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add mimc7 & fields

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arnaucube
2019-06-25 15:01:38 +02:00
parent 0f93c8ce38
commit e92a15d3b0
5 changed files with 502 additions and 0 deletions
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3
README.md Normal file
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# 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) [![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 used in iden3

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

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

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mimc7/mimc7.go Normal file
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package mimc7
import (
"errors"
"fmt"
"math/big"
"github.com/ethereum/go-ethereum/crypto"
"github.com/iden3/go-iden3/crypto/field"
)
const SEED = "mimc"
// RElem is a big.Int of maximum 253 bits
type RElem *big.Int
var constants = generateConstantsData()
type constantsData struct {
maxFieldVal *big.Int
seedHash *big.Int
iv *big.Int
fqR field.Fq
nRounds int
cts []*big.Int
}
func getIV(seed string) {
}
func generateConstantsData() constantsData {
var constants constantsData
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
if !ok {
}
fqR := field.NewFq(r)
constants.fqR = fqR
// maxFieldVal is the R value of the Finite Field
constants.maxFieldVal = constants.fqR.Q
constants.seedHash = new(big.Int).SetBytes(crypto.Keccak256([]byte(SEED)))
c := new(big.Int).SetBytes(crypto.Keccak256([]byte(SEED + "_iv")))
constants.iv = new(big.Int).Mod(c, constants.maxFieldVal)
constants.nRounds = 91
cts, err := getConstants(constants.fqR, SEED, constants.nRounds)
if err != nil {
panic(err)
}
constants.cts = cts
return constants
}
// BigIntToRElem checks if given big.Int fits in a Field R element, and returns the RElem type
func BigIntToRElem(a *big.Int) (RElem, error) {
if a.Cmp(constants.maxFieldVal) != -1 {
return RElem(a), errors.New("Given big.Int don't fits in the Finite Field over R")
}
return RElem(a), nil
}
//BigIntsToRElems converts from array of *big.Int to array of RElem
func BigIntsToRElems(arr []*big.Int) ([]RElem, error) {
o := make([]RElem, len(arr))
for i, a := range arr {
e, err := BigIntToRElem(a)
if err != nil {
return o, fmt.Errorf("element in position %v don't fits in Finite Field over R", i)
}
o[i] = e
}
return o, nil
}
// RElemsToBigInts converts from array of RElem to array of *big.Int
func RElemsToBigInts(arr []RElem) []*big.Int {
o := make([]*big.Int, len(arr))
for i, a := range arr {
o[i] = a
}
return o
}
func getConstants(fqR field.Fq, seed string, nRounds int) ([]*big.Int, error) {
cts := make([]*big.Int, nRounds)
cts[0] = big.NewInt(int64(0))
c := new(big.Int).SetBytes(crypto.Keccak256([]byte(SEED)))
for i := 1; i < nRounds; i++ {
c = new(big.Int).SetBytes(crypto.Keccak256(c.Bytes()))
n := fqR.Affine(c)
cts[i] = n
}
return cts, nil
}
// MIMC7HashGeneric performs the MIMC7 hash over a RElem, in a generic way, where it can be specified the Finite Field over R, and the number of rounds
func MIMC7HashGeneric(fqR field.Fq, xIn, k *big.Int, nRounds int) (*big.Int, error) {
cts, err := getConstants(fqR, SEED, nRounds)
if err != nil {
return &big.Int{}, err
}
var r *big.Int
for i := 0; i < nRounds; i++ {
var t *big.Int
if i == 0 {
t = fqR.Add(xIn, k)
} else {
t = fqR.Add(fqR.Add(r, k), cts[i])
}
t2 := fqR.Square(t)
t4 := fqR.Square(t2)
r = fqR.Mul(fqR.Mul(t4, t2), t)
}
return fqR.Affine(fqR.Add(r, k)), nil
}
// HashGeneric performs the MIMC7 hash over a RElem array, in a generic way, where it can be specified the Finite Field over R, and the number of rounds
func HashGeneric(iv *big.Int, arrEl []RElem, fqR field.Fq, nRounds int) (RElem, error) {
arr := RElemsToBigInts(arrEl)
r := iv
var err error
for i := 0; i < len(arr); i++ {
r, err = MIMC7HashGeneric(fqR, r, arr[i], nRounds)
if err != nil {
return r, err
}
}
return RElem(r), nil
}
// MIMC7Hash performs the MIMC7 hash over a RElem, using the Finite Field over R and the number of rounds setted in the `constants` variable
func MIMC7Hash(xIn, k *big.Int) *big.Int {
var r *big.Int
for i := 0; i < constants.nRounds; i++ {
var t *big.Int
if i == 0 {
t = constants.fqR.Add(xIn, k)
} else {
t = constants.fqR.Add(constants.fqR.Add(r, k), constants.cts[i])
}
t2 := constants.fqR.Square(t)
t4 := constants.fqR.Square(t2)
r = constants.fqR.Mul(constants.fqR.Mul(t4, t2), t)
}
return constants.fqR.Affine(constants.fqR.Add(r, k))
}
// Hash performs the MIMC7 hash over a RElem array
func Hash(arrEl []RElem, key *big.Int) RElem {
arr := RElemsToBigInts(arrEl)
var r *big.Int
if key == nil {
r = constants.fqR.Zero()
} else {
r = key
}
// r := constants.iv
for i := 0; i < len(arr); i++ {
r = constants.fqR.Add(
constants.fqR.Add(
r,
arr[i],
),
MIMC7Hash(arr[i], r))
}
return RElem(r)
}

