go-snark/snark.go
snark.goRaw
1package snark
2
3import (
4 "fmt"
5 "math/big"
6 "os"
7
8 "github.com/arnaucube/go-snark/bn128"
9 "github.com/arnaucube/go-snark/circuitcompiler"
10 "github.com/arnaucube/go-snark/fields"
11 "github.com/arnaucube/go-snark/r1csqap"
12)
13
14// Setup is the data structure holding the Trusted Setup data. The Setup.Toxic sub struct must be destroyed after the GenerateTrustedSetup function is completed
15type Setup struct {
16 Toxic struct {
17 T *big.Int // trusted setup secret
18 Ka *big.Int // prover
19 Kb *big.Int // prover
20 Kc *big.Int // prover
21 Kbeta *big.Int
22 Kgamma *big.Int
23 RhoA *big.Int
24 RhoB *big.Int
25 RhoC *big.Int
26 }
27
28 // public
29 G1T [][3]*big.Int // t encrypted in G1 curve
30 G2T [][3][2]*big.Int // t encrypted in G2 curve
31 Pk struct { // Proving Key pk:=(pkA, pkB, pkC, pkH)
32 A [][3]*big.Int
33 B [][3][2]*big.Int
34 C [][3]*big.Int
35 Kp [][3]*big.Int
36 Ap [][3]*big.Int
37 Bp [][3]*big.Int
38 Cp [][3]*big.Int
39 }
40 Vk struct {
41 Vka [3][2]*big.Int
42 Vkb [3]*big.Int
43 Vkc [3][2]*big.Int
44 A [][3]*big.Int
45 G1Kbg [3]*big.Int // g1 * Kbeta * Kgamma
46 G2Kbg [3][2]*big.Int // g2 * Kbeta * Kgamma
47 G2Kg [3][2]*big.Int // g2 * Kgamma
48 Vkz [3][2]*big.Int
49 }
50}
51
52// Proof contains the parameters to proof the zkSNARK
53type Proof struct {
54 PiA [3]*big.Int
55 PiAp [3]*big.Int
56 PiB [3][2]*big.Int
57 PiBp [3]*big.Int
58 PiC [3]*big.Int
59 PiCp [3]*big.Int
60 PiH [3]*big.Int
61 PiKp [3]*big.Int
62 PublicSignals []*big.Int
63}
64
65type utils struct {
66 Bn bn128.Bn128
67 FqR fields.Fq
68 PF r1csqap.PolynomialField
69}
70
71// Utils is the data structure holding the BN128, FqR Finite Field over R, PolynomialField, that will be used inside the snarks operations
72var Utils = prepareUtils()
73
74func prepareUtils() utils {
75 bn, err := bn128.NewBn128()
76 if err != nil {
77 panic(err)
78 }
79 // new Finite Field
80 fqR := fields.NewFq(bn.R)
81 // new Polynomial Field
82 pf := r1csqap.NewPolynomialField(fqR)
83
84 return utils{
85 Bn: bn,
86 FqR: fqR,
87 PF: pf,
88 }
89}
90
91// GenerateTrustedSetup generates the Trusted Setup from a compiled Circuit. The Setup.Toxic sub data structure must be destroyed
92func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, alphas, betas, gammas [][]*big.Int, zx []*big.Int) (Setup, error) {
93 var setup Setup
94 var err error
95 // generate random t value
96 setup.Toxic.T, err = Utils.FqR.Rand()
97 if err != nil {
98 return Setup{}, err
99 }
100
101 // k for calculating pi' and Vk
102 setup.Toxic.Ka, err = Utils.FqR.Rand()
103 if err != nil {
104 return Setup{}, err
105 }
106 setup.Toxic.Kb, err = Utils.FqR.Rand()
107 if err != nil {
108 return Setup{}, err
109 }
110 setup.Toxic.Kc, err = Utils.FqR.Rand()
111 if err != nil {
112 return Setup{}, err
113 }
114
115 // generate Kβ (Kbeta) and Kγ (Kgamma)
116 setup.Toxic.Kbeta, err = Utils.FqR.Rand()
117 if err != nil {
118 return Setup{}, err
119 }
120 setup.Toxic.Kgamma, err = Utils.FqR.Rand()
121 if err != nil {
122 return Setup{}, err
123 }
124
125 // generate ρ (Rho): ρA, ρB, ρC
126 setup.Toxic.RhoA, err = Utils.FqR.Rand()
127 if err != nil {
128 return Setup{}, err
129 }
130 setup.Toxic.RhoB, err = Utils.FqR.Rand()
131 if err != nil {
132 return Setup{}, err
133 }
134 setup.Toxic.RhoC = Utils.FqR.Mul(setup.Toxic.RhoA, setup.Toxic.RhoB)
135
136 // encrypt t values with curve generators
137 var gt1 [][3]*big.Int
138 var gt2 [][3][2]*big.Int
139 for i := 0; i < witnessLength; i++ {
140 tPow := Utils.FqR.Exp(setup.Toxic.T, big.NewInt(int64(i)))
141 tEncr1 := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, tPow)
142 gt1 = append(gt1, tEncr1)
143 tEncr2 := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, tPow)
144 gt2 = append(gt2, tEncr2)
145 }
146 // gt1: g1, g1*t, g1*t^2, g1*t^3, ...
