+	MOVQ DI, 24(AX)
+	RET

ff/element_ops_noasm.go

@@ -0,0 +1,78 @@
+//go:build !amd64
+// +build !amd64
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ff
+
+// /!\ WARNING /!\
+// this code has not been audited and is provided as-is. In particular,
+// there is no security guarantees such as constant time implementation
+// or side-channel attack resistance
+// /!\ WARNING /!\
+
+// MulBy3 x *= 3
+func MulBy3(x *Element) {
+	mulByConstant(x, 3)
+}
+
+// MulBy5 x *= 5
+func MulBy5(x *Element) {
+	mulByConstant(x, 5)
+}
+
+// MulBy13 x *= 13
+func MulBy13(x *Element) {
+	mulByConstant(x, 13)
+}
+
+// Butterfly sets
+// a = a + b
+// b = a - b
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
+
+func mul(z, x, y *Element) {
+	_mulGeneric(z, x, y)
+}
+
+// FromMont converts z in place (i.e. mutates) from Montgomery to regular representation
+// sets and returns z = z * 1
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+func add(z, x, y *Element) {
+	_addGeneric(z, x, y)
+}
+
+func double(z, x *Element) {
+	_doubleGeneric(z, x)
+}
+
+func sub(z, x, y *Element) {
+	_subGeneric(z, x, y)
+}
+
+func neg(z, x *Element) {
+	_negGeneric(z, x)
+}
+
+func reduce(z *Element) {
+	_reduceGeneric(z)
+}

ff/util.go

@@ -1,6 +0,0 @@
-package ff
-
-// NewElement returns a new empty *Element
-func NewElement() *Element {
-	return &Element{}
-}

ffg/arith.go

@@ -0,0 +1,30 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ffg
+
+import (
+	"math/bits"
+)
+
+// 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
+}

ffg/asm.go

@@ -0,0 +1,24 @@
+//go:build !noadx
+// +build !noadx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ffg
+
+import "golang.org/x/sys/cpu"
+
+var supportAdx = cpu.X86.HasADX && cpu.X86.HasBMI2

ffg/asm_noadx.go

@@ -0,0 +1,25 @@
+//go:build noadx
+// +build noadx
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ffg
+
+// note: this is needed for test purposes, as dynamically changing supportAdx doesn't flag
+// certain errors (like fatal error: missing stackmap)
+// this ensures we test all asm path.
+var supportAdx = false

ffg/doc.go

@@ -0,0 +1,43 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+// Package ffg contains field arithmetic operations for modulus = 0xffffff...000001.
+//
+// The API is similar to math/big (big.Int), but the operations are significantly faster (up to 20x for the modular multiplication on amd64, see also https://hackmd.io/@zkteam/modular_multiplication)
+//
+// The modulus is hardcoded in all the operations.
+//
+// Field elements are represented as an array, and assumed to be in Montgomery form in all methods:
+// 	type Element [1]uint64
+//
+// Example API signature
+// 	// Mul z = x * y mod q
+// 	func (z *Element) Mul(x, y *Element) *Element
+//
+// and can be used like so:
+// 	var a, b Element
+// 	a.SetUint64(2)
+// 	b.SetString("984896738")
+// 	a.Mul(a, b)
+// 	a.Sub(a, a)
+// 	 .Add(a, b)
+// 	 .Inv(a)
+// 	b.Exp(b, new(big.Int).SetUint64(42))
+//
+// Modulus
+// 	0xffffffff00000001 // base 16
+// 	18446744069414584321 // base 10
+package ffg

