doing trusted setup

zk/zk.go

@@ -0,0 +1,69 @@
+package zk
+
+import (
+	"crypto/rand"
+	"fmt"
+	"math/big"
+
+	"github.com/arnaucube/go-snark/bn128"
+)
+
+const bits = 512
+
+func GenerateTrustedSetup(bn bn128.Bn128, pollength int) ([][3]*big.Int, [][3][2]*big.Int, error) {
+	// generate random t value
+	t, err := rand.Prime(rand.Reader, bits)
+	if err != nil {
+		return [][3]*big.Int{}, [][3][2]*big.Int{}, err
+	}
+	fmt.Print("trusted t: ")
+	fmt.Println(t)
+
+	// encrypt t values with curve generators
+	var gt1 [][3]*big.Int
+	var gt2 [][3][2]*big.Int
+	for i := 0; i < pollength; i++ {
+		tPow := bn.Fq1.Exp(t, big.NewInt(int64(i)))
+		tEncr1 := bn.G1.MulScalar(bn.G1.G, tPow)
+		gt1 = append(gt1, tEncr1)
+		tEncr2 := bn.G2.MulScalar(bn.G2.G, tPow)
+		gt2 = append(gt2, tEncr2)
+	}
+	// gt1: g1, g1*t, g1*t^2, g1*t^3, ...
+	// gt2: g2, g2*t, g2*t^2, ...
+	return gt1, gt2, nil
+}
+func GenerateProofs(bn bn128.Bn128, gt1 [][3]*big.Int, gt2 [][3][2]*big.Int, ax, bx, cx, hx, zx []*big.Int) ([3]*big.Int, [3][2]*big.Int, [3]*big.Int, [3]*big.Int, [3][2]*big.Int) {
+
+	// multiply g1*A(x), g2*B(x), g1*C(x), g1*H(x)
+
+	// g1*A(x)
+	g1At := [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(gt1[i], ax[i])
+		g1At = bn.G1.Add(g1At, m)
+	}
+	g2Bt := bn.Fq6.Zero()
+	for i := 0; i < len(bx); i++ {
+		m := bn.G2.MulScalar(gt2[i], bx[i])
+		g2Bt = bn.G2.Add(g2Bt, m)
+	}
+
+	g1Ct := [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(gt1[i], cx[i])
+		g1Ct = bn.G1.Add(g1Ct, m)
+	}
+	g1Ht := [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(gt1[i], hx[i])
+		g1Ht = bn.G1.Add(g1Ht, m)
+	}
+	g2Zt := bn.Fq6.Zero()
+	for i := 0; i < len(bx); i++ {
+		m := bn.G2.MulScalar(gt2[i], zx[i])
+		g2Zt = bn.G2.Add(g2Zt, m)
+	}
+
+	return g1At, g2Bt, g1Ct, g1Ht, g2Zt
+}

zk/zk_test.go

@@ -0,0 +1,96 @@
+package zk
+
+import (
+	"fmt"
+	"math/big"
+	"testing"
+
+	"github.com/arnaucube/go-snark/bn128"
+	"github.com/arnaucube/go-snark/fields"
+	"github.com/arnaucube/go-snark/r1csqap"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestZk(t *testing.T) {
+	bn, err := bn128.NewBn128()
+	assert.Nil(t, err)
+
+	// new Finite Field
+	f := fields.NewFq(bn.R)
+
+	// new Polynomial Field
+	pf := r1csqap.NewPolynomialField(f)
+
+	b0 := big.NewInt(int64(0))
+	b1 := big.NewInt(int64(1))
+	b3 := big.NewInt(int64(3))
+	b5 := big.NewInt(int64(5))
+	b9 := big.NewInt(int64(9))
+	b27 := big.NewInt(int64(27))
+	b30 := big.NewInt(int64(30))
+	b35 := big.NewInt(int64(35))
+	a := [][]*big.Int{
+		[]*big.Int{b0, b1, b0, b0, b0, b0},
+		[]*big.Int{b0, b0, b0, b1, b0, b0},
+		[]*big.Int{b0, b1, b0, b0, b1, b0},
+		[]*big.Int{b5, b0, b0, b0, b0, b1},
+	}
+	b := [][]*big.Int{
+		[]*big.Int{b0, b1, b0, b0, b0, b0},
+		[]*big.Int{b0, b1, b0, b0, b0, b0},
+		[]*big.Int{b1, b0, b0, b0, b0, b0},
+		[]*big.Int{b1, b0, b0, b0, b0, b0},
+	}
+	c := [][]*big.Int{
+		[]*big.Int{b0, b0, b0, b1, b0, b0},
+		[]*big.Int{b0, b0, b0, b0, b1, b0},
+		[]*big.Int{b0, b0, b0, b0, b0, b1},
+		[]*big.Int{b0, b0, b1, b0, b0, b0},
+	}
+	alphas, betas, gammas, zx := pf.R1CSToQAP(a, b, c)
+
+	w := []*big.Int{b1, b3, b35, b9, b27, b30}
+	ax, bx, cx, px := pf.CombinePolynomials(w, alphas, betas, gammas)
+
+	hx := pf.DivisorPolinomial(px, zx)
+
+	// hx==px/zx so px==hx*zx
+	assert.Equal(t, px, pf.Mul(hx, zx))
+
+	// p(x) = a(x) * b(x) - c(x) == h(x) * z(x)
+	abc := pf.Sub(pf.Mul(ax, bx), cx)
+	assert.Equal(t, abc, px)
+	hz := pf.Mul(hx, zx)
+	assert.Equal(t, abc, hz)
+
+	// calculate trusted setup
+	gt1, gt2, err := GenerateTrustedSetup(bn, len(ax))
+	assert.Nil(t, err)
+	fmt.Println("trusted setup:")
+	fmt.Println(gt1)
+	fmt.Println(gt2)
+
+	// piA = g1 * A(t), piB = g2 * B(t), piC = g1 * C(t), piH = g1 * H(t)
+	piA, piB, piC, piH, piZ := GenerateProofs(bn, gt1, gt2, ax, bx, cx, hx, zx)
+	fmt.Println("proofs:")
+	fmt.Println(piA)
+	fmt.Println(piB)
+	fmt.Println(piC)
+	fmt.Println(piH)
+	fmt.Println(piZ)
+
+	// pairing
+	fmt.Println("pairing")
+	pairingAB, err := bn.Pairing(piA, piB)
+	assert.Nil(t, err)
+	pairingCg2, err := bn.Pairing(piC, bn.G2.G)
+	assert.Nil(t, err)
+	pairingLeft := bn.Fq12.Div(pairingAB, pairingCg2)
+	pairingHg2Z, err := bn.Pairing(piH, piZ)
+	assert.Nil(t, err)
+
+	fmt.Println(bn.Fq12.Affine(pairingLeft))
+	fmt.Println(bn.Fq12.Affine(pairingHg2Z))
+
+	assert.True(t, bn.Fq12.Equal(pairingLeft, pairingHg2Z))
+}