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go-snark-study
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bn128.NewFqR with field over R. Setup.Pk & .Vk

pull/5/head
arnaucube 6 years ago
parent
439d894ee7
commit
7aafcfd5f3
4 changed files with 140 additions and 78 deletions
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  1. +3
    -3
      README.md
  2. +9
    -0
      bn128/bn128.go
  3. +124
    -66
      snark.go
  4. +4
    -9
      snark_test.go

+ 3
- 3
README.md
View File

@ -8,9 +8,9 @@ zkSNARK library implementation in Go
### Usage
- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark?status.svg)](https://godoc.org/github.com/arnaucube/go-snark) zkSnark
- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/bn128?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/bn128) bn128 (more details: https://github.com/arnaucube/go-snark/tree/master/bn128)
- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/fields?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/fields) Finite Fields operations
- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/r1csqap?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/r1csqap) R1CS to QAP (more details: https://github.com/arnaucube/go-snark/tree/master/r1csqap)
- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/bn128?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/bn128) bn128 (more details: https://github.com/arnaucube/go-snark/tree/master/bn128)
- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/fields?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/fields) Finite Fields operations
- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/r1csqap?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/r1csqap) R1CS to QAP (more details: https://github.com/arnaucube/go-snark/tree/master/r1csqap)
Example:
```go

+ 9
- 0
bn128/bn128.go
View File

@ -105,6 +105,15 @@ func NewBn128() (Bn128, error) {
return b, nil
}
func NewFqR() (fields.Fq, error){
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
if !ok {
return fields.Fq{}, errors.New("err parsing R")
}
fqR := fields.NewFq(r)
return fqR, nil
}
func (bn128 *Bn128) preparePairing() error {
var ok bool
bn128.LoopCount, ok = new(big.Int).SetString("29793968203157093288", 10)

+ 124
- 66
snark.go
View File

@ -2,10 +2,12 @@ package snark
import (
"crypto/rand"
"fmt"
"math/big"
"github.com/arnaucube/go-snark/bn128"
"github.com/arnaucube/go-snark/fields"
"github.com/arnaucube/go-snark/r1csqap"
)
type Setup struct {
@ -22,11 +24,26 @@ type Setup struct {
}
// public
G1T [][3]*big.Int // t encrypted in G1 curve
G2T [][3][2]*big.Int // t encrypted in G2 curve
G1Kbg [3]*big.Int // g1 * Kbeta * Kgamma
G2Kbg [3][2]*big.Int // g2 * Kbeta * Kgamma
G2Kg [3][2]*big.Int // g2 * Kgamma
G1T [][3]*big.Int // t encrypted in G1 curve
G2T [][3][2]*big.Int // t encrypted in G2 curve
Pk struct { // Proving Key pk:=(pkA, pkB, pkC, pkH)
A [][3]*big.Int
B [][3][2]*big.Int
C [][3]*big.Int
Kp [][3]*big.Int
Ap [][3]*big.Int
Bp [][3]*big.Int
Cp [][3]*big.Int
}
Vk struct {
A [3][2]*big.Int
B [3]*big.Int
C [3][2]*big.Int
G1Kbg [3]*big.Int // g1 * Kbeta * Kgamma
G2Kbg [3][2]*big.Int // g2 * Kbeta * Kgamma