ffg/element.go

@@ -0,0 +1,759 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ffg
+
+// /!\ WARNING /!\
+// this code has not been audited and is provided as-is. In particular,
+// there is no security guarantees such as constant time implementation
+// or side-channel attack resistance
+// /!\ WARNING /!\
+
+import (
+	"crypto/rand"
+	"encoding/binary"
+	"errors"
+	"io"
+	"math/big"
+	"math/bits"
+	"reflect"
+	"strconv"
+	"sync"
+)
+
+// Element represents a field element stored on 1 words (uint64)
+// Element are assumed to be in Montgomery form in all methods
+// field modulus q =
+//
+// 18446744069414584321
+type Element [1]uint64
+
+// Limbs number of 64 bits words needed to represent Element
+const Limbs = 1
+
+// Bits number bits needed to represent Element
+const Bits = 64
+
+// Bytes number bytes needed to represent Element
+const Bytes = Limbs * 8
+
+// field modulus stored as big.Int
+var _modulus big.Int
+
+// Modulus returns q as a big.Int
+// q =
+//
+// 18446744069414584321
+func Modulus() *big.Int {
+	return new(big.Int).Set(&_modulus)
+}
+
+// q (modulus)
+var qElement = Element{
+	18446744069414584321,
+}
+
+// rSquare
+var rSquare = Element{
+	18446744065119617025,
+}
+
+var bigIntPool = sync.Pool{
+	New: func() interface{} {
+		return new(big.Int)
+	},
+}
+
+func init() {
+	_modulus.SetString("18446744069414584321", 10)
+}
+
+// NewElement returns a new Element
+func NewElement() *Element {
+	return &Element{}
+}
+
+// NewElementFromUint64 returns a new Element from a uint64 value
+//
+// it is equivalent to
+// 		var v NewElement
+// 		v.SetUint64(...)
+func NewElementFromUint64(v uint64) *Element {
+	z := Element{v}
+	z.Mul(&z, &rSquare)
+	return &z
+}
+
+// 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 = Element{v}
+	return z.Mul(z, &rSquare) // z.ToMont()
+}
+
+// Set z = x
+func (z *Element) Set(x *Element) *Element {
+	z[0] = x[0]
+	return z
+}
+
+// SetInterface converts provided interface into Element
+// returns an error if provided type is not supported
+// supported types: Element, *Element, uint64, int, string (interpreted as base10 integer),
+// *big.Int, big.Int, []byte
+func (z *Element) SetInterface(i1 interface{}) (*Element, error) {
+	switch c1 := i1.(type) {
+	case Element:
+		return z.Set(&c1), nil
+	case *Element:
+		return z.Set(c1), nil
+	case uint64:
+		return z.SetUint64(c1), nil
+	case int:
+		return z.SetString(strconv.Itoa(c1)), nil
+	case string:
+		return z.SetString(c1), nil
+	case *big.Int:
+		return z.SetBigInt(c1), nil
+	case big.Int:
+		return z.SetBigInt(&c1), nil
+	case []byte:
+		return z.SetBytes(c1), nil
+	default:
+		return nil, errors.New("can't set ffg.Element from type " + reflect.TypeOf(i1).String())
+	}
+}
+
+// SetZero z = 0
+func (z *Element) SetZero() *Element {
+	z[0] = 0
+	return z
+}
+
+// SetOne z = 1 (in Montgomery form)
+func (z *Element) SetOne() *Element {
+	z[0] = 4294967295
+	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
+}
+
+// Bit returns the i'th bit, with lsb == bit 0.
+// It is the responsability of the caller to convert from Montgomery to Regular form if needed
+func (z *Element) Bit(i uint64) uint64 {
+	j := i / 64
+	if j >= 1 {
+		return 0
+	}
+	return uint64(z[j] >> (i % 64) & 1)
+}
+
+// Equal returns z == x
+func (z *Element) Equal(x *Element) bool {
+	return (z[0] == x[0])
+}
+
+// IsZero returns z == 0
+func (z *Element) IsZero() bool {
+	return (z[0]) == 0
+}
+
+// IsUint64 returns true if z[0] >= 0 and all other words are 0
+func (z *Element) IsUint64() bool {
+	return true
+}
+
+// Cmp compares (lexicographic order) z and x and returns:
+//
+//   -1 if z <  x
+//    0 if z == x
+//   +1 if z >  x
+//
+func (z *Element) Cmp(x *Element) int {
+	_z := *z
+	_x := *x
+	_z.FromMont()
+	_x.FromMont()
+	if _z[0] > _x[0] {
+		return 1
+	} else if _z[0] < _x[0] {
+		return -1
+	}
+	return 0
+}
+
+// LexicographicallyLargest returns true if this element is strictly lexicographically
+// larger than its negation, false otherwise
+func (z *Element) LexicographicallyLargest() bool {
+	// adapted from github.com/zkcrypto/bls12_381
+	// we check if the element is larger than (q-1) / 2
+	// if z - (((q -1) / 2) + 1) have no underflow, then z > (q-1) / 2
+
+	_z := *z
+	_z.FromMont()
+
+	var b uint64
+	_, b = bits.Sub64(_z[0], 9223372034707292161, 0)
+
+	return b == 0
+}
+
+// SetRandom sets z to a random element < q
+func (z *Element) SetRandom() (*Element, error) {
+	var bytes [8]byte
+	if _, err := io.ReadFull(rand.Reader, bytes[:]); err != nil {
+		return nil, err
+	}
+	z[0] = binary.BigEndian.Uint64(bytes[0:8])
+	z[0] %= 18446744069414584321
+
+	// if z > q --> z -= q
+	// note: this is NOT constant time
+	if !(z[0] < 18446744069414584321) {
+		z[0], _ = bits.Sub64(z[0], 18446744069414584321, 0)
+	}
+
+	return z, nil
+}
+
+// One returns 1 (in montgommery form)
+func One() Element {
+	var one Element
+	one.SetOne()
+	return one
+}
+
+// Halve sets z to z / 2 (mod p)
+func (z *Element) Halve() {
+	var twoInv Element
+	twoInv.SetOne().Double(&twoInv).Inverse(&twoInv)
+	z.Mul(z, &twoInv)
+
+}
+
+// API with assembly impl
+
+// Mul z = x * y mod q
+// see https://hackmd.io/@zkteam/modular_multiplication
+func (z *Element) Mul(x, y *Element) *Element {
+	mul(z, x, y)
+	return z
+}
+
+// Square z = x * x mod q
+// see https://hackmd.io/@zkteam/modular_multiplication
+func (z *Element) Square(x *Element) *Element {
+	mul(z, x, 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 {
+	fromMont(z)
+	return z
+}
+
+// Add z = x + y mod q
+func (z *Element) Add(x, y *Element) *Element {
+	add(z, x, y)
+	return z
+}
+
+// Double z = x + x mod q, aka Lsh 1
+func (z *Element) Double(x *Element) *Element {
+	double(z, x)
+	return z
+}
+
+// Sub  z = x - y mod q
+func (z *Element) Sub(x, y *Element) *Element {
+	sub(z, x, y)
+	return z
+}
+
+// Neg z = q - x
+func (z *Element) Neg(x *Element) *Element {
+	neg(z, x)
+	return z
+}
+
+// Generic (no ADX instructions, no AMD64) versions of multiplication and squaring algorithms
+
+func _mulGeneric(z, x, y *Element) {
+
+	var t [2]uint64
+	var D uint64
+	var m, C uint64
+	// -----------------------------------
+	// First loop
+
+	C, t[0] = bits.Mul64(y[0], x[0])
+
+	t[1], D = bits.Add64(t[1], C, 0)
+
+	// m = t[0]n'[0] mod W
+	m = t[0] * 18446744069414584319
+
+	// -----------------------------------
+	// Second loop
+	C = madd0(m, 18446744069414584321, t[0])
+
+	t[0], C = bits.Add64(t[1], C, 0)
+	t[1], _ = bits.Add64(0, D, C)
+
+	if t[1] != 0 {
+		// we need to reduce, we have a result on 2 words
+		z[0], _ = bits.Sub64(t[0], 18446744069414584321, 0)
+
+		return
+
+	}
+
+	// copy t into z
+	z[0] = t[0]
+
+	// if z > q --> z -= q
+	// note: this is NOT constant time
+	if !(z[0] < 18446744069414584321) {
+		z[0], _ = bits.Sub64(z[0], 18446744069414584321, 0)
+	}
+}
+
+func _fromMontGeneric(z *Element) {
+	// the following lines implement z = z * 1
+	// with a modified CIOS montgomery multiplication
+	{
+		// m = z[0]n'[0] mod W
+		m := z[0] * 18446744069414584319
+		C := madd0(m, 18446744069414584321, z[0])
+		z[0] = C
+	}
+
+	// if z > q --> z -= q
+	// note: this is NOT constant time
+	if !(z[0] < 18446744069414584321) {
+		z[0], _ = bits.Sub64(z[0], 18446744069414584321, 0)
+	}
+}
+
+func _addGeneric(z, x, y *Element) {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], y[0], 0)
+	// if we overflowed the last addition, z >= q
+	// if z >= q, z = z - q
+	if carry != 0 {
+		// we overflowed, so z >= q
+		z[0], _ = bits.Sub64(z[0], 18446744069414584321, 0)
+		return
+	}
+
+	// if z > q --> z -= q
+	// note: this is NOT constant time
+	if !(z[0] < 18446744069414584321) {
+		z[0], _ = bits.Sub64(z[0], 18446744069414584321, 0)
+	}
+}
+
+func _doubleGeneric(z, x *Element) {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], x[0], 0)
+	// if we overflowed the last addition, z >= q
+	// if z >= q, z = z - q
+	if carry != 0 {
+		// we overflowed, so z >= q
+		z[0], _ = bits.Sub64(z[0], 18446744069414584321, 0)
+		return
+	}
+
+	// if z > q --> z -= q
+	// note: this is NOT constant time
+	if !(z[0] < 18446744069414584321) {
+		z[0], _ = bits.Sub64(z[0], 18446744069414584321, 0)
+	}
+}
+
+func _subGeneric(z, x, y *Element) {
+	var b uint64
+	z[0], b = bits.Sub64(x[0], y[0], 0)
+	if b != 0 {
+		z[0], _ = bits.Add64(z[0], 18446744069414584321, 0)
+	}
+}
+
+func _negGeneric(z, x *Element) {
+	if x.IsZero() {
+		z.SetZero()
+		return
+	}
+	z[0], _ = bits.Sub64(18446744069414584321, x[0], 0)
+}
+
+func _reduceGeneric(z *Element) {
+
+	// if z > q --> z -= q
+	// note: this is NOT constant time
+	if !(z[0] < 18446744069414584321) {
+		z[0], _ = bits.Sub64(z[0], 18446744069414584321, 0)
+	}
+}
+
+func mulByConstant(z *Element, c uint8) {
+	switch c {
+	case 0:
+		z.SetZero()
+		return
+	case 1:
+		return
+	case 2:
+		z.Double(z)
+		return
+	case 3:
+		_z := *z
+		z.Double(z).Add(z, &_z)
+	case 5:
+		_z := *z
+		z.Double(z).Double(z).Add(z, &_z)
+	default:
+		var y Element
+		y.SetUint64(uint64(c))
+		z.Mul(z, &y)
+	}
+}
+
+// BatchInvert returns a new slice with every element inverted.
+// Uses Montgomery batch inversion trick
+func BatchInvert(a []Element) []Element {
+	res := make([]Element, len(a))
+	if len(a) == 0 {
+		return res
+	}
+
+	zeroes := make([]bool, len(a))
+	accumulator := One()
+
+	for i := 0; i < len(a); i++ {
+		if a[i].IsZero() {
+			zeroes[i] = true
+			continue
+		}
+		res[i] = accumulator
+		accumulator.Mul(&accumulator, &a[i])
+	}
+
+	accumulator.Inverse(&accumulator)
+
+	for i := len(a) - 1; i >= 0; i-- {
+		if zeroes[i] {
+			continue
+		}
+		res[i].Mul(&res[i], &accumulator)
+		accumulator.Mul(&accumulator, &a[i])
+	}
+
+	return res
+}
+
+func _butterflyGeneric(a, b *Element) {
+	t := *a
+	a.Add(a, b)
+	b.Sub(&t, b)
+}
+
+// BitLen returns the minimum number of bits needed to represent z
+// returns 0 if z == 0
+func (z *Element) BitLen() int {
+	return bits.Len64(z[0])
+}
+
+// Exp z = x^exponent mod q
+func (z *Element) Exp(x Element, exponent *big.Int) *Element {
+	var bZero big.Int
+	if exponent.Cmp(&bZero) == 0 {
+		return z.SetOne()
+	}
+
+	z.Set(&x)
+
+	for i := exponent.BitLen() - 2; i >= 0; i-- {
+		z.Square(z)
+		if exponent.Bit(i) == 1 {
+			z.Mul(z, &x)
+		}
+	}
+
+	return z
+}
+
+// ToMont converts z to Montgomery form
+// sets and returns z = z * r^2
+func (z *Element) ToMont() *Element {
+	return z.Mul(z, &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 {
+	zz := *z
+	zz.FromMont()
+	if zz.IsUint64() {
+		return strconv.FormatUint(zz[0], 10)
+	} else {
+		var zzNeg Element
+		zzNeg.Neg(z)
+		zzNeg.FromMont()
+		if zzNeg.IsUint64() {
+			return "-" + strconv.FormatUint(zzNeg[0], 10)
+		}
+	}
+	vv := bigIntPool.Get().(*big.Int)
+	defer bigIntPool.Put(vv)
+	return zz.ToBigInt(vv).String()
+}
+
+// ToBigInt returns z as a big.Int in Montgomery form
+func (z *Element) ToBigInt(res *big.Int) *big.Int {
+	var b [Limbs * 8]byte
+	binary.BigEndian.PutUint64(b[0:8], z[0])
+
+	return res.SetBytes(b[:])
+}
+
+// ToBigIntRegular returns z as a big.Int in regular form
+func (z Element) ToBigIntRegular(res *big.Int) *big.Int {
+	z.FromMont()
+	return z.ToBigInt(res)
+}
+
+// ToUint64Regular returns z as a uint64 in regular form
+func (z Element) ToUint64Regular() uint64 {
+	z.FromMont()
+	return z[0]
+}
+
+// Bytes returns the regular (non montgomery) value
+// of z as a big-endian byte array.
+func (z *Element) Bytes() (res [Limbs * 8]byte) {
+	_z := z.ToRegular()
+	binary.BigEndian.PutUint64(res[0:8], _z[0])
+
+	return
+}
+
+// Marshal returns the regular (non montgomery) value
+// of z as a big-endian byte slice.
+func (z *Element) Marshal() []byte {
+	b := z.Bytes()
+	return b[:]
+}
+
+// SetBytes interprets e as the bytes of a big-endian unsigned integer,
+// sets z to that value (in Montgomery form), and returns z.
+func (z *Element) SetBytes(e []byte) *Element {
+	// get a big int from our pool
+	vv := bigIntPool.Get().(*big.Int)
+	vv.SetBytes(e)
+
+	// set big int
+	z.SetBigInt(vv)
+
+	// put temporary object back in pool
+	bigIntPool.Put(vv)
+
+	return z
+}
+
+// SetBigInt sets z to v (regular form) and returns z in Montgomery form
+func (z *Element) SetBigInt(v *big.Int) *Element {
+	z.SetZero()
+
+	var zero big.Int
+
+	// fast path
+	c := v.Cmp(&_modulus)
+	if c == 0 {
+		// v == 0
+		return z
+	} else if c != 1 && v.Cmp(&zero) != -1 {
+		// 0 < v < q
+		return z.setBigInt(v)
+	}
+
+	// get temporary big int from the pool
+	vv := bigIntPool.Get().(*big.Int)
+
+	// copy input + modular reduction
+	vv.Set(v)
+	vv.Mod(v, &_modulus)
+
+	// set big int byte value
+	z.setBigInt(vv)
+
+	// release object into pool
+	bigIntPool.Put(vv)
+	return z
+}
+
+// setBigInt assumes 0 <= v < q
+func (z *Element) setBigInt(v *big.Int) *Element {
+	vBits := v.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 {
+	// get temporary big int from the pool
+	vv := bigIntPool.Get().(*big.Int)
+
+	if _, ok := vv.SetString(s, 10); !ok {
+		panic("Element.SetString failed -> can't parse number in base10 into a big.Int")
+	}
+	z.SetBigInt(vv)
+
+	// release object into pool
+	bigIntPool.Put(vv)
+
+	return z
+}
+
+var (
+	_bLegendreExponentElement *big.Int
+	_bSqrtExponentElement     *big.Int
+)
+
+func init() {
+	_bLegendreExponentElement, _ = new(big.Int).SetString("7fffffff80000000", 16)
+	const sqrtExponentElement = "7fffffff"
+	_bSqrtExponentElement, _ = new(big.Int).SetString(sqrtExponentElement, 16)
+}
+
+// Legendre returns the Legendre symbol of z (either +1, -1, or 0.)
+func (z *Element) Legendre() int {
+	var l Element
+	// z^((q-1)/2)
+	l.Exp(*z, _bLegendreExponentElement)
+
+	if l.IsZero() {
+		return 0
+	}
+
+	// if l == 1
+	if l[0] == 4294967295 {
+		return 1
+	}
+	return -1
+}
+
+// Sqrt z = √x mod q
+// if the square root doesn't exist (x is not a square mod q)
+// Sqrt leaves z unchanged and returns nil
+func (z *Element) Sqrt(x *Element) *Element {
+	// q ≡ 1 (mod 4)
+	// see modSqrtTonelliShanks in math/big/int.go
+	// using https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020786.02p0470a.pdf
+
+	var y, b, t, w Element
+	// w = x^((s-1)/2))
+	w.Exp(*x, _bSqrtExponentElement)
+
+	// y = x^((s+1)/2)) = w * x
+	y.Mul(x, &w)
+
+	// b = x^s = w * w * x = y * x
+	b.Mul(&w, &y)
+
+	// g = nonResidue ^ s
+	var g = Element{
+		15733474329512464024,
+	}
+	r := uint64(32)
+
+	// compute legendre symbol
+	// t = x^((q-1)/2) = r-1 squaring of x^s
+	t = b
+	for i := uint64(0); i < r-1; i++ {
+		t.Square(&t)
+	}
+	if t.IsZero() {
+		return z.SetZero()
+	}
+	if !(t[0] == 4294967295) {
+		// t != 1, we don't have a square root
+		return nil
+	}
+	for {
+		var m uint64
+		t = b
+
+		// for t != 1
+		for !(t[0] == 4294967295) {
+			t.Square(&t)
+			m++
+		}
+
+		if m == 0 {
+			return z.Set(&y)
+		}
+		// t = g^(2^(r-m-1)) mod q
+		ge := int(r - m - 1)
+		t = g
+		for ge > 0 {
+			t.Square(&t)
+			ge--
+		}
+
+		g.Square(&t)
+		y.Mul(&y, &t)
+		b.Mul(&b, &g)
+		r = m
+	}
+}
+
+// Inverse z = x^-1 mod q
+// note: allocates a big.Int (math/big)
+func (z *Element) Inverse(x *Element) *Element {
+	var _xNonMont big.Int
+	x.ToBigIntRegular(&_xNonMont)
+	_xNonMont.ModInverse(&_xNonMont, Modulus())
+	z.SetBigInt(&_xNonMont)
+	return z
+}

