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package prover
import (
"crypto/rand"
"math"
"math/big"
"runtime"
"sync"
bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
"github.com/iden3/go-circom-prover-verifier/types"
"github.com/iden3/go-iden3-crypto/utils"
)
// Proof is the data structure of the Groth16 zkSNARK proof
type Proof struct {
A *bn256.G1
B *bn256.G2
C *bn256.G1
}
// Pk holds the data structure of the ProvingKey
type Pk struct {
A []*bn256.G1
B2 []*bn256.G2
B1 []*bn256.G1
C []*bn256.G1
NVars int
NPublic int
VkAlpha1 *bn256.G1
VkDelta1 *bn256.G1
VkBeta1 *bn256.G1
VkBeta2 *bn256.G2
VkDelta2 *bn256.G2
HExps []*bn256.G1
DomainSize int
PolsA []map[int]*big.Int
PolsB []map[int]*big.Int
PolsC []map[int]*big.Int
}
// Witness contains the witness
type Witness []*big.Int
func randBigInt() (*big.Int, error) {
maxbits := types.R.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, types.R)
return rq, nil
}
// GenerateProof generates the Groth16 zkSNARK proof
func GenerateProof(pk *types.Pk, w types.Witness) (*types.Proof, []*big.Int, error) {
var proof types.Proof
r, err := randBigInt()
if err != nil {
return nil, nil, err
}
s, err := randBigInt()
if err != nil {
return nil, nil, err
}
numcpu := runtime.NumCPU()
proofA := arrayOfZeroesG1(numcpu)
proofB := arrayOfZeroesG2(numcpu)
proofC := arrayOfZeroesG1(numcpu)
proofBG1 := arrayOfZeroesG1(numcpu)
var wg1 sync.WaitGroup
wg1.Add(numcpu)
for _cpu, _ranges := range ranges(pk.NVars, numcpu) {
// split 1
go func(cpu int, ranges [2]int) {
tmpG1 := new(bn256.G1).ScalarBaseMult(big.NewInt(0))
tmpG2 := new(bn256.G2).ScalarBaseMult(big.NewInt(0))
for i := ranges[0]; i < ranges[1]; i++ {
proofA[cpu].Add(proofA[cpu], tmpG1.ScalarMult(pk.A[i], w[i]))
proofB[cpu].Add(proofB[cpu], tmpG2.ScalarMult(pk.B2[i], w[i]))
proofBG1[cpu].Add(proofBG1[cpu], tmpG1.ScalarMult(pk.B1[i], w[i]))
if i >= pk.NPublic+1 {
proofC[cpu].Add(proofC[cpu], tmpG1.ScalarMult(pk.C[i], w[i]))
}
}
wg1.Done()
}(_cpu, _ranges)
}
wg1.Wait()
// join 1
for cpu := 1; cpu < numcpu; cpu++ {
proofA[0].Add(proofA[0], proofA[cpu])
proofB[0].Add(proofB[0], proofB[cpu])
proofC[0].Add(proofC[0], proofC[cpu])
proofBG1[0].Add(proofBG1[0], proofBG1[cpu])
}
proof.A = proofA[0]
proof.B = proofB[0]
proof.C = proofC[0]
h := calculateH(pk, w)
println("len(h)", len(h))
proof.A.Add(proof.A, pk.VkAlpha1)
proof.A.Add(proof.A, new(bn256.G1).ScalarMult(pk.VkDelta1, r))
proof.B.Add(proof.B, pk.VkBeta2)
proof.B.Add(proof.B, new(bn256.G2).ScalarMult(pk.VkDelta2, s))
proofBG1[0].Add(proofBG1[0], pk.VkBeta1)
proofBG1[0].Add(proofBG1[0], new(bn256.G1).ScalarMult(pk.VkDelta1, s))
proofC = arrayOfZeroesG1(numcpu)
var wg2 sync.WaitGroup
wg2.Add(numcpu)
for _cpu, _ranges := range ranges(len(h), numcpu) {
// split 2
go func(cpu int, ranges [2]int) {
tmpG1 := new(bn256.G1).ScalarBaseMult(big.NewInt(0))
for i := ranges[0]; i < ranges[1]; i++ {
proofC[cpu].Add(proofC[cpu], tmpG1.ScalarMult(pk.HExps[i], h[i]))
}
wg2.Done()
}(_cpu, _ranges)
}
wg2.Wait()
// join 2
for cpu := 1; cpu < numcpu; cpu++ {
proofC[0].Add(proofC[0], proofC[cpu])
}
proof.C.Add(proof.C, proofC[0])
proof.C.Add(proof.C, new(bn256.G1).ScalarMult(proof.A, s))
proof.C.Add(proof.C, new(bn256.G1).ScalarMult(proofBG1[0], r))
rsneg := new(big.Int).Mod(new(big.Int).Neg(new(big.Int).Mul(r, s)), types.R) // fAdd & fMul
proof.C.Add(proof.C, new(bn256.G1).ScalarMult(pk.VkDelta1, rsneg))
pubSignals := w[1 : pk.NPublic+1]
return &proof, pubSignals, nil
}
func calculateH(pk *types.Pk, w types.Witness) []*big.Int {
m := pk.DomainSize
polAT := arrayOfZeroes(m)
polBT := arrayOfZeroes(m)
for i := 0; i < pk.NVars; i++ {
for j := range pk.PolsA[i] {
polAT[j] = fAdd(polAT[j], fMul(w[i], pk.PolsA[i][j]))
}
for j := range pk.PolsB[i] {
polBT[j] = fAdd(polBT[j], fMul(w[i], pk.PolsB[i][j]))
}
}
polATe := utils.BigIntArrayToElementArray(polAT)
polBTe := utils.BigIntArrayToElementArray(polBT)
polASe := ifft(polATe)
polBSe := ifft(polBTe)
r := int(math.Log2(float64(m))) + 1
roots := newRootsT()
roots.setRoots(r)
for i := 0; i < len(polASe); i++ {
polASe[i].Mul(polASe[i], roots.roots[r][i])
polBSe[i].Mul(polBSe[i], roots.roots[r][i])
}
polATodd := fft(polASe)
polBTodd := fft(polBSe)
polABT := arrayOfZeroesE(len(polASe) * 2)
for i := 0; i < len(polASe); i++ {
polABT[2*i].Mul(polATe[i], polBTe[i])
polABT[2*i+1].Mul(polATodd[i], polBTodd[i])
}
hSeFull := ifft(polABT)
hSe := hSeFull[m:]
return utils.ElementArrayToBigIntArray(hSe)
}
func ranges(n, parts int) [][2]int {
s := make([][2]int, parts)
p := float64(n) / float64(parts)
for i := 0; i < parts; i++ {
a, b := int(float64(i)*p), int(float64(i+1)*p)
s[i] = [2]int{a, b}
}
return s
}