G2Kg [3][2]*big.Int // g2 * Kgamma
Vkz [3][2]*big.Int
}
}
type Proof struct {
@ -37,16 +54,12 @@ type Proof struct {
PiC [3]*big.Int
PiCp [3]*big.Int
PiH [3]*big.Int
PiK [3]*big.Int
Va [3][2]*big.Int
Vb [3]*big.Int
Vc [3][2]*big.Int
Vz [3][2]*big.Int
PiKp [3]*big.Int
}
const bits = 512
func GenerateTrustedSetup(bn bn128.Bn128, polLength int) (Setup, error) {
func GenerateTrustedSetup(bn bn128.Bn128, pf r1csqap.PolynomialField, witnessLength int, alphas, betas, gammas [][]*big.Int, ax, bx, cx, hx, zx []*big.Int) (Setup, error) {
var setup Setup
var err error
// generate random t value
@ -93,7 +106,7 @@ func GenerateTrustedSetup(bn bn128.Bn128, polLength int) (Setup, error) {
// encrypt t values with curve generators
var gt1 [][3]*big.Int
var gt2 [][3][2]*big.Int
for i := 0; i < polLength; i++ {
for i := 0; i < witnessLength; i++ {
tPow := bn.Fq1.Exp(setup.Toxic.T, big.NewInt(int64(i)))
tEncr1 := bn.G1.MulScalar(bn.G1.G, tPow)
gt1 = append(gt1, tEncr1)
@ -105,6 +118,10 @@ func GenerateTrustedSetup(bn bn128.Bn128, polLength int) (Setup, error) {
setup.G1T = gt1
setup.G2T = gt2
setup.Vk.A = bn.G2.MulScalar(bn.G2.G, setup.Toxic.Ka)
setup.Vk.B = bn.G1.MulScalar(bn.G1.G, setup.Toxic.Kb)
setup.Vk.C = bn.G2.MulScalar(bn.G2.G, setup.Toxic.Kc)
/*
Verification keys:
- Vk_betagamma1: setup.G1Kbg = g1 * Kbeta*Kgamma
@ -112,62 +129,66 @@ func GenerateTrustedSetup(bn bn128.Bn128, polLength int) (Setup, error) {
- Vk_gamma: setup.G2Kg = g2 * Kgamma
*/
kbg := bn.Fq1.Mul(setup.Toxic.Kbeta, setup.Toxic.Kgamma)
setup.G1Kbg = bn.G1.MulScalar(bn.G1.G, kbg)
setup.G2Kbg = bn.G2.MulScalar(bn.G2.G, kbg)
setup.G2Kg = bn.G2.MulScalar(bn.G2.G, setup.Toxic.Kgamma)
setup.Vk.G1Kbg = bn.G1.MulScalar(bn.G1.G, kbg)
setup.Vk.G2Kbg = bn.G2.MulScalar(bn.G2.G, kbg)
setup.Vk.G2Kg = bn.G2.MulScalar(bn.G2.G, setup.Toxic.Kgamma)
for i := 0; i < witnessLength; i++ {
// A[i] = g1 * ax[t]
at := pf.Eval(alphas[i], setup.Toxic.T)
a := bn.G1.MulScalar(bn.G1.G, at)
setup.Pk.A = append(setup.Pk.A, a)
bt := pf.Eval(betas[i], setup.Toxic.T)
bg1 := bn.G1.MulScalar(bn.G1.G, bt)
bg2 := bn.G2.MulScalar(bn.G2.G, bt)
setup.Pk.B = append(setup.Pk.B, bg2)
ct := pf.Eval(gammas[i], setup.Toxic.T)
c := bn.G1.MulScalar(bn.G1.G, ct)
setup.Pk.C = append(setup.Pk.C, c)
kt := bn.Fq1.Add(bn.Fq1.Add(at, bt), ct)
k := bn.G1.MulScalar(bn.G1.G, kt)
setup.Pk.Ap = append(setup.Pk.Ap, bn.G1.MulScalar(a, setup.Toxic.Ka))
setup.Pk.Bp = append(setup.Pk.Bp, bn.G1.MulScalar(bg1, setup.Toxic.Kb))
setup.Pk.Cp = append(setup.Pk.Cp, bn.G1.MulScalar(c, setup.Toxic.Kc))
setup.Pk.Kp = append(setup.Pk.Kp, bn.G1.MulScalar(k, setup.Toxic.Kbeta))
}
setup.Vk.Vkz = bn.G2.MulScalar(bn.G2.G, pf.Eval(zx, setup.Toxic.T))
return setup, nil
}
func GenerateProofs(bn bn128.Bn128, f fields.Fq, setup Setup, w, ax, bx, cx, hx, zx []*big.Int) (Proof, error) {
func GenerateProofs(bn bn128.Bn128, f fields.Fq, setup Setup, hx []*big.Int, w []*big.Int) (Proof, error) {
var proof Proof
// g1*A(t)
proof.PiA = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
for i := 0; i < len(ax); i++ {
m := bn.G1.MulScalar(setup.G1T[i], ax[i])
proof.PiA = bn.G1.Add(proof.PiA, m)
}