ffg/element_fuzz.go

@@ -0,0 +1,113 @@
+//go:build gofuzz
+// +build gofuzz
+
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ffg
+
+import (
+	"bytes"
+	"encoding/binary"
+	"io"
+	"math/big"
+	"math/bits"
+)
+
+const (
+	fuzzInteresting = 1
+	fuzzNormal      = 0
+	fuzzDiscard     = -1
+)
+
+// Fuzz arithmetic operations fuzzer
+func Fuzz(data []byte) int {
+	r := bytes.NewReader(data)
+
+	var e1, e2 Element
+	e1.SetRawBytes(r)
+	e2.SetRawBytes(r)
+
+	{
+		// mul assembly
+
+		var c, _c Element
+		a, _a, b, _b := e1, e1, e2, e2
+		c.Mul(&a, &b)
+		_mulGeneric(&_c, &_a, &_b)
+
+		if !c.Equal(&_c) {
+			panic("mul asm != mul generic on Element")
+		}
+	}
+
+	{
+		// inverse
+		inv := e1
+		inv.Inverse(&inv)
+
+		var bInv, b1, b2 big.Int
+		e1.ToBigIntRegular(&b1)
+		bInv.ModInverse(&b1, Modulus())
+		inv.ToBigIntRegular(&b2)
+
+		if b2.Cmp(&bInv) != 0 {
+			panic("inverse operation doesn't match big int result")
+		}
+	}
+
+	{
+		// a + -a == 0
+		a, b := e1, e1
+		b.Neg(&b)
+		a.Add(&a, &b)
+		if !a.IsZero() {
+			panic("a + -a != 0")
+		}
+	}
+
+	return fuzzNormal
+
+}
+
+// SetRawBytes reads up to Bytes (bytes needed to represent Element) from reader
+// and interpret it as big endian uint64
+// used for fuzzing purposes only
+func (z *Element) SetRawBytes(r io.Reader) {
+
+	buf := make([]byte, 8)
+
+	for i := 0; i < len(z); i++ {
+		if _, err := io.ReadFull(r, buf); err != nil {
+			goto eof
+		}
+		z[i] = binary.BigEndian.Uint64(buf[:])
+	}
+eof:
+	z[0] %= qElement[0]
+
+	if z.BiggerModulus() {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], qElement[0], 0)
+	}
+
+	return
+}
+
+func (z *Element) BiggerModulus() bool {
+
+	return z[0] >= qElement[0]
+}

ffg/element_ops_amd64.go

@@ -0,0 +1,17 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ffg

ffg/element_ops_noasm.go

@@ -0,0 +1,75 @@
+// Copyright 2020 ConsenSys Software Inc.
+//
+// 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 consensys/gnark-crypto DO NOT EDIT
+
+package ffg
+
+// /!\ WARNING /!\
+// this code has not been audited and is provided as-is. In particular,
+// there is no security guarantees such as constant time implementation
+// or side-channel attack resistance
+// /!\ WARNING /!\
+
+// MulBy3 x *= 3
+func MulBy3(x *Element) {
+	mulByConstant(x, 3)
+}
+
+// MulBy5 x *= 5
+func MulBy5(x *Element) {
+	mulByConstant(x, 5)
+}
+
+// MulBy13 x *= 13
+func MulBy13(x *Element) {
+	mulByConstant(x, 13)
+}
+
+// Butterfly sets
+// a = a + b
+// b = a - b
+func Butterfly(a, b *Element) {
+	_butterflyGeneric(a, b)
+}
+
+func mul(z, x, y *Element) {
+	_mulGeneric(z, x, y)
+}
+
+// FromMont converts z in place (i.e. mutates) from Montgomery to regular representation
+// sets and returns z = z * 1
+func fromMont(z *Element) {
+	_fromMontGeneric(z)
+}
+
+func add(z, x, y *Element) {
+	_addGeneric(z, x, y)
+}
+
+func double(z, x *Element) {
+	_doubleGeneric(z, x)
+}
+
+func sub(z, x, y *Element) {
+	_subGeneric(z, x, y)
+}
+
+func neg(z, x *Element) {
+	_negGeneric(z, x)
+}
+
+func reduce(z *Element) {
+	_reduceGeneric(z)
+}

go.mod

@@ -1,11 +1,17 @@
 module github.com/iden3/go-iden3-crypto
 
-go 1.12
+go 1.18
 
 require (
 	github.com/dchest/blake512 v1.0.0
-	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
+	github.com/leanovate/gopter v0.2.9
+	github.com/stretchr/testify v1.8.2
+	golang.org/x/crypto v0.7.0
+	golang.org/x/sys v0.6.0
+)
+
+require (
+	github.com/davecgh/go-spew v1.1.1 // indirect
+	github.com/pmezard/go-difflib v1.0.0 // indirect
+	gopkg.in/yaml.v3 v3.0.1 // indirect
 )

go.sum

@@ -1,173 +1,25 @@
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 gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
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goldenposeidon/constants.go

