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arithmetic.go
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arithmetic.go
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package prover
import (
"bytes"
"math/big"
bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
"github.com/iden3/go-iden3-crypto/ff"
"github.com/taubyte/go-snark/types"
)
func arrayOfZeroes(n int) []*big.Int {
r := make([]*big.Int, n)
for i := 0; i < n; i++ {
r[i] = new(big.Int).SetInt64(0)
}
return r[:]
}
func arrayOfZeroesE(n int) []*ff.Element {
r := make([]*ff.Element, n)
for i := 0; i < n; i++ {
r[i] = ff.NewElement()
}
return r[:]
}
func arrayOfZeroesG1(n int) []*bn256.G1 {
r := make([]*bn256.G1, n)
for i := 0; i < n; i++ {
r[i] = new(bn256.G1).ScalarBaseMult(big.NewInt(0))
}
return r[:]
}
func arrayOfZeroesG2(n int) []*bn256.G2 {
r := make([]*bn256.G2, n)
for i := 0; i < n; i++ {
r[i] = new(bn256.G2).ScalarBaseMult(big.NewInt(0))
}
return r[:]
}
func fAdd(a, b *big.Int) *big.Int {
ab := new(big.Int).Add(a, b)
return ab.Mod(ab, types.R)
}
func fSub(a, b *big.Int) *big.Int {
ab := new(big.Int).Sub(a, b)
return new(big.Int).Mod(ab, types.R)
}
func fMul(a, b *big.Int) *big.Int {
ab := new(big.Int).Mul(a, b)
return ab.Mod(ab, types.R)
}
func fDiv(a, b *big.Int) *big.Int {
ab := new(big.Int).Mul(a, new(big.Int).ModInverse(b, types.R))
return new(big.Int).Mod(ab, types.R)
}
//nolint:unused,deadcode // TODO check
func fNeg(a *big.Int) *big.Int {
return new(big.Int).Mod(new(big.Int).Neg(a), types.R)
}
func fInv(a *big.Int) *big.Int {
return new(big.Int).ModInverse(a, types.R)
}
func fExp(base *big.Int, e *big.Int) *big.Int {
res := big.NewInt(1)
rem := new(big.Int).Set(e)
exp := base
for !bytes.Equal(rem.Bytes(), big.NewInt(int64(0)).Bytes()) {
// if BigIsOdd(rem) {
if rem.Bit(0) == 1 { // .Bit(0) returns 1 when is odd
res = fMul(res, exp)
}
exp = fMul(exp, exp)
rem.Rsh(rem, 1)
}
return res
}
func max(a, b int) int {
if a > b {
return a
}
return b
}
func polynomialSub(a, b []*big.Int) []*big.Int {
r := arrayOfZeroes(max(len(a), len(b)))
for i := 0; i < len(a); i++ {
r[i] = fAdd(r[i], a[i])
}
for i := 0; i < len(b); i++ {
r[i] = fSub(r[i], b[i])
}
return r
}
func polynomialSubE(a, b []*ff.Element) []*ff.Element {
r := arrayOfZeroesE(max(len(a), len(b)))
for i := 0; i < len(a); i++ {
r[i].Add(r[i], a[i])
}
for i := 0; i < len(b); i++ {
r[i].Sub(r[i], b[i])
}
return r
}
func polynomialMul(a, b []*big.Int) []*big.Int {
r := arrayOfZeroes(len(a) + len(b) - 1)
for i := 0; i < len(a); i++ {
for j := 0; j < len(b); j++ {
r[i+j] = fAdd(r[i+j], fMul(a[i], b[j]))
}
}
return r
}
func polynomialMulE(a, b []*ff.Element) []*ff.Element {
r := arrayOfZeroesE(len(a) + len(b) - 1)
for i := 0; i < len(a); i++ {
for j := 0; j < len(b); j++ {
r[i+j].Add(r[i+j], ff.NewElement().Mul(a[i], b[j]))
}
}
return r
}
func polynomialDiv(a, b []*big.Int) ([]*big.Int, []*big.Int) {
// https://en.wikipedia.org/wiki/Division_algorithm
r := arrayOfZeroes(len(a) - len(b) + 1)
rem := a
for len(rem) >= len(b) {
l := fDiv(rem[len(rem)-1], b[len(b)-1])
pos := len(rem) - len(b)
r[pos] = l
aux := arrayOfZeroes(pos)
aux1 := append(aux, l)
aux2 := polynomialSub(rem, polynomialMul(b, aux1))
rem = aux2[:len(aux2)-1]
}
return r, rem
}
func polynomialDivE(a, b []*ff.Element) ([]*ff.Element, []*ff.Element) {
// https://en.wikipedia.org/wiki/Division_algorithm
r := arrayOfZeroesE(len(a) - len(b) + 1)
rem := a
for len(rem) >= len(b) {
l := ff.NewElement().Div(rem[len(rem)-1], b[len(b)-1])
pos := len(rem) - len(b)
r[pos] = l
aux := arrayOfZeroesE(pos)
aux1 := append(aux, l)
aux2 := polynomialSubE(rem, polynomialMulE(b, aux1))
rem = aux2[:len(aux2)-1]
}
return r, rem
}