147 // gt2: g2, g2*t, g2*t^2, ...
148 setup.G1T = gt1
149 setup.G2T = gt2
150
151 setup.Vk.Vka = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Ka)
152 setup.Vk.Vkb = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, setup.Toxic.Kb)
153 setup.Vk.Vkc = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kc)
154
155 /*
156 Verification keys:
157 - Vk_betagamma1: setup.G1Kbg = g1 * Kbeta*Kgamma
158 - Vk_betagamma2: setup.G2Kbg = g2 * Kbeta*Kgamma
159 - Vk_gamma: setup.G2Kg = g2 * Kgamma
160 */
161 kbg := Utils.FqR.Mul(setup.Toxic.Kbeta, setup.Toxic.Kgamma)
162 setup.Vk.G1Kbg = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kbg)
163 setup.Vk.G2Kbg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, kbg)
164 setup.Vk.G2Kg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kgamma)
165
166 // for i := 0; i < circuit.NSignals; i++ {
167 for i := 0; i < circuit.NVars; i++ {
168 at := Utils.PF.Eval(alphas[i], setup.Toxic.T)
169 a := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, at)
170 setup.Pk.A = append(setup.Pk.A, a)
171 if i <= circuit.NPublic {
172 setup.Vk.A = append(setup.Vk.A, a)
173 }
174
175 bt := Utils.PF.Eval(betas[i], setup.Toxic.T)
176 bg1 := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, bt)
177 bg2 := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, bt)
178 setup.Pk.B = append(setup.Pk.B, bg2)
179
180 ct := Utils.PF.Eval(gammas[i], setup.Toxic.T)
181 c := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, ct)
182 setup.Pk.C = append(setup.Pk.C, c)
183
184 kt := Utils.FqR.Add(Utils.FqR.Add(at, bt), ct)
185 k := Utils.Bn.G1.Affine(Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kt))
186
187 ktest := Utils.Bn.G1.Affine(Utils.Bn.G1.Add(Utils.Bn.G1.Add(a, bg1), c))
188 if !Utils.Bn.Fq2.Equal(k, ktest) {
189 os.Exit(1)
190 return setup, err
191 }
192
193 setup.Pk.Ap = append(setup.Pk.Ap, Utils.Bn.G1.MulScalar(a, setup.Toxic.Ka))
194 setup.Pk.Bp = append(setup.Pk.Bp, Utils.Bn.G1.MulScalar(bg1, setup.Toxic.Kb))
195 setup.Pk.Cp = append(setup.Pk.Cp, Utils.Bn.G1.MulScalar(c, setup.Toxic.Kc))
196 k_ := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kt)
197 setup.Pk.Kp = append(setup.Pk.Kp, Utils.Bn.G1.MulScalar(k_, setup.Toxic.Kbeta))
198 }
199 setup.Vk.Vkz = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, Utils.PF.Eval(zx, setup.Toxic.T))
200
201 return setup, nil
202}
203
204// GenerateProofs generates all the parameters to proof the zkSNARK from the Circuit, Setup and the Witness
205func GenerateProofs(circuit circuitcompiler.Circuit, setup Setup, hx []*big.Int, w []*big.Int) (Proof, error) {
206 var proof Proof
207 proof.PiA = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
208 proof.PiAp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
209 proof.PiB = Utils.Bn.Fq6.Zero()
210 proof.PiBp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
211 proof.PiC = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
212 proof.PiCp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
213 proof.PiH = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
214 proof.PiKp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
215
216 for i := circuit.NPublic + 1; i < circuit.NVars; i++ {
217 proof.PiA = Utils.Bn.G1.Add(proof.PiA, Utils.Bn.G1.MulScalar(setup.Pk.A[i], w[i]))