@@ -0,0 +1,856 @@
+package poseidon
+
+import "github.com/iden3/go-iden3-crypto/ffg"
+
+const (
+	// NROUNDSF const from original paper
+	NROUNDSF = 8
+	// NROUNDSP const from original paper
+	NROUNDSP = 22
+	// CAPLEN const
+	CAPLEN = 4
+	// mLen const
+	mLen = 12
+)
+
+var (
+	mcirc = []uint64{17, 15, 41, 16, 2, 28, 13, 13, 39, 18, 34, 20}
+	mdiag = []uint64{8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
+
+	c = []uint64{
+		0xb585f766f2144405,
+		0x7746a55f43921ad7,
+		0xb2fb0d31cee799b4,
+		0xf6760a4803427d7,
+		0xe10d666650f4e012,
+		0x8cae14cb07d09bf1,
+		0xd438539c95f63e9f,
+		0xef781c7ce35b4c3d,
+		0xcdc4a239b0c44426,
+		0x277fa208bf337bff,
+		0xe17653a29da578a1,
+		0xc54302f225db2c76,
+		0xac6c9c2b4418dd61,
+		0xe0888eb1e8a01286,
+		0x813dbe952b98904e,
+		0xcc3033609c9cf175,
+		0x72cebc82a59c0f82,
+		0x8150d8525753e741,
+		0xb1122c74b268d66e,
+		0x7c6ddd482375aa2,
+		0xa4dd6f1ef49fb6af,
+		0xd33b0d5b4f7ccfe5,
+		0xc523112247209124,
+		0x464804200134c32d,
+		0xcd09dea180de4f2c,
+		0xadb069225c93e4e6,
+		0xbf01209b8a7c8534,
+		0xb1eb37d319913823,
+		0xdadf943b8d3e5a0d,
+		0x6d15f3cb7a3520ba,
+		0xf07af62b134ef181,
+		0x568355076c6b0de6,
+		0x31ca4bf93cab68b8,
+		0xfbad37a125735ba,
+		0x9d3a9caaf1ac9e0a,
+		0x4f265810f020c095,
+		0x6a84c9524e81a8bc,
+		0x68ba410537925c79,
+		0x422604631b34b07a,
+		0x28e3a001f62f8290,
+		0x3adfdccb8f734d41,
+		0x73503e539baec66a,
+		0xe8c1fd0142d9849c,
+		0xe204ac13660546c5,
+		0x8e2bb3ea97a40c53,
+		0xac2800d1bf56548c,
+		0x9494dca005d180d0,
+		0xf36e1d066383ef53,
+		0x8aa35b97a0e03c04,
+		0xcf42a59addbd1f0c,
+		0xa43ace89f8fdbd79,
+		0x37585d8c243870c,
+		0x4ab94ee3e26596fe,
+		0xcee3abbb50d57b23,
+		0xac91a7101a5ec55b,
+		0x9173aa8462280d2d,
+		0xaec1ca46ccb95105,
+		0x57b2f2845db61e4a,
+		0x95704158500c90c6,
+		0x66e023b0e6c9df5f,
+		0x315f63f4fec360ba,
+		0xf3009795713abcf1,
+		0xf4decc3fb00765ee,
+		0x32620ac918682d50,
+		0x49717d63a5fc742e,
+		0x153516f22014ea2d,
+		0xcc316380a2761fe4,
+		0x2e49b3f7076d203d,
+		0x44ac3e9bf0a2dc89,
+		0x49d1e388d8e35c,
+		0x53ec867cb39989fa,
+		0xd2c9bcc8d65f5a62,
+		0xc0cc930ee8540455,
+		0x40651e0872505e8,
+		0x168973b2ebafbe6c,
+		0x9c7eecb3b40581c2,
+		0x389473bcdfca97a2,
+		0xb1cb0b3abe9753ad,
+		0x41afceccffdb18e6,
+		0x7bf841e237ccd6c9,
+		0x6082a3f101fb888,
+		0x8c1a39196f4163cc,
+		0xb56664760c1c9476,
+		0x2a02ac020d1eb5a3,
+		0x6a9d48e8aa83605d,
+		0x8a0d2f5c4c9c51b2,
+		0x75fc65575b284ad4,
+		0xadaedf7d1ce2a8dd,
+		0x235bc889cc83968e,
+		0xa8c30cf1781738f5,
+		0x546b2a846753bcf8,
+		0x9b68e8c06c04bd25,
+		0x3fdf80794ebb443b,
+		0x92ca132a9bec5a45,
+		0x76133eecfd9bd1ff,
+		0x3fb0fd5381054812,
+		0xf15925978dbd52ff,
+		0x2ee289ac37f0e879,
+		0xd8af8654e9a2e659,
+		0x8595bbd7f34c5e8a,
+		0x206ddbf781e47b2,
+		0xe101a767854a2f97,
+		0xf4d4f0a01072c996,
+		0x197aec2894aab642,
+		0x8d0c3911220db49b,
+		0xa62a8bad609227ca,
+		0x1e4813a7e7b9cbce,
+		0x6b547528731244eb,
+		0xd08e48512bfea84e,
+		0xb2920c88d3885857,
+		0x1f0cd5d7a309fcc2,
+		0x99a0ea0842fdb4fb,
+		0xc227210554b6c53d,
+		0x70e5269708f6f3a9,
+		0xbe8f71c8c98bb3bd,
+		0xf96fb39adc4baaf6,
+		0x7f9a7555c60fc6c7,
+		0xccaa5446d71fe6a5,
+	}
+
+	p = [][]uint64{
+		{
+			0x19,
+			0x78566230aa7cc5d0,
+			0xdbf23e50005e7f24,
+			0xb4a02c5c826d523e,
+			0x466d8f66a8f9fed5,
+			0x68da2264f65ec3e,
+			0xb59f9ff0ac6d5d78,
+			0xcfb03c902d447551,
+			0x2044ce14eaf8f5d9,
+			0xfb9373c8481e0f0d,
+			0x72af70cdcb99214f,
+			0xe3ef40eacc6ff78d,
+		},
+		{
+			0xf,
+			0x817bd8a7869ed1b5,
+			0x819f2c14a8366b1f,
+			0x7a5cf5b7b922e946,
+			0x727eca45c8d7bb71,
+			0x605a82c52b5ad2f1,
+			0x59ccc4d5184bc93a,
+			0x66c8bab2096cfd38,
+			0xeb4c0ce280c3e935,
+			0x17f9202c16676b2f,
+			0x9b6e5164ed35d878,
+			0x6fadc9347faeee81,
+		},
+		{
+			0x29,
+			0xd267254bea1097f4,
+			0x2dc10fce3233f443,
+			0xfa9db0de2d852e7a,
+			0xde2a0516f8c9d943,
+			0xe6fdf23648931b99,
+			0x3743057c07a5dbfa,
+			0xa6fdb8ebccc51667,
+			0x2c4916605e3dea58,
+			0xe95c10ae32e05085,
+			0x97f9b7d2cfc2ade5,
+			0x9b6e5164ed35d878,
+		},
+		{
+			0x10,
+			0x60c33ebd1e023f0a,
+			0xdb6945a20d277091,
+			0x383dd77e07998487,
+			0xe04ea1957ad8305c,
+			0xd499fcbf63fbd266,
+			0x462269e4b04620a5,
+			0x63c9679d8572a867,
+			0x81c44e9699915693,
+			0x62ecbe05e02433fc,
+			0xe95c10ae32e05085,
+			0x17f9202c16676b2f,
+		},
+		{
+			0x2,
+			0xa89ef32ae1462322,
+			0x77c1a153e73659e8,
+			0x2aec981be4b62ed5,
+			0xb70fb5f2b4f1f85f,
+			0x7c66d474cd2087cb,
+			0x39302966be7df654,
+			0xb827c807875511c0,
+			0xa4daffb3ffd0e78f,
+			0x81c44e9699915693,
+			0x2c4916605e3dea58,
+			0xeb4c0ce280c3e935,
+		},
+		{
+			0x1c,
+			0x6250f5f176d483e7,
+			0xaad1255d46e78f07,
+			0x8a00c7c83c762584,
+			0xc734f3829ed30b0c,
+			0xb1a0132288b1619b,
+			0x88685b4f0798dfd1,
+			0xfc02e869e21b72f8,
+			0xb827c807875511c0,
+			0x63c9679d8572a867,
+			0xa6fdb8ebccc51667,
+			0x66c8bab2096cfd38,
+		},
+		{
+			0xd,
+			0xe16a6c1dee3ba347,
+			0x13d316e45539aef4,
+			0x577e0472764f061d,
+			0x226a4dcf5db3316d,
+			0x3373035a3ca3dac6,
+			0x441f3a3747b5adb7,
+			0x88685b4f0798dfd1,
+			0x39302966be7df654,
+			0x462269e4b04620a5,
+			0x3743057c07a5dbfa,
+			0x59ccc4d5184bc93a,
+		},
+		{
+			0xd,
+			0xec9730136b7c2c05,
+			0xe1ecc5c21eec0646,
+			0x956d3c8b5528e064,
+			0x6df1d31fa84398f4,
+			0xf4898a1a3554ee49,
+			0x3373035a3ca3dac6,
+			0xb1a0132288b1619b,
+			0x7c66d474cd2087cb,
+			0xd499fcbf63fbd266,
+			0xe6fdf23648931b99,
+			0x605a82c52b5ad2f1,
+		},
+		{
+			0x27,
+			0x3cf7c3a39d94c236,
+			0x9e62c7d7b000cb0b,
+			0xe202be7ad7265af6,
+			0x82178371fa5fff69,
+			0x6df1d31fa84398f4,
+			0x226a4dcf5db3316d,
+			0xc734f3829ed30b0c,
+			0xb70fb5f2b4f1f85f,
+			0xe04ea1957ad8305c,
+			0xde2a0516f8c9d943,
+			0x727eca45c8d7bb71,
+		},
+		{
+			0x12,
+			0xb4707207455f57e3,
+			0x8e1de42b665c6706,
+			0xee7b04568203481,
+			0xe202be7ad7265af6,
+			0x956d3c8b5528e064,
+			0x577e0472764f061d,
+			0x8a00c7c83c762584,
+			0x2aec981be4b62ed5,
+			0x383dd77e07998487,
+			0xfa9db0de2d852e7a,
+			0x7a5cf5b7b922e946,
+		},
+		{
+			0x22,
+			0xaadb39e83e76a9e0,
+			0xcd9bf0bd292c5fda,
+			0x8e1de42b665c6706,
+			0x9e62c7d7b000cb0b,
+			0xe1ecc5c21eec0646,
+			0x13d316e45539aef4,
+			0xaad1255d46e78f07,
+			0x77c1a153e73659e8,
+			0xdb6945a20d277091,
+			0x2dc10fce3233f443,
+			0x819f2c14a8366b1f,
+		},
+		{
+			0x14,
+			0x32f8ae916e567d39,
+			0xaadb39e83e76a9e0,
+			0xb4707207455f57e3,
+			0x3cf7c3a39d94c236,
+			0xec9730136b7c2c05,
+			0xe16a6c1dee3ba347,
+			0x6250f5f176d483e7,
+			0xa89ef32ae1462322,
+			0x60c33ebd1e023f0a,
+			0xd267254bea1097f4,
+			0x817bd8a7869ed1b5,
+		},
+	}
+
+	s = []uint64{
+		0x19,
+		0x3d999c961b7c63b0,
+		0x814e82efcd172529,
+		0x2421e5d236704588,
+		0x887af7d4dd482328,
+		0xa5e9c291f6119b27,
+		0xbdc52b2676a4b4aa,
+		0x64832009d29bcf57,
+		0x9c4155174a552cc,
+		0x463f9ee03d290810,
+		0xc810936e64982542,
+		0x43b1c289f7bc3ac,
+		0x94877900674181c3,
+		0xc6c67cc37a2a2bbd,
+		0xd667c2055387940f,
+		0xba63a63e94b5ff0,
+		0x99460cc41b8f079f,
+		0x7ff02375ed524bb3,
+		0xea0870b47a8caf0e,
+		0xabcad82633b7bc9d,
+		0x3b8d135261052241,
+		0xfb4515f5e5b0d539,
+		0x3ee8011c2b37f77c,
+		0x19,
+		0x673655aae8be5a8b,
+		0xd510fe714f39fa10,
+		0x2c68a099b51c9e73,
+		0xa667bfa9aa96999d,
+		0x4d67e72f063e2108,
+		0xf84dde3e6acda179,
+		0x40f9cc8c08f80981,
+		0x5ead032050097142,
+		0x6591b02092d671bb,
+		0xe18c71963dd1b7,
+		0x8a21bcd24a14218a,
+		0xadef3740e71c726,
+		0xa37bf67c6f986559,
+		0xc6b16f7ed4fa1b00,
+		0x6a065da88d8bfc3c,
+		0x4cabc0916844b46f,
+		0x407faac0f02e78d1,
+		0x7a786d9cf0852cf,
+		0x42433fb6949a629a,
+		0x891682a147ce43b0,
+		0x26cfd58e7b003b55,
+		0x2bbf0ed7b657acb3,
+		0x19,
+		0x202800f4addbdc87,
+		0xe4b5bdb1cc3504ff,
+		0xbe32b32a825596e7,
+		0x8e0f68c5dc223b9a,
+		0x58022d9e1c256ce3,
+		0x584d29227aa073ac,
+		0x8b9352ad04bef9e7,
+		0xaead42a3f445ecbf,
+		0x3c667a1d833a3cca,
+		0xda6f61838efa1ffe,
+		0xe8f749470bd7c446,
+		0x481ac7746b159c67,
+		0xe367de32f108e278,
+		0x73f260087ad28bec,
+		0x5cfc82216bc1bdca,
+		0xcaccc870a2663a0e,
+		0xdb69cd7b4298c45d,
+		0x7bc9e0c57243e62d,
+		0x3cc51c5d368693ae,
+		0x366b4e8cc068895b,
+		0x2bd18715cdabbca4,
+		0xa752061c4f33b8cf,
+		0x19,
+		0xc5b85bab9e5b3869,
+		0x45245258aec51cf7,
+		0x16e6b8e68b931830,
+		0xe2ae0f051418112c,
+		0x470e26a0093a65b,
+		0x6bef71973a8146ed,
+		0x119265be51812daf,
+		0xb0be7356254bea2e,
+		0x8584defff7589bd7,
+		0x3c5fe4aeb1fb52ba,
+		0x9e7cd88acf543a5e,
+		0xb22d2432b72d5098,
+		0x9e18a487f44d2fe4,
+		0x4b39e14ce22abd3c,
+		0x9e77fde2eb315e0d,
+		0xca5e0385fe67014d,
+		0xc2cb99bf1b6bddb,
+		0x99ec1cd2a4460bfe,
+		0x8577a815a2ff843f,
+		0x7d80a6b4fd6518a5,
+		0xeb6c67123eab62cb,
+		0x8f7851650eca21a5,
+		0x19,
+		0x179be4bba87f0a8c,
+		0xacf63d95d8887355,
+		0x6696670196b0074f,
+		0xd99ddf1fe75085f9,
+		0xc2597881fef0283b,
+		0xcf48395ee6c54f14,
+		0x15226a8e4cd8d3b6,
+		0xc053297389af5d3b,
+		0x2c08893f0d1580e2,
+		0xed3cbcff6fcc5ba,
+		0xc82f510ecf81f6d0,
+		0x11ba9a1b81718c2a,
+		0x9f7d798a3323410c,
+		0xa821855c8c1cf5e5,
+		0x535e8d6fac0031b2,
