mirror of
https://github.com/arnaucube/go-snark-study.git
synced 2026-02-02 17:26:41 +01:00
r1cs to qap over finite field
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arnaucube
157
r1csqap/r1csqap.go
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157
r1csqap/r1csqap.go
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@@ -0,0 +1,157 @@
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package r1csqap
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import (
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"math/big"
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"github.com/arnaucube/go-snark/fields"
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)
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func Transpose(matrix [][]*big.Int) [][]*big.Int {
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var r [][]*big.Int
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for i := 0; i < len(matrix[0]); i++ {
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var row []*big.Int
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for j := 0; j < len(matrix); j++ {
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row = append(row, matrix[j][i])
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}
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r = append(r, row)
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}
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return r
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}
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func ArrayOfBigZeros(num int) []*big.Int {
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bigZero := big.NewInt(int64(0))
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var r []*big.Int
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for i := 0; i < num; i++ {
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r = append(r, bigZero)
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}
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return r
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}
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type PolynomialField struct {
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F fields.Fq
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}
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func NewPolynomialField(f fields.Fq) PolynomialField {
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return PolynomialField{
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f,
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}
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}
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func (pf PolynomialField) Mul(a, b []*big.Int) []*big.Int {
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r := ArrayOfBigZeros(len(a) + len(b) - 1)
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for i := 0; i < len(a); i++ {
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for j := 0; j < len(b); j++ {
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r[i+j] = pf.F.Add(
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r[i+j],
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pf.F.Mul(a[i], b[j]))
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}
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}
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return r
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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func (pf PolynomialField) Add(a, b []*big.Int) []*big.Int {
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r := ArrayOfBigZeros(max(len(a), len(b)))
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for i := 0; i < len(a); i++ {
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r[i] = pf.F.Add(r[i], a[i])
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}
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for i := 0; i < len(b); i++ {
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r[i] = pf.F.Add(r[i], b[i])
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}
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return r
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}
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func (pf PolynomialField) Sub(a, b []*big.Int) []*big.Int {
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r := ArrayOfBigZeros(max(len(a), len(b)))
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for i := 0; i < len(a); i++ {
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r[i] = pf.F.Add(r[i], a[i])
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}
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for i := 0; i < len(b); i++ {
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// bneg := pf.F.Mul(b[i], big.NewInt(int64(-1)))
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// r[i] = pf.F.Add(r[i], bneg)
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r[i] = pf.F.Sub(r[i], b[i])
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}
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return r
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}
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// func FloatPow(a *big.Int, e int) *big.Int {
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// if e == 0 {
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// return big.NewInt(int64(1))
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// }
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// result := new(big.Int).Copy(a)
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// for i := 0; i < e-1; i++ {
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// result = new(big.Int).Mul(result, a)
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// }
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// return result
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// }
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func (pf PolynomialField) Eval(v []*big.Int, x *big.Int) *big.Int {
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r := big.NewInt(int64(0))
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for i := 0; i < len(v); i++ {
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// xi := FloatPow(x, i)
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xi := pf.F.Exp(x, big.NewInt(int64(i)))
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elem := pf.F.Mul(v[i], xi)
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r = pf.F.Add(r, elem)
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}
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return r
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}
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func (pf PolynomialField) NewPolZeroAt(pointPos, totalPoints int, height *big.Int) []*big.Int {
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fac := 1
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for i := 1; i < totalPoints+1; i++ {
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if i != pointPos {
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fac = fac * (pointPos - i)
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}
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}
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facBig := big.NewInt(int64(fac))
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hf := pf.F.Div(height, facBig)
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r := []*big.Int{hf}
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for i := 1; i < totalPoints+1; i++ {
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if i != pointPos {
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ineg := big.NewInt(int64(-i))
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b1 := big.NewInt(int64(1))
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r = pf.Mul(r, []*big.Int{ineg, b1})
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}
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}
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return r
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}
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func (pf PolynomialField) LagrangeInterpolation(v []*big.Int) []*big.Int {
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// https://en.wikipedia.org/wiki/Lagrange_polynomial
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var r []*big.Int
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for i := 0; i < len(v); i++ {
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r = pf.Add(r, pf.NewPolZeroAt(i+1, len(v), v[i]))
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}
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//
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return r
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}
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func (pf PolynomialField) R1CSToQAP(a, b, c [][]*big.Int) ([][]*big.Int, [][]*big.Int, [][]*big.Int, []*big.Int) {
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aT := Transpose(a)
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bT := Transpose(b)
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cT := Transpose(c)
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var alpha [][]*big.Int
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for i := 0; i < len(aT); i++ {
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alpha = append(alpha, pf.LagrangeInterpolation(aT[i]))
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}
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var beta [][]*big.Int
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for i := 0; i < len(bT); i++ {
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beta = append(beta, pf.LagrangeInterpolation(bT[i]))
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}
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var gamma [][]*big.Int
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for i := 0; i < len(cT); i++ {
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gamma = append(gamma, pf.LagrangeInterpolation(cT[i]))
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}
