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369 lines
12 KiB
369 lines
12 KiB
// implementation of https://eprint.iacr.org/2013/879.pdf
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package snark
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import (
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"fmt"
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"math/big"
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"os"
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"github.com/arnaucube/go-snark-study/bn128"
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"github.com/arnaucube/go-snark-study/circuitcompiler"
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"github.com/arnaucube/go-snark-study/fields"
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"github.com/arnaucube/go-snark-study/r1csqap"
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)
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type Pk struct { // Proving Key pk:=(pkA, pkB, pkC, pkH)
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G1T [][3]*big.Int // t encrypted in G1 curve, G1T == Pk.H
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A [][3]*big.Int
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B [][3][2]*big.Int
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C [][3]*big.Int
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Kp [][3]*big.Int
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Ap [][3]*big.Int
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Bp [][3]*big.Int
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Cp [][3]*big.Int
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Z []*big.Int
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}
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type Vk struct {
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Vka [3][2]*big.Int
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Vkb [3]*big.Int
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Vkc [3][2]*big.Int
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IC [][3]*big.Int
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G1Kbg [3]*big.Int // g1 * Kbeta * Kgamma
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G2Kbg [3][2]*big.Int // g2 * Kbeta * Kgamma
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G2Kg [3][2]*big.Int // g2 * Kgamma
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Vkz [3][2]*big.Int
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}
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// Setup is the data structure holding the Trusted Setup data. The Setup.Toxic sub struct must be destroyed after the GenerateTrustedSetup function is completed
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type Setup struct {
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Toxic struct {
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T *big.Int // trusted setup secret
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Ka *big.Int // prover
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Kb *big.Int // prover
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Kc *big.Int // prover
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Kbeta *big.Int
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Kgamma *big.Int
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RhoA *big.Int
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RhoB *big.Int
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RhoC *big.Int
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}
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// public
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Pk Pk
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Vk Vk
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}
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// Proof contains the parameters to proof the zkSNARK
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type Proof struct {
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PiA [3]*big.Int
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PiAp [3]*big.Int
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PiB [3][2]*big.Int
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PiBp [3]*big.Int
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PiC [3]*big.Int
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PiCp [3]*big.Int
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PiH [3]*big.Int
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PiKp [3]*big.Int
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// PublicSignals []*big.Int
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}
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type utils struct {
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Bn bn128.Bn128
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FqR fields.Fq
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PF r1csqap.PolynomialField
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}
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// Utils is the data structure holding the BN128, FqR Finite Field over R, PolynomialField, that will be used inside the snarks operations
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var Utils = prepareUtils()
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func prepareUtils() utils {
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bn, err := bn128.NewBn128()
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if err != nil {
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panic(err)
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}
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// new Finite Field
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fqR := fields.NewFq(bn.R)
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// new Polynomial Field
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pf := r1csqap.NewPolynomialField(fqR)
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return utils{
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Bn: bn,
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FqR: fqR,
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PF: pf,
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}
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}
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// GenerateTrustedSetup generates the Trusted Setup from a compiled Circuit. The Setup.Toxic sub data structure must be destroyed
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func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, alphas, betas, gammas [][]*big.Int) (Setup, error) {
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var setup Setup
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var err error
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// input soundness
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// for i := 0; i < len(alphas); i++ {
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// for j := 0; j < len(alphas[i]); j++ {
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// if j <= circuit.NPublic {
