add Groth16 setup calculation

fields/fq.go

@@ -32,35 +32,30 @@ func (fq Fq) One() *big.Int {
 func (fq Fq) Add(a, b *big.Int) *big.Int {
 	r := new(big.Int).Add(a, b)
 	return new(big.Int).Mod(r, fq.Q)
-	// return r
 }
 
 // Double performs a doubling on the Fq
 func (fq Fq) Double(a *big.Int) *big.Int {
 	r := new(big.Int).Add(a, a)
 	return new(big.Int).Mod(r, fq.Q)
-	// return r
 }
 
 // Sub performs a subtraction on the Fq
 func (fq Fq) Sub(a, b *big.Int) *big.Int {
 	r := new(big.Int).Sub(a, b)
 	return new(big.Int).Mod(r, fq.Q)
-	// return r
 }
 
 // Neg performs a negation on the Fq
 func (fq Fq) Neg(a *big.Int) *big.Int {
 	m := new(big.Int).Neg(a)
 	return new(big.Int).Mod(m, fq.Q)
-	// return m
 }
 
 // Mul performs a multiplication on the Fq
 func (fq Fq) Mul(a, b *big.Int) *big.Int {
 	m := new(big.Int).Mul(a, b)
 	return new(big.Int).Mod(m, fq.Q)
-	// return m
 }
 
 func (fq Fq) MulScalar(base, e *big.Int) *big.Int {
@@ -125,8 +120,6 @@ func (fq Fq) Rand() (*big.Int, error) {
 
 	maxbits := fq.Q.BitLen()
 	b := make([]byte, (maxbits/8)-1)
-	// b := make([]byte, 3)
-	// b := make([]byte, 3)
 	_, err := rand.Read(b)
 	if err != nil {
 		return nil, err
@@ -134,7 +127,7 @@ func (fq Fq) Rand() (*big.Int, error) {
 	r := new(big.Int).SetBytes(b)
 	rq := new(big.Int).Mod(r, fq.Q)
 
-	// return r over q, nil
+	// r over q, nil
 	return rq, nil
 }
 
@@ -170,3 +163,9 @@ func (fq Fq) Equal(a, b *big.Int) bool {
 	bAff := fq.Affine(b)
 	return bytes.Equal(aAff.Bytes(), bAff.Bytes())
 }
+
+func BigIsOdd(n *big.Int) bool {
+	one := big.NewInt(int64(1))
+	and := new(big.Int).And(n, one)
+	return bytes.Equal(and.Bytes(), big.NewInt(int64(1)).Bytes())
+}

fields/fq12.go

@@ -136,12 +136,6 @@ func (fq12 Fq12) Square(a [2][3][2]*big.Int) [2][3][2]*big.Int {
 	}
 }
 
-func BigIsOdd(n *big.Int) bool {
-	one := big.NewInt(int64(1))
-	and := new(big.Int).And(n, one)
-	return bytes.Equal(and.Bytes(), big.NewInt(int64(1)).Bytes())
-}
-
 func (fq12 Fq12) Exp(base [2][3][2]*big.Int, e *big.Int) [2][3][2]*big.Int {
 	// TODO fix bottleneck
 

groth16/groth16.go

@@ -0,0 +1,218 @@
+// 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
+}