go-snark/groth16/groth16.go

// implementation of https://eprint.iacr.org/2016/260.pdf

package groth16

import (
	"math/big"

	"github.com/arnaucube/go-snark/bn128"
	"github.com/arnaucube/go-snark/circuitcompiler"
	"github.com/arnaucube/go-snark/fields"
	"github.com/arnaucube/go-snark/r1csqap"
)

// Setup is the data structure holding the Trusted Setup data. The Setup.Toxic sub struct must be destroyed after the GenerateTrustedSetup function is completed
type Setup struct {
	Toxic struct {
		T      *big.Int // trusted setup secret
		Kalpha *big.Int
		Kbeta  *big.Int
		Kgamma *big.Int
		Kdelta *big.Int
	}

	// public
	Pk struct { // Proving Key
		BACDelta [][3]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / γ } from 0 to l
		Z        []*big.Int
		G1       struct {
			Alpha    [3]*big.Int
			Beta     [3]*big.Int
			Delta    [3]*big.Int
			At       [][3]*big.Int // {a(τ)} from 0 to m
			BACGamma [][3]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m
		}
		G2 struct {
			Beta     [3][2]*big.Int
			Gamma    [3][2]*big.Int
			Delta    [3][2]*big.Int
			BACGamma [][3][2]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m
		}
		PowersTauDelta [][3]*big.Int // powers of τ encrypted in G1 curve, divided by δ
	}
	Vk struct {
		IC [][3]*big.Int
		G1 struct {
			Alpha [3]*big.Int
		}
		G2 struct {
			Beta  [3][2]*big.Int
			Gamma [3][2]*big.Int
			Delta [3][2]*big.Int
		}
	}
}

// ProofGroth contains the parameters to proof the zkSNARK
type ProofGroth struct {
	PiA [3]*big.Int
	PiB [3][2]*big.Int
	PiC [3]*big.Int
}

type utils struct {
	Bn  bn128.Bn128
	FqR fields.Fq
	PF  r1csqap.PolynomialField
}

// Utils is the data structure holding the BN128, FqR Finite Field over R, PolynomialField, that will be used inside the snarks operations
var Utils = prepareUtils()

func prepareUtils() utils {
	bn, err := bn128.NewBn128()
	if err != nil {
		panic(err)
	}
	// new Finite Field
	fqR := fields.NewFq(bn.R)
	// new Polynomial Field
	pf := r1csqap.NewPolynomialField(fqR)

	return utils{
		Bn:  bn,
		FqR: fqR,
		PF:  pf,
	}
}

// GenerateTrustedSetup generates the Trusted Setup from a compiled Circuit. The Setup.Toxic sub data structure must be destroyed
func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, alphas, betas, gammas [][]*big.Int) (Setup, error) {
	var setup Setup
	var err error

	// generate random t value
	setup.Toxic.T, err = Utils.FqR.Rand()
	if err != nil {
		return Setup{}, err
	}

	setup.Toxic.Kalpha, err = Utils.FqR.Rand()
	if err != nil {
		return Setup{}, err
	}
	setup.Toxic.Kbeta, err = Utils.FqR.Rand()
	if err != nil {
		return Setup{}, err
	}
	setup.Toxic.Kgamma, err = Utils.FqR.Rand()
	if err != nil {
		return Setup{}, err
	}
	setup.Toxic.Kdelta, err = Utils.FqR.Rand()
	if err != nil {
		return Setup{}, err
	}

	// z pol
	zpol := []*big.Int{big.NewInt(int64(1))}
	for i := 1; i < len(alphas)-1; i++ {
		zpol = Utils.PF.Mul(
			zpol,
			[]*big.Int{
				Utils.FqR.Neg(
					big.NewInt(int64(i))),
				big.NewInt(int64(1)),
			})
	}
	setup.Pk.Z = zpol
	zt := Utils.PF.Eval(zpol, setup.Toxic.T)
	invDelta := Utils.FqR.Inverse(setup.Toxic.Kdelta)
	ztinvDelta := Utils.FqR.Mul(invDelta, zt)