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// if bytes.Equal(alphas[i][j].Bytes(), Utils.FqR.Zero().Bytes()) {
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// alphas[i][j] = Utils.FqR.One()
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// }
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// }
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// }
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// }
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// generate random t value
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setup.Toxic.T, err = Utils.FqR.Rand()
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if err != nil {
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return Setup{}, err
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}
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// k for calculating pi' and Vk
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setup.Toxic.Ka, err = Utils.FqR.Rand()
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if err != nil {
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return Setup{}, err
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}
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setup.Toxic.Kb, err = Utils.FqR.Rand()
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if err != nil {
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return Setup{}, err
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}
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setup.Toxic.Kc, err = Utils.FqR.Rand()
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if err != nil {
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return Setup{}, err
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}
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// generate Kβ (Kbeta) and Kγ (Kgamma)
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setup.Toxic.Kbeta, err = Utils.FqR.Rand()
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if err != nil {
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return Setup{}, err
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}
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setup.Toxic.Kgamma, err = Utils.FqR.Rand()
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if err != nil {
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return Setup{}, err
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}
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// generate ρ (Rho): ρA, ρB, ρC
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setup.Toxic.RhoA, err = Utils.FqR.Rand()
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if err != nil {
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return Setup{}, err
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}
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setup.Toxic.RhoB, err = Utils.FqR.Rand()
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if err != nil {
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return Setup{}, err
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}
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setup.Toxic.RhoC = Utils.FqR.Mul(setup.Toxic.RhoA, setup.Toxic.RhoB)
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// calculated more down
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// for i := 0; i < witnessLength; i++ {
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// tPow := Utils.FqR.Exp(setup.Toxic.T, big.NewInt(int64(i)))
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// tEncr1 := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, tPow)
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// gt1 = append(gt1, tEncr1)
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// tEncr2 := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, tPow)
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// gt2 = append(gt2, tEncr2)
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// }
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// gt1: g1, g1*t, g1*t^2, g1*t^3, ...
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// gt2: g2, g2*t, g2*t^2, ...
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setup.Vk.Vka = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Ka)
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setup.Vk.Vkb = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, setup.Toxic.Kb)
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setup.Vk.Vkc = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kc)
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/*
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Verification keys:
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- Vk_betagamma1: setup.G1Kbg = g1 * Kbeta*Kgamma
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- Vk_betagamma2: setup.G2Kbg = g2 * Kbeta*Kgamma
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- Vk_gamma: setup.G2Kg = g2 * Kgamma
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*/
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kbg := Utils.FqR.Mul(setup.Toxic.Kbeta, setup.Toxic.Kgamma)
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setup.Vk.G1Kbg = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kbg)
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setup.Vk.G2Kbg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, kbg)
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setup.Vk.G2Kg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kgamma)
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// for i := 0; i < circuit.NVars; i++ {
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for i := 0; i < len(circuit.Signals); i++ {
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at := Utils.PF.Eval(alphas[i], setup.Toxic.T)
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// rhoAat := Utils.Bn.Fq1.Mul(setup.Toxic.RhoA, at)
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rhoAat := Utils.FqR.Mul(setup.Toxic.RhoA, at)
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a := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoAat)
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setup.Pk.A = append(setup.Pk.A, a)
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if i <= circuit.NPublic {
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setup.Vk.IC = append(setup.Vk.IC, a)
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}
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bt := Utils.PF.Eval(betas[i], setup.Toxic.T)
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// rhoBbt := Utils.Bn.Fq1.Mul(setup.Toxic.RhoB, bt)
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rhoBbt := Utils.FqR.Mul(setup.Toxic.RhoB, bt)
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bg1 := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoBbt)
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bg2 := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, rhoBbt)
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setup.Pk.B = append(setup.Pk.B, bg2)
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ct := Utils.PF.Eval(gammas[i], setup.Toxic.T)