proof.PiAp = bn.G1.MulScalar(proof.PiA, setup.Toxic.Ka) // move this in the setup step
// g2*B(t)
proof.PiAp = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
proof.PiB = bn.Fq6.Zero()
// g1*B(t)
pib1 := [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
for i := 0; i < len(bx); i++ {
m := bn.G2.MulScalar(setup.G2T[i], bx[i])
proof.PiB = bn.G2.Add(proof.PiB, m)
m1 := bn.G1.MulScalar(setup.G1T[i], bx[i])
pib1 = bn.G1.Add(pib1, m1)
}
proof.PiBp = bn.G1.MulScalar(pib1, setup.Toxic.Kb) // this in the setup step
// g1*C(t)
proof.PiBp = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
proof.PiC = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
for i := 0; i < len(cx); i++ {
m := bn.G1.MulScalar(setup.G1T[i], cx[i])
proof.PiC = bn.G1.Add(proof.PiC, m)
}
proof.PiCp = bn.G1.MulScalar(proof.PiC, setup.Toxic.Kc) // this in the setup step
// g1*H(t)
proof.PiCp = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
proof.PiH = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
for i := 0; i < len(hx); i++ {
m := bn.G1.MulScalar(setup.G1T[i], hx[i])
proof.PiH = bn.G1.Add(proof.PiH, m)
}
proof.PiKp = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
proof.Vz = bn.Fq6.Zero()
for i := 0; i < len(bx); i++ {
m := bn.G2.MulScalar(setup.G2T[i], zx[i])
proof.Vz = bn.G2.Add(proof.Vz, m)
for i := 0; i < len(w); i++ {
proof.PiA = bn.G1.Add(proof.PiA, bn.G1.MulScalar(setup.Pk.A[i], w[i]))
proof.PiAp = bn.G1.Add(proof.PiAp, bn.G1.MulScalar(setup.Pk.Ap[i], w[i]))
}
// proof.Vz = g2Zt
proof.Va = bn.G2.MulScalar(bn.G2.G, setup.Toxic.Ka) // this in the setup step
proof.Vb = bn.G1.MulScalar(bn.G1.G, setup.Toxic.Kb) // this in the setup step
for i := 0; i < len(w); i++ {
proof.PiB = bn.G2.Add(proof.PiB, bn.G2.MulScalar(setup.Pk.B[i], w[i]))
proof.PiBp = bn.G1.Add(proof.PiBp, bn.G1.MulScalar(setup.Pk.Bp[i], w[i]))
proof.PiC = bn.G1.Add(proof.PiC, bn.G1.MulScalar(setup.Pk.C[i], w[i]))
proof.PiCp = bn.G1.Add(proof.PiCp, bn.G1.MulScalar(setup.Pk.Cp[i], w[i]))
proof.Vc = bn.G2.MulScalar(bn.G2.G, setup.Toxic.Kc) // this in the setup step
proof.PiKp = bn.G1.Add(proof.PiKp, bn.G1.MulScalar(setup.Pk.Kp[i], w[i]))
}
for i := 0; i < len(hx); i++ {
proof.PiH = bn.G1.Add(proof.PiH, bn.G1.MulScalar(setup.G1T[i], hx[i]))
}
return proof, nil
}
@ -175,7 +196,7 @@ func GenerateProofs(bn bn128.Bn128, f fields.Fq, setup Setup, w, ax, bx, cx, hx,
func VerifyProof(bn bn128.Bn128, setup Setup, proof Proof) bool {
// e(piA, Va) == e(piA', g2)
pairingPiaVa, err := bn.Pairing(proof.PiA, proof.Va)
pairingPiaVa, err := bn.Pairing(proof.PiA, setup.Vk.A)
if err != nil {
return false
}
@ -185,10 +206,12 @@ func VerifyProof(bn bn128.Bn128, setup Setup, proof Proof) bool {
}
if !bn.Fq12.Equal(pairingPiaVa, pairingPiapG2) {
return false
} else {
fmt.Println("valid knowledge commitment for A")
}
// e(Vb, piB) == e(piB', g2)
pairingVbPib, err := bn.Pairing(proof.Vb, proof.PiB)
pairingVbPib, err := bn.Pairing(setup.Vk.B, proof.PiB)
if err != nil {
return false
}
@ -198,10 +221,12 @@ func VerifyProof(bn bn128.Bn128, setup Setup, proof Proof) bool {
}
if !bn.Fq12.Equal(pairingVbPib, pairingPibpG2) {
return false
} else {
fmt.Println("valid knowledge commitment for B")
}
// e(piC, Vc) == e(piC', g2)