+		0x404e7c751b634320,
+		0xa729353f6e55d354,
+		0x4db97d92e58bb831,
+		0xb53926c27897bf7d,
+		0x965040d52fe115c5,
+		0x9565fa41ebd31fd7,
+		0xaae4438c877ea8f4,
+		0x19,
+		0x94b06183acb715cc,
+		0x500392ed0d431137,
+		0x861cc95ad5c86323,
+		0x5830a443f86c4ac,
+		0x3b68225874a20a7c,
+		0x10b3309838e236fb,
+		0x9b77fc8bcd559e2c,
+		0xbdecf5e0cb9cb213,
+		0x30276f1221ace5fa,
+		0x7935dd342764a144,
+		0xeac6db520bb03708,
+		0x37f4e36af6073c6e,
+		0x4edc0918210800e9,
+		0xc44998e99eae4188,
+		0x9f4310d05d068338,
+		0x9ec7fe4350680f29,
+		0xc5b2c1fdc0b50874,
+		0xa01920c5ef8b2ebe,
+		0x59fa6f8bd91d58ba,
+		0x8bfc9eb89b515a82,
+		0xbe86a7a2555ae775,
+		0xcbb8bbaa3810babf,
+		0x19,
+		0x7186a80551025f8f,
+		0x622247557e9b5371,
+		0xc4cbe326d1ad9742,
+		0x55f1523ac6a23ea2,
+		0xa13dfe77a3d52f53,
+		0xe30750b6301c0452,
+		0x8bd488070a3a32b,
+		0xcd800caef5b72ae3,
+		0x83329c90f04233ce,
+		0xb5b99e6664a0a3ee,
+		0x6b0731849e200a7f,
+		0x577f9a9e7ee3f9c2,
+		0x88c522b949ace7b1,
+		0x82f07007c8b72106,
+		0x8283d37c6675b50e,
+		0x98b074d9bbac1123,
+		0x75c56fb7758317c1,
+		0xfed24e206052bc72,
+		0x26d7c3d1bc07dae5,
+		0xf88c5e441e28dbb4,
+		0x4fe27f9f96615270,
+		0x514d4ba49c2b14fe,
+		0x19,
+		0xec3fabc192b01799,
+		0x382b38cee8ee5375,
+		0x3bfb6c3f0e616572,
+		0x514abd0cf6c7bc86,
+		0x47521b1361dcc546,
+		0x178093843f863d14,
+		0xad1003c5d28918e7,
+		0x738450e42495bc81,
+		0xaf947c59af5e4047,
+		0x4653fb0685084ef2,
+		0x57fde2062ae35bf,
+		0xf02a3ac068ee110b,
+		0xa3630dafb8ae2d7,
+		0xce0dc874eaf9b55c,
+		0x9a95f6cff5b55c7e,
+		0x626d76abfed00c7b,
+		0xa0c1cf1251c204ad,
+		0xdaebd3006321052c,
+		0x3d4bd48b625a8065,
+		0x7f1e584e071f6ed2,
+		0x720574f0501caed3,
+		0xe3260ba93d23540a,
+		0x19,
+		0xe376678d843ce55e,
+		0x66f3860d7514e7fc,
+		0x7817f3dfff8b4ffa,
+		0x3929624a9def725b,
+		0x126ca37f215a80a,
+		0xfce2f5d02762a303,
+		0x1bc927375febbad7,
+		0x85b481e5243f60bf,
+		0x2d3c5f42a39c91a0,
+		0x811719919351ae8,
+		0xf669de0add993131,
+		0xab1cbd41d8c1e335,
+		0x9322ed4c0bc2df01,
+		0x51c3c0983d4284e5,
+		0x94178e291145c231,
+		0xfd0f1a973d6b2085,
+		0xd427ad96e2b39719,
+		0x8a52437fecaac06b,
+		0xdc20ee4b8c4c9a80,
+		0xa2c98e9549da2100,
+		0x1603fe12613db5b6,
+		0xe174929433c5505,
+		0x19,
+		0x7de38bae084da92d,
+		0x5b848442237e8a9b,
+		0xf6c705da84d57310,
+		0x31e6a4bdb6a49017,
+		0x889489706e5c5c0f,
+		0xe4a205459692a1b,
+		0xbac3fa75ee26f299,
+		0x5f5894f4057d755e,
+		0xb0dc3ecd724bb076,
+		0x5e34d8554a6452ba,
+		0x4f78fd8c1fdcc5f,
+		0x3d4eab2b8ef5f796,
+		0xcfff421583896e22,
+		0x4143cb32d39ac3d9,
+		0x22365051b78a5b65,
+		0x6f7fd010d027c9b6,
+		0xd9dd36fba77522ab,
+		0xa44cf1cb33e37165,
+		0x3fc83d3038c86417,
+		0xc4588d418e88d270,
+		0xce1320f10ab80fe2,
+		0xdb5eadbbec18de5d,
+		0x19,
+		0x4dd19c38779512ea,
+		0xdb79ba02704620e9,
+		0x92a29a3675a5d2be,
+		0xd5177029fe495166,
+		0xd32b3298a13330c1,
+		0x251c4a3eb2c5f8fd,
+		0xe1c48b26e0d98825,
+		0x3301d3362a4ffccb,
+		0x9bb6c88de8cd178,
+		0xdc05b676564f538a,
+		0x60192d883e473fee,
+		0x1183dfce7c454afd,
+		0x21cea4aa3d3ed949,
+		0xfce6f70303f2304,
+		0x19557d34b55551be,
+		0x4c56f689afc5bbc9,
+		0xa1e920844334f944,
+		0xbad66d423d2ec861,
+		0xf318c785dc9e0479,
+		0x99e2032e765ddd81,
+		0x400ccc9906d66f45,
+		0xe1197454db2e0dd9,
+		0x19,
+		0x16b9774801ac44a0,
+		0x3cb8411e786d3c8e,
+		0xa86e9cf505072491,
+		0x178928152e109ae,
+		0x5317b905a6e1ab7b,
+		0xda20b3be7f53d59f,
+		0xcb97dedecebee9ad,
+		0x4bd545218c59f58d,
+		0x77dc8d856c05a44a,
+		0x87948589e4f243fd,
+		0x7e5217af969952c2,
+		0x84d1ecc4d53d2ff1,
+		0xd8af8b9ceb4e11b6,
+		0x335856bb527b52f4,
+		0xc756f17fb59be595,
+		0xc0654e4ea5553a78,
+		0x9e9a46b61f2ea942,
+		0x14fc8b5b3b809127,
+		0xd7009f0f103be413,
+		0x3e0ee7b7a9fb4601,
+		0xa74e888922085ed7,
+		0xe80a7cde3d4ac526,
+		0x19,
+		0xbc58987d06a84e4d,
+		0xb5d420244c9cae3,
+		0xa3c4711b938c02c0,
+		0x3aace640a3e03990,
+		0x865a0f3249aacd8a,
+		0x8d00b2a7dbed06c7,
+		0x6eacb905beb7e2f8,
+		0x45322b216ec3ec7,
+		0xeb9de00d594828e6,
+		0x88c5f20df9e5c26,
+		0xf555f4112b19781f,
+		0x238aa6daa612186d,
+		0x9137a5c630bad4b4,
+		0xc7db3817870c5eda,
+		0x217e4f04e5718dc9,
+		0xcae814e2817bd99d,
+		0xe3292e7ab770a8ba,
+		0x7bb36ef70b6b9482,
+		0x3c7835fb85bca2d3,
+		0xfe2cdf8ee3c25e86,
+		0x61b3915ad7274b20,
+		0xeab75ca7c918e4ef,
+		0x19,
+		0xa8cedbff1813d3a7,
+		0x50dcaee0fd27d164,
+		0xf1cb02417e23bd82,
+		0xfaf322786e2abe8b,
+		0x937a4315beb5d9b6,
+		0x1b18992921a11d85,
+		0x7d66c4368b3c497b,
+		0xe7946317a6b4e99,
+		0xbe4430134182978b,
+		0x3771e82493ab262d,
+		0xa671690d8095ce82,
+		0xd6e15ffc055e154e,
+		0xec67881f381a32bf,
+		0xfbb1196092bf409c,
+		0xdc9d2e07830ba226,
+		0x698ef3245ff7988,
+		0x194fae2974f8b576,
+		0x7a5d9bea6ca4910e,
+		0x7aebfea95ccdd1c9,
+		0xf9bd38a67d5f0e86,
+		0xfa65539de65492d8,
+		0xf0dfcbe7653ff787,
+		0x19,
+		0xb035585f6e929d9d,
+		0xba1579c7e219b954,
+		0xcb201cf846db4ba3,
+		0x287bf9177372cf45,
+		0xa350e4f61147d0a6,
+		0xd5d0ecfb50bcff99,
+		0x2e166aa6c776ed21,
+		0xe1e66c991990e282,
+		0x662b329b01e7bb38,
+		0x8aa674b36144d9a9,
+		0xcbabf78f97f95e65,
+		0xbd87ad390420258,
+		0xad8617bca9e33c8,
+		0xc00ad377a1e2666,
+		0xac6fc58b3f0518f,
+		0xc0cc8a892cc4173,
+		0xc210accb117bc21,
+		0xb73630dbb46ca18,
+		0xc8be4920cbd4a54,
+		0xbfe877a21be1690,
+		0xae790559b0ded81,
+		0xbf50db2f8d6ce31,
+		0x19,
+		0xeec24b15a06b53fe,
+		0xc8a7aa07c5633533,
+		0xefe9c6fa4311ad51,
+		0xb9173f13977109a1,
+		0x69ce43c9cc94aedc,
+		0xecf623c9cd118815,
+		0x28625def198c33c7,
+		0xccfc5f7de5c3636a,
+		0xf5e6c40f1621c299,
+		0xcec0e58c34cb64b1,
+		0xa868ea113387939f,
+		0xcf29427ff7c58,
+		0xbd9b3cf49eec8,
+		0xd1dc8aa81fb26,
+		0xbc792d5c394ef,
+		0xd2ae0b2266453,
+		0xd413f12c496c1,
+		0xc84128cfed618,
+		0xdb5ebd48fc0d4,
+		0xd1b77326dcb90,
+		0xbeb0ccc145421,
+		0xd10e5b22b11d1,
+		0x19,
+		0xd8dddbdc5ce4ef45,
+		0xacfc51de8131458c,
+		0x146bb3c0fe499ac0,
+		0x9e65309f15943903,
+		0x80d0ad980773aa70,
+		0xf97817d4ddbf0607,
+		0xe4626620a75ba276,
+		0xdfdc7fd6fc74f66,
+		0xf464864ad6f2bb93,
+		0x2d55e52a5d44414,
+		0xdd8de62487c40925,
+		0xe24c99adad8,
+		0xcf389ed4bc8,
+		0xe580cbf6966,
+		0xcde5fd7e04f,
+		0xe63628041b3,
+		0xe7e81a87361,
+		0xdabe78f6d98,
+		0xefb14cac554,
+		0xe5574743b10,
+		0xd05709f42c1,
+		0xe4690c96af1,
+		0x19,
+		0xc15acf44759545a3,
+		0xcbfdcf39869719d4,
+		0x33f62042e2f80225,
+		0x2599c5ead81d8fa3,
+		0xb306cb6c1d7c8d0,
+		0x658c80d3df3729b1,
+		0xe8d1b2b21b41429c,
+		0xa1b67f09d4b3ccb8,
+		0xe1adf8b84437180,
+		0xd593a5e584af47b,
+		0xa023d94c56e151c7,
+		0xf7157bc98,
+		0xe3006d948,
+		0xfa65811e6,
+		0xe0d127e2f,
+		0xfc18bfe53,
+		0xfd002d901,
+		0xeed6461d8,
+		0x1068562754,
+		0xfa0236f50,
+		0xe3af13ee1,
+		0xfa460f6d1,
+		0x19,
+		0x49026cc3a4afc5a6,
+		0xe06dff00ab25b91b,
+		0xab38c561e8850ff,
+		0x92c3c8275e105eeb,
+		0xb65256e546889bd0,
+		0x3c0468236ea142f6,
+		0xee61766b889e18f2,
+		0xa206f41b12c30415,
+		0x2fe9d756c9f12d1,
+		0xe9633210630cbf12,
+		0x1ffea9fe85a0b0b1,
+		0x11131738,
+		0xf56d588,
+		0x11050f86,
+		0xf848f4f,
+		0x111527d3,
+		0x114369a1,
+		0x106f2f38,
+		0x11e2ca94,
+		0x110a29f0,
+		0xfa9f5c1,
+		0x10f625d1,
+		0x19,
+		0x81d1ae8cc50240f3,
+		0xf4c77a079a4607d7,
+		0xed446b2315e3efc1,
+		0xb0a6b70915178c3,
+		0xb11ff3e089f15d9a,
+		0x1d4dba0b7ae9cc18,
+		0x65d74e2f43b48d05,
+		0xa2df8c6b8ae0804a,
+		0xa4e6f0a8c33348a6,
+		0xc0a26efc7be5669b,
+		0xa6b6582c547d0d60,
+		0x11f718,
+		0x10b6c8,
+		0x134a96,
+		0x10cf7f,
+		0x124d03,
+		0x13f8a1,
+		0x117c58,
+		0x132c94,
+		0x134fc0,
+		0x10a091,
+		0x128961,
+		0x19,
+		0x84afc741f1c13213,
+		0x2f8f43734fc906f3,
+		0xde682d72da0a02d9,
+		0xbb005236adb9ef2,
+		0x5bdf35c10a8b5624,
+		0x739a8a343950010,
+		0x52f515f44785cfbc,
+		0xcbaf4e5d82856c60,
+		0xac9ea09074e3e150,
+		0x8f0fa011a2035fb0,
+		0x1a37905d8450904a,
+		0x1300,
+		0x1750,
+		0x114e,
+		0x131f,
+		0x167b,
+		0x1371,
+		0x1230,
+		0x182c,
+		0x1368,
+		0xf31,
+		0x15c9,
+		0x19,
+		0x3abeb80def61cc85,
+		0x9d19c9dd4eac4133,
+		0x75a652d9641a985,
+		0x9daf69ae1b67e667,
+		0x364f71da77920a18,
+		0x50bd769f745c95b1,
+		0xf223d1180dbbf3fc,
+		0x2f885e584e04aa99,
+		0xb69a0fa70aea684a,
+		0x9584acaa6e062a0,
+		0xbc051640145b19b,
+		0x14,
+		0x22,
+		0x12,
+		0x27,
+		0xd,
+		0xd,
+		0x1c,
+		0x2,
+		0x10,
+		0x29,
+		0xf,
+	}
+
+	// C is a constant array of element
+	C []*ffg.Element
+	// M is a matrix
+	M [][]*ffg.Element
+	// P is a matrix
+	P [][]*ffg.Element
+	// S is a array of element
+	S []*ffg.Element
+)
+
+func init() {
+	for i := 0; i < len(c); i++ {
+		C = append(C, ffg.NewElementFromUint64(c[i]))
+	}
+
+	for i := 0; i < len(s); i++ {
+		S = append(S, ffg.NewElementFromUint64(s[i]))
+	}
+
+	for i := 0; i < mLen; i++ {
+		var (
+			mRow []*ffg.Element
+			pRow []*ffg.Element
+		)
+		for j := 0; j < mLen; j++ {
+			ele := ffg.NewElementFromUint64(mcirc[(i-j+mLen)%mLen])
+			if i == j {
+				ele = ffg.NewElementFromUint64(mcirc[0] + mdiag[i])
+			}
+			mRow = append(mRow, ele)
+			pRow = append(pRow, ffg.NewElementFromUint64(p[i][j]))
+		}
+		M = append(M, mRow)
+		P = append(P, pRow)
+	}
+}