	// encrypt t values with curve generators
	// powers of tau divided by delta
	var ptd [][3]*big.Int
	ini := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, ztinvDelta)
	ptd = append(ptd, ini)
	tEncr := setup.Toxic.T
	for i := 1; i < len(zpol); i++ {
		ptd = append(ptd, Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, Utils.FqR.Mul(tEncr, ztinvDelta)))
		tEncr = Utils.FqR.Mul(tEncr, setup.Toxic.T)
	}
	// powers of τ encrypted in G1 curve, divided by δ
	// (G1 * τ) / δ
	setup.Pk.PowersTauDelta = ptd

	setup.Pk.G1.Alpha = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, setup.Toxic.Kalpha)
	setup.Pk.G1.Beta = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, setup.Toxic.Kbeta)
	setup.Pk.G1.Delta = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, setup.Toxic.Kdelta)
	setup.Pk.G2.Beta = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kbeta)
	setup.Pk.G2.Delta = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kdelta)

	setup.Vk.G1.Alpha = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, setup.Toxic.Kalpha)
	setup.Vk.G2.Beta = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kbeta)
	setup.Vk.G2.Gamma = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kgamma)
	setup.Vk.G2.Delta = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kdelta)

	for i := 0; i < len(circuit.Signals); i++ {
		// Pk.G1.At: {a(τ)} from 0 to m
		at := Utils.PF.Eval(alphas[i], setup.Toxic.T)
		a := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, at)
		setup.Pk.G1.At = append(setup.Pk.G1.At, a)

		bt := Utils.PF.Eval(betas[i], setup.Toxic.T)
		g1bt := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, bt)
		g2bt := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, bt)
		// G1.BACGamma: {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m in G1
		setup.Pk.G1.BACGamma = append(setup.Pk.G1.BACGamma, g1bt)
		// G2.BACGamma: {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m in G2
		setup.Pk.G2.BACGamma = append(setup.Pk.G2.BACGamma, g2bt)
	}

	zero3 := [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
	for i := 0; i < circuit.NPublic+1; i++ {
		setup.Pk.BACDelta = append(setup.Pk.BACDelta, zero3)
	}
	for i := circuit.NPublic + 1; i < circuit.NVars; i++ {
		// TODO calculate all at, bt, ct outside, to avoid repeating calculations
		at := Utils.PF.Eval(alphas[i], setup.Toxic.T)
		bt := Utils.PF.Eval(betas[i], setup.Toxic.T)
		ct := Utils.PF.Eval(gammas[i], setup.Toxic.T)
		c := Utils.FqR.Mul(
			invDelta,
			Utils.FqR.Add(
				Utils.FqR.Add(
					Utils.FqR.Mul(at, setup.Toxic.Kbeta),
					Utils.FqR.Mul(bt, setup.Toxic.Kalpha),
				),
				ct,
			),
		)
		g1c := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, c)

		// Pk.BACDelta: {( βui(x)+αvi(x)+wi(x) ) / γ } from 0 to l
		setup.Pk.BACDelta = append(setup.Pk.BACDelta, g1c)
	}

	for i := 0; i <= circuit.NPublic; i++ {
		at := Utils.PF.Eval(alphas[i], setup.Toxic.T)
		bt := Utils.PF.Eval(betas[i], setup.Toxic.T)
		ct := Utils.PF.Eval(gammas[i], setup.Toxic.T)
		ic := Utils.FqR.Mul(
			Utils.FqR.Inverse(setup.Toxic.Kgamma),
			Utils.FqR.Add(
				Utils.FqR.Add(
					Utils.FqR.Mul(at, setup.Toxic.Kbeta),
					Utils.FqR.Mul(bt, setup.Toxic.Kalpha),
				),
				ct,
			),
		)
		g1ic := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, ic)
		// used in verifier
		setup.Vk.IC = append(setup.Vk.IC, g1ic)
	}

	return setup, nil
}