218 proof.PiAp = Utils.Bn.G1.Add(proof.PiAp, Utils.Bn.G1.MulScalar(setup.Pk.Ap[i], w[i]))
219 }
220
221 for i := 0; i < circuit.NVars; i++ {
222 proof.PiB = Utils.Bn.G2.Add(proof.PiB, Utils.Bn.G2.MulScalar(setup.Pk.B[i], w[i]))
223 proof.PiBp = Utils.Bn.G1.Add(proof.PiBp, Utils.Bn.G1.MulScalar(setup.Pk.Bp[i], w[i]))
224
225 proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(setup.Pk.C[i], w[i]))
226 proof.PiCp = Utils.Bn.G1.Add(proof.PiCp, Utils.Bn.G1.MulScalar(setup.Pk.Cp[i], w[i]))
227
228 proof.PiKp = Utils.Bn.G1.Add(proof.PiKp, Utils.Bn.G1.MulScalar(setup.Pk.Kp[i], w[i]))
229 }
230
231 for i := 0; i < len(hx); i++ {
232 proof.PiH = Utils.Bn.G1.Add(proof.PiH, Utils.Bn.G1.MulScalar(setup.G1T[i], hx[i]))
233 }
234 proof.PublicSignals = w[1 : circuit.NPublic+1]
235
236 return proof, nil
237}
238
239// VerifyProof verifies over the BN128 the Pairings of the Proof
240func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof) bool {
241 // e(piA, Va) == e(piA', g2)
242 pairingPiaVa := Utils.Bn.Pairing(proof.PiA, setup.Vk.Vka)
243 pairingPiapG2 := Utils.Bn.Pairing(proof.PiAp, Utils.Bn.G2.G)
244 if !Utils.Bn.Fq12.Equal(pairingPiaVa, pairingPiapG2) {
245 return false
246 }
247 fmt.Println("✓ e(piA, Va) == e(piA', g2), valid knowledge commitment for A")
248
249 // e(Vb, piB) == e(piB', g2)
250 pairingVbPib := Utils.Bn.Pairing(setup.Vk.Vkb, proof.PiB)
251 pairingPibpG2 := Utils.Bn.Pairing(proof.PiBp, Utils.Bn.G2.G)
252 if !Utils.Bn.Fq12.Equal(pairingVbPib, pairingPibpG2) {
253 return false
254 }
255 fmt.Println("✓ e(Vb, piB) == e(piB', g2), valid knowledge commitment for B")
256
257 // e(piC, Vc) == e(piC', g2)
258 pairingPicVc := Utils.Bn.Pairing(proof.PiC, setup.Vk.Vkc)
259 pairingPicpG2 := Utils.Bn.Pairing(proof.PiCp, Utils.Bn.G2.G)
260 if !Utils.Bn.Fq12.Equal(pairingPicVc, pairingPicpG2) {
261 return false
262 }
263 fmt.Println("✓ e(piC, Vc) == e(piC', g2), valid knowledge commitment for C")
264
265 // Vkx, to then calculate Vkx+piA
266 vkxpia := setup.Vk.A[0]
267 for i := 0; i < circuit.NPublic; i++ {
268 vkxpia = Utils.Bn.G1.Add(vkxpia, Utils.Bn.G1.MulScalar(setup.Vk.A[i+1], proof.PublicSignals[i]))
269 }
270
271 // e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2)
272 if !Utils.Bn.Fq12.Equal(
273 Utils.Bn.Pairing(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiB),
274 Utils.Bn.Fq12.Mul(
275 Utils.Bn.Pairing(proof.PiH, setup.Vk.Vkz),
276 Utils.Bn.Pairing(proof.PiC, Utils.Bn.G2.G))) {
277 return false
278 }
279 fmt.Println("✓ e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2), QAP disibility checked")
280
281 // e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB)
282 // == e(piK, g2Kgamma)
283 piApiC := Utils.Bn.G1.Add(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiC)
284 pairingPiACG2Kbg := Utils.Bn.Pairing(piApiC, setup.Vk.G2Kbg)
285 pairingG1KbgPiB := Utils.Bn.Pairing(setup.Vk.G1Kbg, proof.PiB)
286 pairingL := Utils.Bn.Fq12.Mul(pairingPiACG2Kbg, pairingG1KbgPiB)
287 pairingR := Utils.Bn.Pairing(proof.PiKp, setup.Vk.G2Kg)
288 if !Utils.Bn.Fq12.Equal(pairingL, pairingR) {
289 return false
290 }
291 fmt.Println("✓ e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB) == e(piK, g2Kgamma)")
292
293 return true
294}