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mimc7/mimc7_test.go Normal file
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package mimc7
import (
"encoding/hex"
"math/big"
"testing"
"github.com/iden3/go-iden3/crypto/field"
"github.com/stretchr/testify/assert"
)
func TestUtils(t *testing.T) {
b1 := big.NewInt(int64(1))
b2 := big.NewInt(int64(2))
b3 := big.NewInt(int64(3))
arrBigInt := []*big.Int{b1, b2, b3}
// *big.Int array to RElem array
rElems, err := BigIntsToRElems(arrBigInt)
assert.Nil(t, err)
// RElem array to *big.Int array
bElems := RElemsToBigInts(rElems)
assert.Equal(t, arrBigInt, bElems)
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
assert.True(t, ok)
// greater or equal than R will give error when passing bigInts to RElems, to fit in the R Finite Field
overR, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495618", 10)
assert.True(t, ok)
_, err = BigIntsToRElems([]*big.Int{b1, overR, b2})
assert.True(t, err != nil)
_, err = BigIntsToRElems([]*big.Int{b1, r, b2})
assert.True(t, err != nil)
// smaller than R will not give error when passing bigInts to RElems, to fit in the R Finite Field
underR, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495616", 10)
assert.True(t, ok)
_, err = BigIntsToRElems([]*big.Int{b1, underR, b2})
assert.Nil(t, err)
}
func TestMIMC7Generic(t *testing.T) {
b1 := big.NewInt(int64(1))
b2 := big.NewInt(int64(2))
b3 := big.NewInt(int64(3))
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
assert.True(t, ok)
fqR := field.NewFq(r)
bigArray := []*big.Int{b1, b2, b3}
elementsArray, err := BigIntsToRElems(bigArray)
assert.Nil(t, err)
// Generic Hash
mhg, err := MIMC7HashGeneric(fqR, b1, b2, 91)
assert.Nil(t, err)
assert.Equal(t, "10594780656576967754230020536574539122676596303354946869887184401991294982664", mhg.String())
hg, err := HashGeneric(fqR.Zero(), elementsArray, fqR, 91)
assert.Nil(t, err)
assert.Equal(t, "6464402164086696096195815557694604139393321133243036833927490113253119343397", (*big.Int)(hg).String())
}
func TestMIMC7(t *testing.T) {
b12 := big.NewInt(int64(12))
b45 := big.NewInt(int64(45))
b78 := big.NewInt(int64(78))
b41 := big.NewInt(int64(41))
// h1, hash of 1 elements
bigArray1 := []*big.Int{b12}
elementsArray1, err := BigIntsToRElems(bigArray1)
assert.Nil(t, err)
h1 := Hash(elementsArray1, nil)
assert.Nil(t, err)
// same hash value than the iden3js and circomlib tests:
assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h1).Bytes()), "0x237c92644dbddb86d8a259e0e923aaab65a93f1ec5758b8799988894ac0958fd")
// h2a, hash of 2 elements
bigArray2a := []*big.Int{b78, b41}
elementsArray2a, err := BigIntsToRElems(bigArray2a)
assert.Nil(t, err)
mh2a := MIMC7Hash(b12, b45)
assert.Nil(t, err)
assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(mh2a).Bytes()), "0x2ba7ebad3c6b6f5a20bdecba2333c63173ca1a5f2f49d958081d9fa7179c44e4")
h2a := Hash(elementsArray2a, nil)
assert.Nil(t, err)
// same hash value than the iden3js and circomlib tests:
assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h2a).Bytes()), "0x067f3202335ea256ae6e6aadcd2d5f7f4b06a00b2d1e0de903980d5ab552dc70")
// h2b, hash of 2 elements
bigArray2b := []*big.Int{b12, b45}
elementsArray2b, err := BigIntsToRElems(bigArray2b)
assert.Nil(t, err)
mh2b := MIMC7Hash(b12, b45)
assert.Nil(t, err)
assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(mh2b).Bytes()), "0x2ba7ebad3c6b6f5a20bdecba2333c63173ca1a5f2f49d958081d9fa7179c44e4")
h2b := Hash(elementsArray2b, nil)
assert.Nil(t, err)
// same hash value than the iden3js and circomlib tests:
assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h2b).Bytes()), "0x15ff7fe9793346a17c3150804bcb36d161c8662b110c50f55ccb7113948d8879")
// h4, hash of 4 elements
bigArray4 := []*big.Int{b12, b45, b78, b41}
elementsArray4, err := BigIntsToRElems(bigArray4)
assert.Nil(t, err)
h4 := Hash(elementsArray4, nil)
assert.Nil(t, err)
// same hash value than the iden3js and circomlib tests:
assert.Equal(t, "0x"+hex.EncodeToString((*big.Int)(h4).Bytes()), "0x284bc1f34f335933a23a433b6ff3ee179d682cd5e5e2fcdd2d964afa85104beb")
}
func BenchmarkMIMC7(b *testing.B) {
b12 := big.NewInt(int64(12))
b45 := big.NewInt(int64(45))
b78 := big.NewInt(int64(78))
b41 := big.NewInt(int64(41))
bigArray4 := []*big.Int{b12, b45, b78, b41}
elementsArray4, err := BigIntsToRElems(bigArray4)
assert.Nil(b, err)
var h4 RElem
for i := 0; i < b.N; i++ {
h4 = Hash(elementsArray4, nil)
}
println(h4)
}