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z := []*big.Int{big.NewInt(int64(1))}
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for i := 1; i < len(aT[0])+1; i++ {
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ineg := big.NewInt(int64(-i))
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b1 := big.NewInt(int64(1))
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z = pf.Mul(z, []*big.Int{ineg, b1})
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}
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return alpha, beta, gamma, z
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}
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136
r1csqap/r1csqap_test.go
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136
r1csqap/r1csqap_test.go
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@@ -0,0 +1,136 @@
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package r1csqap
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import (
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"bytes"
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"fmt"
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"math/big"
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"testing"
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"github.com/arnaucube/go-snark/fields"
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"github.com/stretchr/testify/assert"
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)
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func TestTranspose(t *testing.T) {
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b0 := big.NewInt(int64(0))
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b1 := big.NewInt(int64(1))
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bFive := big.NewInt(int64(5))
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a := [][]*big.Int{
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[]*big.Int{b0, b1, b0, b0, b0, b0},
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[]*big.Int{b0, b0, b0, b1, b0, b0},
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[]*big.Int{b0, b1, b0, b0, b1, b0},
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[]*big.Int{bFive, b0, b0, b0, b0, b1},
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}
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aT := Transpose(a)
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assert.Equal(t, aT, [][]*big.Int{
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[]*big.Int{b0, b0, b0, bFive},
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[]*big.Int{b1, b0, b1, b0},
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[]*big.Int{b0, b0, b0, b0},
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[]*big.Int{b0, b1, b0, b0},
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[]*big.Int{b0, b0, b1, b0},
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[]*big.Int{b0, b0, b0, b1},
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})
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}
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func TestPol(t *testing.T) {
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b0 := big.NewInt(int64(0))
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b1 := big.NewInt(int64(1))
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b3 := big.NewInt(int64(3))
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b4 := big.NewInt(int64(4))
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b5 := big.NewInt(int64(5))
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b6 := big.NewInt(int64(6))
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b16 := big.NewInt(int64(16))
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a := []*big.Int{b1, b0, b5}
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b := []*big.Int{b3, b0, b1}
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// new Finite Field
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r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
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assert.True(nil, ok)
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f := fields.NewFq(r)
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// new Polynomial Field
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pf := NewPolynomialField(f)
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// polynomial multiplication
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o := pf.Mul(a, b)
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assert.Equal(t, o, []*big.Int{b3, b0, b16, b0, b5})
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// polynomial addition
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o = pf.Add(a, b)
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assert.Equal(t, o, []*big.Int{b4, b0, b6})
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// polynomial subtraction
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o1 := pf.Sub(a, b)
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o2 := pf.Sub(b, a)
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o = pf.Add(o1, o2)
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assert.True(t, bytes.Equal(b0.Bytes(), o[0].Bytes()))
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assert.True(t, bytes.Equal(b0.Bytes(), o[1].Bytes()))
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assert.True(t, bytes.Equal(b0.Bytes(), o[2].Bytes()))
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c := []*big.Int{b5, b6, b1}
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d := []*big.Int{b1, b3}
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o = pf.Sub(c, d)
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assert.Equal(t, o, []*big.Int{b4, b3, b1})
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// NewPolZeroAt
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o = pf.NewPolZeroAt(3, 4, b4)
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assert.Equal(t, pf.Eval(o, big.NewInt(3)), b4)
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o = pf.NewPolZeroAt(2, 4, b3)
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assert.Equal(t, pf.Eval(o, big.NewInt(2)), b3)
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}
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func TestLagrangeInterpolation(t *testing.T) {
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// new Finite Field
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r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
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assert.True(nil, ok)
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f := fields.NewFq(r)
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// new Polynomial Field
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pf := NewPolynomialField(f)
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b0 := big.NewInt(int64(0))
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b5 := big.NewInt(int64(5))
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a := []*big.Int{b0, b0, b0, b5}
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alpha := pf.LagrangeInterpolation(a)
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assert.Equal(t, pf.Eval(alpha, big.NewInt(int64(4))), b5)
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aux := pf.Eval(alpha, big.NewInt(int64(3))).Int64()
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assert.Equal(t, aux, int64(0))
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}
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func TestR1CSToQAP(t *testing.T) {
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// new Finite Field
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r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
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assert.True(nil, ok)
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f := fields.NewFq(r)
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// new Polynomial Field
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pf := NewPolynomialField(f)
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b0 := big.NewInt(int64(0))
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b1 := big.NewInt(int64(1))
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b5 := big.NewInt(int64(5))
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a := [][]*big.Int{
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[]*big.Int{b0, b1, b0, b0, b0, b0},
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[]*big.Int{b0, b0, b0, b1, b0, b0},
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[]*big.Int{b0, b1, b0, b0, b1, b0},
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[]*big.Int{b5, b0, b0, b0, b0, b1},
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}
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b := [][]*big.Int{
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[]*big.Int{b0, b1, b0, b0, b0, b0},
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[]*big.Int{b0, b1, b0, b0, b0, b0},
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[]*big.Int{b1, b0, b0, b0, b0, b0},
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[]*big.Int{b1, b0, b0, b0, b0, b0},
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}
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c := [][]*big.Int{
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[]*big.Int{b0, b0, b0, b1, b0, b0},
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[]*big.Int{b0, b0, b0, b0, b1, b0},
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[]*big.Int{b0, b0, b0, b0, b0, b1},
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[]*big.Int{b0, b0, b1, b0, b0, b0},
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}
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alpha, beta, gamma, z := pf.R1CSToQAP(a, b, c)
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fmt.Println(alpha)
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fmt.Println(beta)
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fmt.Println(gamma)
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fmt.Println(z)
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}
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