goldenposeidon/poseidon.go

@@ -0,0 +1,107 @@
+package poseidon
+
+import (
+	"math/big"
+
+	"github.com/iden3/go-iden3-crypto/ffg"
+)
+
+func zero() *ffg.Element {
+	return ffg.NewElement()
+}
+
+var big7 = big.NewInt(7)
+
+// exp7 performs x^7 mod p
+func exp7(a *ffg.Element) {
+	a.Exp(*a, big7)
+}
+
+// exp7state perform exp7 for whole state
+func exp7state(state []*ffg.Element) {
+	for i := 0; i < len(state); i++ {
+		exp7(state[i])
+	}
+}
+
+// ark computes Add-Round Key, from the paper https://eprint.iacr.org/2019/458.pdf
+func ark(state []*ffg.Element, it int) {
+	for i := 0; i < len(state); i++ {
+		state[i].Add(state[i], C[it+i])
+	}
+}
+
+// mix returns [[matrix]] * [vector]
+func mix(state []*ffg.Element, opt bool) []*ffg.Element {
+	mul := zero()
+	newState := make([]*ffg.Element, mLen)
+	for i := 0; i < mLen; i++ {
+		newState[i] = zero()
+	}
+	for i := 0; i < mLen; i++ {
+		newState[i].SetUint64(0)
+		for j := 0; j < mLen; j++ {
+			if opt {
+				mul.Mul(P[j][i], state[j])
+			} else {
+				mul.Mul(M[j][i], state[j])
+			}
+			newState[i].Add(newState[i], mul)
+		}
+	}
+	return newState
+}
+
+// Hash computes the hash for the given inputs
+func Hash(inpBI [NROUNDSF]uint64, capBI [CAPLEN]uint64) ([CAPLEN]uint64, error) {
+	state := make([]*ffg.Element, mLen)
+	for i := 0; i < NROUNDSF; i++ {
+		state[i] = ffg.NewElement().SetUint64(inpBI[i])
+	}
+	for i := 0; i < CAPLEN; i++ {
+		state[i+NROUNDSF] = ffg.NewElement().SetUint64(capBI[i])
+	}
+
+	for i := 0; i < mLen; i++ {
+		state[i].Add(state[i], C[i])
+	}
+
+	for r := 0; r < NROUNDSF/2; r++ {
+		exp7state(state)
+		ark(state, (r+1)*mLen)
+		state = mix(state, r == NROUNDSF/2-1)
+	}
+
+	for r := 0; r < NROUNDSP; r++ {
+		exp7(state[0])
+		state[0].Add(state[0], C[(NROUNDSF/2+1)*mLen+r])
+
+		s0 := zero()
+		mul := zero()
+		mul.Mul(S[(mLen*2-1)*r], state[0])
+		s0.Add(s0, mul)
+		for i := 1; i < mLen; i++ {
+			mul.Mul(S[(mLen*2-1)*r+i], state[i])
+			s0.Add(s0, mul)
+			mul.Mul(S[(mLen*2-1)*r+mLen+i-1], state[0])
+			state[i].Add(state[i], mul)
+		}
+		state[0] = s0
+	}
+
+	for r := 0; r < NROUNDSF/2; r++ {
+		exp7state(state)
+		if r < NROUNDSF/2-1 {
+			ark(state, (NROUNDSF/2+1+r)*mLen+NROUNDSP)
+		}
+
+		state = mix(state, false)
+	}
+
+	return [CAPLEN]uint64{
+		state[0].ToUint64Regular(),
+		state[1].ToUint64Regular(),
+		state[2].ToUint64Regular(),
+		state[3].ToUint64Regular(),
+	}, nil
+}

