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proofs

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arnaucube
2018-12-06 17:39:21 +01:00
parent 6cd494f36f
commit 917eecaee0
3 changed files with 125 additions and 48 deletions
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2
README.md
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@@ -112,4 +112,4 @@ assert.True(t, bn128.Fq12.Equal(pA, pB))
## Caution
Not finished, work in progress (implementing this in my free time to understand it better, so I don't have much time).
Thanks to @jbaylina, @bellesmarta, @adriamb for their explanations that helped to understand a little bit this.
Thanks to [@jbaylina](https://github.com/jbaylina), [@bellesmarta](https://github.com/bellesmarta), [@adriamb](https://github.com/adriamb) for their explanations that helped to understand this a little bit.

138
zk/zk.go
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@@ -8,22 +8,48 @@ import (
"github.com/arnaucube/go-snark/bn128"
)
type Setup struct {
T *big.Int // trusted setup secret
Ka *big.Int // trusted setup
Kb *big.Int // trusted setup
Kc *big.Int // trusted setup
// public
G1T [][3]*big.Int // t encrypted in G1 curve
G2T [][3][2]*big.Int // t encrypted in G2 curve
}
type Proof struct {
PiA [3]*big.Int
PiAp [3]*big.Int
PiB [3][2]*big.Int
PiBp [3][2]*big.Int
PiC [3]*big.Int
PiCp [3]*big.Int
PiH [3]*big.Int
Va [3][2]*big.Int
Vb [3][2]*big.Int
Vc [3][2]*big.Int
Vz [3][2]*big.Int
}
const bits = 512
func GenerateTrustedSetup(bn bn128.Bn128, pollength int) ([][3]*big.Int, [][3][2]*big.Int, error) {
func GenerateTrustedSetup(bn bn128.Bn128, pollength int) (Setup, error) {
var setup Setup
var err error
// generate random t value
t, err := rand.Prime(rand.Reader, bits)
setup.T, err = rand.Prime(rand.Reader, bits)
if err != nil {
return [][3]*big.Int{}, [][3][2]*big.Int{}, err
return Setup{}, err
}
fmt.Print("trusted t: ")
fmt.Println(t)
fmt.Println(setup.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)))
tPow := bn.Fq1.Exp(setup.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)
@@ -31,39 +57,103 @@ func GenerateTrustedSetup(bn bn128.Bn128, pollength int) ([][3]*big.Int, [][3][2
}
// 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) {
setup.G1T = gt1
setup.G2T = gt2
// multiply g1*A(x), g2*B(x), g1*C(x), g1*H(x)
// k for pi'
setup.Ka, err = rand.Prime(rand.Reader, bits)
if err != nil {
return Setup{}, err
}
setup.Kb, err = rand.Prime(rand.Reader, bits)
if err != nil {
return Setup{}, err
}
setup.Kc, err = rand.Prime(rand.Reader, bits)
if err != nil {
return Setup{}, err
}
return setup, nil
}
func GenerateProofs(bn bn128.Bn128, setup Setup, ax, bx, cx, hx, zx []*big.Int) Proof {
var proof Proof
// g1*A(x)
g1At := [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
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(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)
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.Ka)
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)
// g1*B(x)
proof.PiB = bn.Fq6.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)
}
proof.PiBp = bn.G2.MulScalar(proof.PiB, setup.Kb)
// g1*C(x)
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.Kc)
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])
m := bn.G1.MulScalar(setup.G1T[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])
m := bn.G2.MulScalar(setup.G2T[i], zx[i])
g2Zt = bn.G2.Add(g2Zt, m)
}
proof.PiH = g1Ht
proof.Vz = g2Zt
proof.Va = bn.G2.MulScalar(bn.G2.G, setup.Ka)
proof.Vb = bn.G2.MulScalar(bn.G2.G, setup.Kb)
proof.Vc = bn.G2.MulScalar(bn.G2.G, setup.Kc)
return g1At, g2Bt, g1Ct, g1Ht, g2Zt
return proof
}
func VerifyProof(bn bn128.Bn128, setup Setup, proof Proof) bool {
// e(piA, Va) == e(piA', g2)
pairingPiaVa, err := bn.Pairing(proof.PiA, proof.Va)
if err != nil {
return false
}
pairingPiapG2, err := bn.Pairing(proof.PiAp, bn.G2.G)
if err != nil {
return false
}
if !bn.Fq12.Equal(pairingPiaVa, pairingPiapG2) {
return false
}
// e(piB, Vb) == e(piB', g2)
// e(piC, Vc) == e(piC', g2)
pairingPicVc, err := bn.Pairing(proof.PiC, proof.Vc)
if err != nil {
return false
}
pairingPicpG2, err := bn.Pairing(proof.PiCp, bn.G2.G)
if err != nil {
return false
}
if !bn.Fq12.Equal(pairingPicVc, pairingPicpG2) {
return false
}
//
return true
}

33
zk/zk_test.go
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@@ -64,33 +64,20 @@ func TestZk(t *testing.T) {
assert.Equal(t, abc, hz)
// calculate trusted setup
gt1, gt2, err := GenerateTrustedSetup(bn, len(ax))
setup, err := GenerateTrustedSetup(bn, len(ax))
assert.Nil(t, err)
fmt.Println("trusted setup:")
fmt.Println(gt1)
fmt.Println(gt2)
fmt.Println(setup.G1T)
fmt.Println(setup.G2T)
// 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)
proof := GenerateProofs(bn, setup, ax, bx, cx, hx, zx)
fmt.Println("proofs:")
fmt.Println(piA)
fmt.Println(piB)
fmt.Println(piC)
fmt.Println(piH)
fmt.Println(piZ)
fmt.Println(proof.PiA)
fmt.Println(proof.PiB)
fmt.Println(proof.PiC)
fmt.Println(proof.PiH)
fmt.Println(proof.Vz)
// 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))
assert.True(t, VerifyProof(bn, setup, proof))
}