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// rhoCct := Utils.Bn.Fq1.Mul(setup.Toxic.RhoC, ct)
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rhoCct := Utils.FqR.Mul(setup.Toxic.RhoC, ct)
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c := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoCct)
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setup.Pk.C = append(setup.Pk.C, c)
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kt := Utils.FqR.Add(Utils.FqR.Add(rhoAat, rhoBbt), rhoCct)
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k := Utils.Bn.G1.Affine(Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kt))
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ktest := Utils.Bn.G1.Affine(Utils.Bn.G1.Add(Utils.Bn.G1.Add(a, bg1), c))
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if !Utils.Bn.Fq2.Equal(k, ktest) {
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os.Exit(1)
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return setup, err
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}
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setup.Pk.Ap = append(setup.Pk.Ap, Utils.Bn.G1.MulScalar(a, setup.Toxic.Ka))
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setup.Pk.Bp = append(setup.Pk.Bp, Utils.Bn.G1.MulScalar(bg1, setup.Toxic.Kb))
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setup.Pk.Cp = append(setup.Pk.Cp, Utils.Bn.G1.MulScalar(c, setup.Toxic.Kc))
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k_ := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kt)
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setup.Pk.Kp = append(setup.Pk.Kp, Utils.Bn.G1.MulScalar(k_, setup.Toxic.Kbeta))
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}
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// z pol
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zpol := []*big.Int{big.NewInt(int64(1))}
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// for i := 0; i < len(circuit.Constraints); i++ {
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for i := 1; i < len(alphas)-1; i++ {
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zpol = Utils.PF.Mul(
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zpol,
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[]*big.Int{
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Utils.FqR.Neg( // neg over R
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big.NewInt(int64(i))),
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big.NewInt(int64(1)),
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})
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}
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setup.Pk.Z = zpol
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zt := Utils.PF.Eval(zpol, setup.Toxic.T)
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// rhoCzt := Utils.Bn.Fq1.Mul(setup.Toxic.RhoC, zt)
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rhoCzt := Utils.FqR.Mul(setup.Toxic.RhoC, zt)
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setup.Vk.Vkz = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, rhoCzt)
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// encrypt t values with curve generators
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var gt1 [][3]*big.Int
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gt1 = append(gt1, Utils.Bn.G1.G) // the first is t**0 * G1 = 1 * G1 = G1
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tEncr := setup.Toxic.T
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for i := 1; i < len(zpol); i++ { //should be G1T = pkH = (tau**i * G1) from i=0 to d, where d is degree of pol Z(x)
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gt1 = append(gt1, Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, tEncr))
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// tEncr = Utils.Bn.Fq1.Mul(tEncr, setup.Toxic.T)
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tEncr = Utils.FqR.Mul(tEncr, setup.Toxic.T)
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}
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setup.Pk.G1T = gt1
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return setup, nil
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}
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// GenerateProofs generates all the parameters to proof the zkSNARK from the Circuit, Setup and the Witness
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func GenerateProofs(circuit circuitcompiler.Circuit, pk Pk, w []*big.Int, px []*big.Int) (Proof, error) {
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var proof Proof
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proof.PiA = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
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proof.PiAp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
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proof.PiB = Utils.Bn.Fq6.Zero()
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proof.PiBp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
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proof.PiC = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
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proof.PiCp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
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proof.PiH = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
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proof.PiKp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
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for i := circuit.NPublic + 1; i < circuit.NVars; i++ {
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proof.PiA = Utils.Bn.G1.Add(proof.PiA, Utils.Bn.G1.MulScalar(pk.A[i], w[i]))
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proof.PiAp = Utils.Bn.G1.Add(proof.PiAp, Utils.Bn.G1.MulScalar(pk.Ap[i], w[i]))
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}
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for i := 0; i < circuit.NVars; i++ {
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proof.PiB = Utils.Bn.G2.Add(proof.PiB, Utils.Bn.G2.MulScalar(pk.B[i], w[i]))
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proof.PiBp = Utils.Bn.G1.Add(proof.PiBp, Utils.Bn.G1.MulScalar(pk.Bp[i], w[i]))
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proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(pk.C[i], w[i]))
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proof.PiCp = Utils.Bn.G1.Add(proof.PiCp, Utils.Bn.G1.MulScalar(pk.Cp[i], w[i]))
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proof.PiKp = Utils.Bn.G1.Add(proof.PiKp, Utils.Bn.G1.MulScalar(pk.Kp[i], w[i]))
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}
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hx := Utils.PF.DivisorPolynomial(px, pk.Z) // maybe move this calculation to a previous step
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// piH = pkH,0 + sum ( hi * pk H,i ), where pkH = G1T, hi=hx
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// proof.PiH = Utils.Bn.G1.Add(proof.PiH, pk.G1T[0])