goldenposeidon/poseidon_test.go

@@ -0,0 +1,107 @@
+package poseidon
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+const prime uint64 = 18446744069414584321
+
+func TestPoseidonHashCompare(t *testing.T) {
+	b0 := uint64(0)
+	b1 := uint64(1)
+	bm1 := prime - 1
+	bM := prime
+
+	h, err := Hash([NROUNDSF]uint64{b0, b0, b0, b0, b0, b0, b0, b0},
+		[CAPLEN]uint64{b0, b0, b0, b0})
+	assert.Nil(t, err)
+	assert.Equal(t,
+		[CAPLEN]uint64{
+			4330397376401421145,
+			14124799381142128323,
+			8742572140681234676,
+			14345658006221440202,
+		}, h,
+	)
+
+	h, err = Hash([NROUNDSF]uint64{b1, b1, b1, b1, b1, b1, b1, b1},
+		[CAPLEN]uint64{b1, b1, b1, b1})
+	assert.Nil(t, err)
+	assert.Equal(t,
+		[CAPLEN]uint64{
+			16428316519797902711,
+			13351830238340666928,
+			682362844289978626,
+			12150588177266359240,
+		}, h,
+	)
+
+	h, err = Hash([NROUNDSF]uint64{b1, b1, b1, b1, b1, b1, b1, b1},
+		[CAPLEN]uint64{b1, b1, b1, b1})
+	assert.Nil(t, err)
+	assert.Equal(t,
+		[CAPLEN]uint64{
+			16428316519797902711,
+			13351830238340666928,
+			682362844289978626,
+			12150588177266359240,
+		}, h,
+	)
+
+	h, err = Hash(
+		[NROUNDSF]uint64{bm1, bm1, bm1, bm1, bm1, bm1, bm1, bm1},
+		[CAPLEN]uint64{bm1, bm1, bm1, bm1},
+	)
+	assert.Nil(t, err)
+	assert.Equal(t,
+		[CAPLEN]uint64{
+			13691089994624172887,
+			15662102337790434313,
+			14940024623104903507,
+			10772674582659927682,
+		}, h,
+	)
+
+	h, err = Hash([NROUNDSF]uint64{bM, bM, bM, bM, bM, bM, bM, bM},
+		[CAPLEN]uint64{b0, b0, b0, b0})
+	assert.Nil(t, err)
+	assert.Equal(t,
+		[CAPLEN]uint64{
+			4330397376401421145,
+			14124799381142128323,
+			8742572140681234676,
+			14345658006221440202,
+		}, h,
+	)
+
+	h, err = Hash([NROUNDSF]uint64{
+		uint64(923978),
+		uint64(235763497586),
+		uint64(9827635653498),
+		uint64(112870),
+		uint64(289273673480943876),
+		uint64(230295874986745876),
+		uint64(6254867324987),
+		uint64(2087),
+	}, [CAPLEN]uint64{b0, b0, b0, b0})
+	assert.Nil(t, err)
+	assert.Equal(t,
+		[CAPLEN]uint64{
+			1892171027578617759,
+			984732815927439256,
+			7866041765487844082,
+			8161503938059336191,
+		}, h,
+	)
+}
+
+func BenchmarkNeptuneHash(b *testing.B) {
+	inp := [NROUNDSF]uint64{1, 2, 3, 4, 5, 6, 7, 8}
+	_cap := [CAPLEN]uint64{10, 11, 12, 13}
+
+	for i := 0; i < b.N; i++ {
+		_, _ = Hash(inp, _cap)
+	}
+}

keccak256/keccac256.go

@@ -0,0 +1,14 @@
+package keccak256
+
+import (
+	"golang.org/x/crypto/sha3"
+)
+
+// Hash generates a Keccak256 hash from a byte array
+func Hash(data ...[]byte) []byte {
+	hash := sha3.NewLegacyKeccak256()
+	for _, d := range data {
+		hash.Write(d) //nolint:errcheck,gosec
+	}
+	return hash.Sum(nil)
+}

keccak256/keccac256_test.go

@@ -0,0 +1,21 @@
+package keccak256
+
+import (
+	"encoding/hex"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestKeccak256(t *testing.T) {
+	const SEED = "mimc"
+	res := Hash([]byte(SEED))
+	assert.Equal(t,
+		"b6e489e6b37224a50bebfddbe7d89fa8fdcaa84304a70bd13f79b5d9f7951e9e",
+		hex.EncodeToString(res))
+	c := new(big.Int).SetBytes(Hash([]byte(SEED)))
+	assert.Equal(t,
+		"82724731331859054037315113496710413141112897654334566532528783843265082629790",
+		c.String())
+}

mimc7/mimc7.go

@@ -4,9 +4,9 @@ import (
 	"errors"
 	"math/big"
 
-	"github.com/ethereum/go-ethereum/crypto"
 	_constants "github.com/iden3/go-iden3-crypto/constants"
 	"github.com/iden3/go-iden3-crypto/ff"
+	"github.com/iden3/go-iden3-crypto/keccak256"
 	"github.com/iden3/go-iden3-crypto/utils"
 )
 
@@ -23,24 +23,24 @@ type constantsData struct {
 }
 
 func generateConstantsData() constantsData {
-	var constants constantsData
+	var consts constantsData
 
-	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.Q)
+	consts.seedHash = new(big.Int).SetBytes(keccak256.Hash([]byte(SEED)))
+	c := new(big.Int).SetBytes(keccak256.Hash([]byte(SEED + "_iv")))
+	consts.iv = new(big.Int).Mod(c, _constants.Q)
 
-	constants.nRounds = 91
-	cts := getConstants(SEED, constants.nRounds)
-	constants.cts = cts
-	return constants
+	consts.nRounds = 91
+	cts := getConstants(SEED, consts.nRounds)
+	consts.cts = cts
+	return consts
 }
 
 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)))
+	c := new(big.Int).SetBytes(keccak256.Hash([]byte(seed)))
 	for i := 1; i < nRounds; i++ {
-		c = new(big.Int).SetBytes(crypto.Keccak256(c.Bytes()))
+		c = new(big.Int).SetBytes(keccak256.Hash(c.Bytes()))
 
 		n := new(big.Int).Mod(c, _constants.Q)
 		cts[i] = ff.NewElement().SetBigInt(n)

mimc7/mimc7_test.go

@@ -5,21 +5,9 @@ import (
 	"math/big"
 	"testing"
 
-	"github.com/ethereum/go-ethereum/crypto"
 	"github.com/stretchr/testify/assert"
 )
 
-func TestKeccak256(t *testing.T) {
-	res := crypto.Keccak256([]byte(SEED))
-	assert.Equal(t,
-		"b6e489e6b37224a50bebfddbe7d89fa8fdcaa84304a70bd13f79b5d9f7951e9e",
-		hex.EncodeToString(res))
-	c := new(big.Int).SetBytes(crypto.Keccak256([]byte(SEED)))
-	assert.Equal(t,
-		"82724731331859054037315113496710413141112897654334566532528783843265082629790",
-		c.String())
-}
-
 func TestMIMC7Generic(t *testing.T) {
 	b1 := big.NewInt(int64(1))
 	b2 := big.NewInt(int64(2))
@@ -36,7 +24,7 @@ func TestMIMC7Generic(t *testing.T) {
 	assert.Nil(t, err)
 	assert.Equal(t,
 		"6464402164086696096195815557694604139393321133243036833927490113253119343397",
-		(*big.Int)(hg).String())
+		hg.String())
 }
 
 func TestMIMC7(t *testing.T) {
@@ -51,7 +39,7 @@ 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()),
+	assert.Equal(t, "0x"+hex.EncodeToString(h1.Bytes()),
 		"0x237c92644dbddb86d8a259e0e923aaab65a93f1ec5758b8799988894ac0958fd")
 
 	// h2a, hash of 2 elements
@@ -60,7 +48,7 @@ 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()),
+	assert.Equal(t, "0x"+hex.EncodeToString(h2a.Bytes()),
 		"0x067f3202335ea256ae6e6aadcd2d5f7f4b06a00b2d1e0de903980d5ab552dc70")
 
 	// h2b, hash of 2 elements
@@ -68,13 +56,13 @@ func TestMIMC7(t *testing.T) {
 
 	mh2b := MIMC7Hash(b12, b45)
 	assert.Nil(t, err)
-	assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(mh2b).Bytes()),
+	assert.Equal(t, "0x"+hex.EncodeToString(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()),
+	assert.Equal(t, "0x"+hex.EncodeToString(h2b.Bytes()),
 		"0x15ff7fe9793346a17c3150804bcb36d161c8662b110c50f55ccb7113948d8879")
 
 	// h4, hash of 4 elements
@@ -83,7 +71,7 @@ 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()),
+	assert.Equal(t, "0x"+hex.EncodeToString(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.") //nolint:lll
@@ -101,6 +89,6 @@ func BenchmarkMIMC7(b *testing.B) {
 	bigArray4 := []*big.Int{b12, b45, b78, b41}
 
 	for i := 0; i < b.N; i++ {
-		Hash(bigArray4, nil) //nolint:errcheck,gosec
+		_, _ = Hash(bigArray4, nil)
 	}
 }

poseidon/poseidon.go

@@ -9,41 +9,48 @@ import (
 	"github.com/iden3/go-iden3-crypto/utils"
 )
 
-const NROUNDSF = 8 //nolint:golint
+// NROUNDSF constant from Poseidon paper
+const NROUNDSF = 8
 
-var NROUNDSP = []int{56, 57, 56, 60, 60, 63, 64, 63} //nolint:golint
+// NROUNDSP constant from Poseidon paper
+var NROUNDSP = []int{56, 57, 56, 60, 60, 63, 64, 63, 60, 66, 60, 65, 70, 60, 64, 68}
+
+const spongeChunkSize = 31
+const spongeInputs = 16
 
 func zero() *ff.Element {
 	return ff.NewElement()
 }
 
+var big5 = big.NewInt(5)
+
+// exp5 performs x^5 mod p
+// https://eprint.iacr.org/2019/458.pdf page 8
+func exp5(a *ff.Element) {
+	a.Exp(*a, big5)
+}
+
+// exp5state perform exp5 for whole state
+func exp5state(state []*ff.Element) {
+	for i := 0; i < len(state); i++ {
+		exp5(state[i])
+	}
+}
+
 // ark computes Add-Round Key, from the paper https://eprint.iacr.org/2019/458.pdf
-func ark(state []*ff.Element, c []*ff.Element, it int) {
+func ark(state, c []*ff.Element, it int) {
 	for i := 0; i < len(state); i++ {
 		state[i].Add(state[i], c[it+i])
 	}
 }
 
-// exp5 performs x^5 mod p
-// https://eprint.iacr.org/2019/458.pdf page 8
-func exp5(a *ff.Element) {
-	a.Exp(*a, 5)
-}
-
-// sbox https://eprint.iacr.org/2019/458.pdf page 6
-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 {
-		exp5(state[0])
-	}
-}
-
 // mix returns [[matrix]] * [vector]
-func mix(state []*ff.Element, newState []*ff.Element, m [][]*ff.Element) {
+func mix(state []*ff.Element, t int, m [][]*ff.Element) []*ff.Element {
 	mul := zero()
+	newState := make([]*ff.Element, t)
+	for i := 0; i < t; i++ {
+		newState[i] = zero()
+	}
 	for i := 0; i < len(state); i++ {
 		newState[i].SetUint64(0)
 		for j := 0; j < len(state); j++ {
@@ -51,41 +58,185 @@ func mix(state []*ff.Element, newState []*ff.Element, m [][]*ff.Element) {
 			newState[i].Add(newState[i], mul)
 		}
 	}
+	return newState
 }
 
