1package zk
  2
  3import (
  4	"crypto/rand"
  5	"fmt"
  6	"math/big"
  7
  8	"github.com/arnaucube/go-snark/bn128"
  9)
 10
 11type Setup struct {
 12	T  *big.Int // trusted setup secret
 13	Ka *big.Int // trusted setup
 14	Kb *big.Int // trusted setup
 15	Kc *big.Int // trusted setup
 16
 17	// public
 18	G1T [][3]*big.Int    // t encrypted in G1 curve
 19	G2T [][3][2]*big.Int // t encrypted in G2 curve
 20}
 21type Proof struct {
 22	PiA  [3]*big.Int
 23	PiAp [3]*big.Int
 24	PiB  [3][2]*big.Int
 25	PiBp [3][2]*big.Int
 26	PiC  [3]*big.Int
 27	PiCp [3]*big.Int
 28	PiH  [3]*big.Int
 29	Va   [3][2]*big.Int
 30	Vb   [3][2]*big.Int
 31	Vc   [3][2]*big.Int
 32	Vz   [3][2]*big.Int
 33}
 34
 35const bits = 512
 36
 37func GenerateTrustedSetup(bn bn128.Bn128, pollength int) (Setup, error) {
 38	var setup Setup
 39	var err error
 40	// generate random t value
 41	setup.T, err = rand.Prime(rand.Reader, bits)
 42	if err != nil {
 43		return Setup{}, err
 44	}
 45	fmt.Print("trusted t: ")
 46	fmt.Println(setup.T)
 47
 48	// encrypt t values with curve generators
 49	var gt1 [][3]*big.Int
 50	var gt2 [][3][2]*big.Int
 51	for i := 0; i < pollength; i++ {
 52		tPow := bn.Fq1.Exp(setup.T, big.NewInt(int64(i)))
 53		tEncr1 := bn.G1.MulScalar(bn.G1.G, tPow)
 54		gt1 = append(gt1, tEncr1)
 55		tEncr2 := bn.G2.MulScalar(bn.G2.G, tPow)
 56		gt2 = append(gt2, tEncr2)
 57	}
 58	// gt1: g1, g1*t, g1*t^2, g1*t^3, ...
 59	// gt2: g2, g2*t, g2*t^2, ...
 60	setup.G1T = gt1
 61	setup.G2T = gt2
 62
 63	// k for pi'
 64	setup.Ka, err = rand.Prime(rand.Reader, bits)
 65	if err != nil {
 66		return Setup{}, err
 67	}
 68	setup.Kb, err = rand.Prime(rand.Reader, bits)
 69	if err != nil {
 70		return Setup{}, err
 71	}
 72	setup.Kc, err = rand.Prime(rand.Reader, bits)
 73	if err != nil {
 74		return Setup{}, err
 75	}
 76
 77	return setup, nil
 78}
 79
 80func GenerateProofs(bn bn128.Bn128, setup Setup, ax, bx, cx, hx, zx []*big.Int) Proof {
 81	var proof Proof
 82
 83	// g1*A(x)
 84	proof.PiA = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
 85	for i := 0; i < len(ax); i++ {
 86		m := bn.G1.MulScalar(setup.G1T[i], ax[i])
 87		proof.PiA = bn.G1.Add(proof.PiA, m)
 88	}
 89	proof.PiAp = bn.G1.MulScalar(proof.PiA, setup.Ka)
 90
 91	// g1*B(x)
 92	proof.PiB = bn.Fq6.Zero()
 93	for i := 0; i < len(bx); i++ {
 94		m := bn.G2.MulScalar(setup.G2T[i], bx[i])
 95		proof.PiB = bn.G2.Add(proof.PiB, m)
 96	}
 97	proof.PiBp = bn.G2.MulScalar(proof.PiB, setup.Kb)
 98
 99	// g1*C(x)
100	proof.PiC = [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
101	for i := 0; i < len(cx); i++ {
102		m := bn.G1.MulScalar(setup.G1T[i], cx[i])
103		proof.PiC = bn.G1.Add(proof.PiC, m)
104	}
105	proof.PiCp = bn.G1.MulScalar(proof.PiC, setup.Kc)
106
107	g1Ht := [3]*big.Int{bn.G1.F.Zero(), bn.G1.F.Zero(), bn.G1.F.Zero()}
108	for i := 0; i < len(hx); i++ {
109		m := bn.G1.MulScalar(setup.G1T[i], hx[i])
110		g1Ht = bn.G1.Add(g1Ht, m)
111	}
112	g2Zt := bn.Fq6.Zero()
113	for i := 0; i < len(bx); i++ {
114		m := bn.G2.MulScalar(setup.G2T[i], zx[i])
115		g2Zt = bn.G2.Add(g2Zt, m)
116	}
117	proof.PiH = g1Ht
118	proof.Vz = g2Zt
119	proof.Va = bn.G2.MulScalar(bn.G2.G, setup.Ka)
120	proof.Vb = bn.G2.MulScalar(bn.G2.G, setup.Kb)
121	proof.Vc = bn.G2.MulScalar(bn.G2.G, setup.Kc)
122
123	return proof
124}
125
126func VerifyProof(bn bn128.Bn128, setup Setup, proof Proof) bool {
127
128	// e(piA, Va) == e(piA', g2)
129	pairingPiaVa, err := bn.Pairing(proof.PiA, proof.Va)
130	if err != nil {
131		return false
132	}
133	pairingPiapG2, err := bn.Pairing(proof.PiAp, bn.G2.G)
134	if err != nil {
135		return false
136	}
137	if !bn.Fq12.Equal(pairingPiaVa, pairingPiapG2) {
138		return false
139	}
140
141	// e(piB, Vb) == e(piB', g2)
142
143	// e(piC, Vc) == e(piC', g2)
144	pairingPicVc, err := bn.Pairing(proof.PiC, proof.Vc)
145	if err != nil {
146		return false
147	}
148	pairingPicpG2, err := bn.Pairing(proof.PiCp, bn.G2.G)
149	if err != nil {
150		return false
151	}
152	if !bn.Fq12.Equal(pairingPicVc, pairingPicpG2) {
153		return false
154	}
155
156	//
157
158	return true
159}