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for i := 0; i < len(hx); i++ {
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proof.PiH = Utils.Bn.G1.Add(proof.PiH, Utils.Bn.G1.MulScalar(pk.G1T[i], hx[i]))
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}
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return proof, nil
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}
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// VerifyProof verifies over the BN128 the Pairings of the Proof
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func VerifyProof(vk Vk, proof Proof, publicSignals []*big.Int, debug bool) bool {
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// e(piA, Va) == e(piA', g2)
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pairingPiaVa := Utils.Bn.Pairing(proof.PiA, vk.Vka)
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pairingPiapG2 := Utils.Bn.Pairing(proof.PiAp, Utils.Bn.G2.G)
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if !Utils.Bn.Fq12.Equal(pairingPiaVa, pairingPiapG2) {
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if debug {
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fmt.Println("❌ e(piA, Va) == e(piA', g2), valid knowledge commitment for A")
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}
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return false
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}
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if debug {
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fmt.Println("✓ e(piA, Va) == e(piA', g2), valid knowledge commitment for A")
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}
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// e(Vb, piB) == e(piB', g2)
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pairingVbPib := Utils.Bn.Pairing(vk.Vkb, proof.PiB)
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pairingPibpG2 := Utils.Bn.Pairing(proof.PiBp, Utils.Bn.G2.G)
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if !Utils.Bn.Fq12.Equal(pairingVbPib, pairingPibpG2) {
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if debug {
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fmt.Println("❌ e(Vb, piB) == e(piB', g2), valid knowledge commitment for B")
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}
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return false
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}
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if debug {
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fmt.Println("✓ e(Vb, piB) == e(piB', g2), valid knowledge commitment for B")
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}
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// e(piC, Vc) == e(piC', g2)
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pairingPicVc := Utils.Bn.Pairing(proof.PiC, vk.Vkc)
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pairingPicpG2 := Utils.Bn.Pairing(proof.PiCp, Utils.Bn.G2.G)
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if !Utils.Bn.Fq12.Equal(pairingPicVc, pairingPicpG2) {
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if debug {
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fmt.Println("❌ e(piC, Vc) == e(piC', g2), valid knowledge commitment for C")
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}
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return false
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}
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if debug {
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fmt.Println("✓ e(piC, Vc) == e(piC', g2), valid knowledge commitment for C")
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}
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// Vkx, to then calculate Vkx+piA
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vkxpia := vk.IC[0]
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for i := 0; i < len(publicSignals); i++ {
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vkxpia = Utils.Bn.G1.Add(vkxpia, Utils.Bn.G1.MulScalar(vk.IC[i+1], publicSignals[i]))
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}
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// e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2)
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if !Utils.Bn.Fq12.Equal(
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Utils.Bn.Pairing(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiB), // TODO Add(vkxpia, proof.PiA) can go outside in order to save computation, as is reused later
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Utils.Bn.Fq12.Mul(
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Utils.Bn.Pairing(proof.PiH, vk.Vkz),
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Utils.Bn.Pairing(proof.PiC, Utils.Bn.G2.G))) {
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if debug {
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fmt.Println("❌ e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2), QAP disibility checked")
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}
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return false
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}
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if debug {
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fmt.Println("✓ e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2), QAP disibility checked")
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}
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// e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB)
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// == e(piK, g2Kgamma)
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piApiC := Utils.Bn.G1.Add(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiC)
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pairingPiACG2Kbg := Utils.Bn.Pairing(piApiC, vk.G2Kbg)
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pairingG1KbgPiB := Utils.Bn.Pairing(vk.G1Kbg, proof.PiB)
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pairingL := Utils.Bn.Fq12.Mul(pairingPiACG2Kbg, pairingG1KbgPiB)
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pairingR := Utils.Bn.Pairing(proof.PiKp, vk.G2Kg)
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if !Utils.Bn.Fq12.Equal(pairingL, pairingR) {
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fmt.Println("❌ e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB) == e(piK, g2Kgamma)")
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return false
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}
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if debug {
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fmt.Println("✓ e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB) == e(piK, g2Kgamma)")
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}
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return true
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}
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