 // 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 len(inpBI) == 0 || len(inpBI) > len(NROUNDSP) {
+		return nil, fmt.Errorf("invalid inputs length %d, max %d", len(inpBI), len(NROUNDSP))
 	}
-	if !utils.CheckBigIntArrayInField(inpBI[:]) {
+	if !utils.CheckBigIntArrayInField(inpBI) {
 		return nil, errors.New("inputs values not inside Finite Field")
 	}
-	inp := utils.BigIntArrayToElementArray(inpBI[:])
-	state := make([]*ff.Element, t)
-	copy(state[:], inp[:])
-	state[len(state)-1] = zero()
+	inp := utils.BigIntArrayToElementArray(inpBI)
 
 	nRoundsF := NROUNDSF
 	nRoundsP := NROUNDSP[t-2]
+	C := c.c[t-2]
+	S := c.s[t-2]
+	M := c.m[t-2]
+	P := c.p[t-2]
 
-	newState := make([]*ff.Element, t)
-	for i := 0; i < t; i++ {
-		newState[i] = zero()
+	state := make([]*ff.Element, t)
+	state[0] = zero()
+	copy(state[1:], inp)
+
+	ark(state, C, 0)
+
+	for i := 0; i < nRoundsF/2-1; i++ {
+		exp5state(state)
+		ark(state, C, (i+1)*t)
+		state = mix(state, t, M)
 	}
+	exp5state(state)
+	ark(state, C, (nRoundsF/2)*t)
+	state = mix(state, t, P)
 
-	// ARK --> SBox --> M, https://eprint.iacr.org/2019/458.pdf pag.5
-	for i := 0; i < nRoundsF+nRoundsP; i++ {
-		ark(state, c.c[t-2], i*t)
-		sbox(nRoundsF, nRoundsP, state, i)
-		if i < nRoundsF+nRoundsP-1 {
-			mix(state, newState, c.m[t-2])
-			state, newState = newState, state
+	mul := zero()
+	for i := 0; i < nRoundsP; i++ {
+		exp5(state[0])
+		state[0].Add(state[0], C[(nRoundsF/2+1)*t+i])
+
+		mul.SetZero()
+		newState0 := zero()
+		for j := 0; j < len(state); j++ {
+			mul.Mul(S[(t*2-1)*i+j], state[j])
+			newState0.Add(newState0, mul)
 		}
+
+		for k := 1; k < t; k++ {
+			mul.SetZero()
+			state[k] = state[k].Add(state[k], mul.Mul(state[0], S[(t*2-1)*i+t+k-1]))
+		}
+		state[0] = newState0
 	}
+
+	for i := 0; i < nRoundsF/2-1; i++ {
+		exp5state(state)
+		ark(state, C, (nRoundsF/2+1)*t+nRoundsP+i*t)
+		state = mix(state, t, M)
+	}
+	exp5state(state)
+	state = mix(state, t, M)
+
 	rE := state[0]
 	r := big.NewInt(0)
 	rE.ToBigIntRegular(r)
 	return r, nil
 }
+
+// HashBytes returns a sponge hash of a msg byte slice split into blocks of 31 bytes
+func HashBytes(msg []byte) (*big.Int, error) {
+	return HashBytesX(msg, spongeInputs)
+}
+
+// HashBytesX returns a sponge hash of a msg byte slice split into blocks of 31 bytes
+func HashBytesX(msg []byte, frameSize int) (*big.Int, error) {
+	if frameSize < 2 || frameSize > 16 {
+		return nil, errors.New("incorrect frame size")
+	}
+
+	// not used inputs default to zero
+	inputs := make([]*big.Int, frameSize)
+	for j := 0; j < frameSize; j++ {
+		inputs[j] = new(big.Int)
+	}
+	dirty := false
+	var hash *big.Int
+	var err error
+
+	k := 0
+	for i := 0; i < len(msg)/spongeChunkSize; i++ {
+		dirty = true
+		inputs[k].SetBytes(msg[spongeChunkSize*i : spongeChunkSize*(i+1)])
+		if k == frameSize-1 {
+			hash, err = Hash(inputs)
+			dirty = false
+			if err != nil {
+				return nil, err
+			}
+			inputs = make([]*big.Int, frameSize)
+			inputs[0] = hash
+			for j := 1; j < frameSize; j++ {
+				inputs[j] = new(big.Int)
+			}
+			k = 1
+		} else {
+			k++
+		}
+	}
+
+	if len(msg)%spongeChunkSize != 0 {
+		// the last chunk of the message is less than 31 bytes
+		// zero padding it, so that 0xdeadbeaf becomes
+		// 0xdeadbeaf000000000000000000000000000000000000000000000000000000
+		var buf [spongeChunkSize]byte
+		copy(buf[:], msg[(len(msg)/spongeChunkSize)*spongeChunkSize:])
+		inputs[k] = new(big.Int).SetBytes(buf[:])
+		dirty = true
+	}
+
+	if dirty {
+		// we haven't hashed something in the main sponge loop and need to do hash here
+		hash, err = Hash(inputs)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	return hash, nil
+}
+
+// SpongeHash returns a sponge hash of inputs (using Poseidon with frame size of 16 inputs)
+func SpongeHash(inputs []*big.Int) (*big.Int, error) {
+	return SpongeHashX(inputs, spongeInputs)
+}
+
+// SpongeHashX returns a sponge hash of inputs using Poseidon with configurable frame size
+func SpongeHashX(inputs []*big.Int, frameSize int) (*big.Int, error) {
+	if frameSize < 2 || frameSize > 16 {
+		return nil, errors.New("incorrect frame size")
+	}
+
+	// not used frame default to zero
+	frame := make([]*big.Int, frameSize)
+	for j := 0; j < frameSize; j++ {
+		frame[j] = new(big.Int)
+	}
+	dirty := false
+	var hash *big.Int
+	var err error
+
+	k := 0
+	for i := 0; i < len(inputs); i++ {
+		dirty = true
+		frame[k] = inputs[i]
+		if k == frameSize-1 {
+			hash, err = Hash(frame)
+			dirty = false
+			if err != nil {
+				return nil, err
+			}
+			frame = make([]*big.Int, frameSize)
+			frame[0] = hash
+			for j := 1; j < frameSize; j++ {
+				frame[j] = new(big.Int)
+			}
+			k = 1
+		} else {
+			k++
+		}
+	}
+
+	if dirty {
+		// we haven't hashed something in the main sponge loop and need to do hash here
+		hash, err = Hash(frame)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	return hash, nil
+}

poseidon/poseidon_wrapper.go

@@ -0,0 +1,60 @@
+package poseidon
+
+import (
+	"bytes"
+	"errors"
+	"hash"
+)
+
+type hasher struct {
+	buf       *bytes.Buffer
+	frameSize int
+}
+
+// Sum returns the Poseidon hash of the input bytes.
+// use frame size of 16 inputs by default
+func Sum(b []byte) []byte {
+	h, _ := New(16)
+	h.Write(b)
+	return h.Sum(nil)
+}
+
+// New returns a new hash.Hash computing the Poseidon hash.
+func New(frameSize int) (hash.Hash, error) {
+	if frameSize < 2 || frameSize > 16 {
+		return nil, errors.New("incorrect frame size")
+	}
+	return &hasher{
+		buf:       bytes.NewBuffer([]byte{}),
+		frameSize: frameSize,
+	}, nil
+}
+
+// Write (via the embedded io.Writer interface) adds more data to the running hash.
+func (h *hasher) Write(p []byte) (n int, err error) {
+	return h.buf.Write(p)
+}
+
+// Sum returns the Poseidon digest of the data.
+func (h *hasher) Sum(b []byte) []byte {
+	hahs, err := HashBytesX(h.buf.Bytes(), h.frameSize)
+	if err != nil {
+		panic(err)
+	}
+	return append(b, hahs.Bytes()...)
+}
+
+// Reset resets the Hash to its initial state.
+func (h *hasher) Reset() {
+	h.buf.Reset()
+}
+
+// Size returns the number of bytes Sum will return.
+func (h *hasher) Size() int {
+	return 32
+}
+
+// BlockSize returns the hash block size.
+func (h *hasher) BlockSize() int {
+	return spongeChunkSize
+}

utils/utils.go

@@ -14,7 +14,7 @@ import (
 // NewIntFromString creates a new big.Int from a decimal integer encoded as a
 // string.  It will panic if the string is not a decimal integer.
 func NewIntFromString(s string) *big.Int {
-	v, ok := new(big.Int).SetString(s, 10)
+	v, ok := new(big.Int).SetString(s, 10) //nolint:gomnd
 	if !ok {
 		panic(fmt.Sprintf("Bad base 10 string %s", s))
 	}
@@ -46,7 +46,7 @@ func SetBigIntFromLEBytes(v *big.Int, leBuf []byte) *big.Int {
 	return v.SetBytes(beBuf)
 }
 
-// Hex is a byte slice type that can be marshalled and unmarshaled in hex
+// Hex is a byte slice type that can be marshaled and unmarshaled in hex
 type Hex []byte
 
 // MarshalText encodes buf as hex
@@ -72,7 +72,7 @@ func HexDecode(h string) ([]byte, error) {
 
 // HexDecodeInto decodes a hex string into an array of bytes (dst), verifying
 // that the decoded array has the same length as dst.
-func HexDecodeInto(dst []byte, h []byte) error {
+func HexDecodeInto(dst, h []byte) error {
 	if bytes.HasPrefix(h, []byte("0x")) {
 		h = h[2:]
 	}
@@ -105,21 +105,21 @@ func CheckBigIntArrayInField(arr []*big.Int) bool {
 
 // BigIntArrayToElementArray converts an array of *big.Int into an array of *ff.Element
 func BigIntArrayToElementArray(bi []*big.Int) []*ff.Element {
-	var o []*ff.Element
+	o := make([]*ff.Element, len(bi))
 	for i := range bi {
-		o = append(o, ff.NewElement().SetBigInt(bi[i]))
+		o[i] = ff.NewElement().SetBigInt(bi[i])
 	}
 	return o
 }
 
 // ElementArrayToBigIntArray converts an array of *ff.Element into an array of *big.Int
 func ElementArrayToBigIntArray(e []*ff.Element) []*big.Int {
-	var o []*big.Int
+	o := make([]*big.Int, len(e))
 	for i := range e {
 		ei := e[i]
 		bi := big.NewInt(0)
 		ei.ToBigIntRegular(bi)
-		o = append(o, bi)
+		o[i] = bi
 	}
 	return o
 }