pairingPicVc, err := bn.Pairing(proof.PiC, proof.Vc)
pairingPicVc, err := bn.Pairing(proof.PiC, setup.Vk.C)
if err != nil {
return false
}
@ -211,38 +236,71 @@ func VerifyProof(bn bn128.Bn128, setup Setup, proof Proof) bool {
}
if !bn.Fq12.Equal(pairingPicVc, pairingPicpG2) {
return false
} else {
fmt.Println("valid knowledge commitment for C")
}
// Vkx, to then calculate Vkx+piA
// e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2)
pairingPiaPib, err := bn.Pairing(proof.PiA, proof.PiB)
if err != nil {
return false
}
pairingPihVkz, err := bn.Pairing(proof.PiH, setup.Vk.Vkz)
if err != nil {
return false
}
pairingPicG2, err := bn.Pairing(proof.PiC, bn.G2.G)
if err != nil {
return false
}
pairingR := bn.Fq12.Mul(pairingPihVkz, pairingPicG2)
if !bn.Fq12.Equal(pairingPiaPib, pairingR) {
fmt.Println("p4")
return false
} else {
fmt.Println("QAP disibility checked")
}
// e(piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB)
// == e(piK, g2Kgamma)
// piApiC := bn.G1.Add(proof.PiA, proof.PiC)
// pairingPiACG2Kbg, err := bn.Pairing(piApiC, setup.G2Kbg)
// pairingPiACG2Kbg, err := bn.Pairing(piApiC, setup.Vk.G2Kbg)
// if err != nil {
// return false
// }
// pairingG1KbgPiB, err := bn.Pairing(setup.Vk.G1Kbg, proof.PiB)
// if err != nil {
// return false
// }
// pairingG1KbgPiB, err := bn.Pairing(setup.G1Kbg, proof.PiB)
// pairingL := bn.Fq12.Mul(pairingPiACG2Kbg, pairingG1KbgPiB)
// pairingR, err := bn.Pairing(proof.PiKp, setup.Vk.G2Kg)
// if err != nil {
// return false
// }
// pairing1 := bn.Fq12.Mul(pairingPiACG2Kbg, pairingG1KbgPiB)
// if !bn.Fq12.Equal(pairingL, pairingR) {
// fmt.Println("p5")
// return false
// }
//
// e(piA, piB) == e(piH, Vz) * e(piC, g2)
// pairingPiaPib, err := bn.Pairing(proof.PiA, proof.PiB)
// if err != nil {
// return false
// return false
// }
// pairingPihVz, err := bn.Pairing(proof.PiH, proof.Vz)
// pairingPihVz, err := bn.Pairing(proof.PiH, setup.Vk.Vkz)
// if err != nil {
// return false
// return false
// }
// pairingPicG2, err := bn.Pairing(proof.PiC, bn.G2.G)
// if err != nil {
// return false
// return false
// }
// if !bn.Fq12.Equal(pairingPiaPib, bn.Fq12.Mul(pairingPihVz, pairingPicG2)) {
// return false
// return false
// }
return true

+ 4
- 9
snark_test.go
View File

@ -64,26 +64,21 @@ func TestZk(t *testing.T) {
assert.Equal(t, abc, hz)
// calculate trusted setup
setup, err := GenerateTrustedSetup(bn, len(ax))
setup, err := GenerateTrustedSetup(bn, pf, len(w), alphas, betas, gammas, ax, bx, cx, hx, zx)
assert.Nil(t, err)
fmt.Println("trusted setup:")
fmt.Println(setup.G1T)
fmt.Println(setup.G2T)
// piA = g1 * A(t), piB = g2 * B(t), piC = g1 * C(t), piH = g1 * H(t)
proof, err := GenerateProofs(bn, f, setup, w, ax, bx, cx, hx, zx)
proof, err := GenerateProofs(bn, f, setup, hx, w)
assert.Nil(t, err)
fmt.Println("proofs:")
fmt.Println(proof.PiA)
fmt.Println(proof.PiB)
fmt.Println(proof.PiC)
fmt.Println(proof.PiH)
fmt.Println(proof.Vz)
// fmt.Println(proof.Vz)
publicSetup := Setup{
G1T: setup.G1T,
G2T: setup.G2T,
}
assert.True(t, VerifyProof(bn, publicSetup, proof))
assert.True(t, VerifyProof(bn, setup, proof))
}

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