go-snark/snark.go
snark.goRaw
1package snark
2
3import (
4 "bytes"
5 "fmt"
6 "math/big"
7 "os"
8
9 "github.com/arnaucube/go-snark/bn128"
10 "github.com/arnaucube/go-snark/circuitcompiler"
11 "github.com/arnaucube/go-snark/fields"
12 "github.com/arnaucube/go-snark/r1csqap"
13)
14
15// Setup is the data structure holding the Trusted Setup data. The Setup.Toxic sub struct must be destroyed after the GenerateTrustedSetup function is completed
16type Setup struct {
17 Toxic struct {
18 T *big.Int // trusted setup secret
19 Ka *big.Int // prover
20 Kb *big.Int // prover
21 Kc *big.Int // prover
22 Kbeta *big.Int
23 Kgamma *big.Int
24 RhoA *big.Int
25 RhoB *big.Int
26 RhoC *big.Int
27 }
28
29 // public
30 G1T [][3]*big.Int // t encrypted in G1 curve
31 G2T [][3][2]*big.Int // t encrypted in G2 curve
32 Pk struct { // Proving Key pk:=(pkA, pkB, pkC, pkH)
33 A [][3]*big.Int
34 B [][3][2]*big.Int
35 C [][3]*big.Int
36 Kp [][3]*big.Int
37 Ap [][3]*big.Int
38 Bp [][3]*big.Int
39 Cp [][3]*big.Int
40 }
41 Vk struct {
42 Vka [3][2]*big.Int
43 Vkb [3]*big.Int
44 Vkc [3][2]*big.Int
45 IC [][3]*big.Int
46 G1Kbg [3]*big.Int // g1 * Kbeta * Kgamma
47 G2Kbg [3][2]*big.Int // g2 * Kbeta * Kgamma
48 G2Kg [3][2]*big.Int // g2 * Kgamma
49 Vkz [3][2]*big.Int
50 }
51}
52
53// Proof contains the parameters to proof the zkSNARK
54type Proof struct {
55 PiA [3]*big.Int
56 PiAp [3]*big.Int
57 PiB [3][2]*big.Int
58 PiBp [3]*big.Int
59 PiC [3]*big.Int
60 PiCp [3]*big.Int
61 PiH [3]*big.Int
62 PiKp [3]*big.Int
63 // PublicSignals []*big.Int
64}
65
66type utils struct {
67 Bn bn128.Bn128
68 FqR fields.Fq
69 PF r1csqap.PolynomialField
70}
71
72// Utils is the data structure holding the BN128, FqR Finite Field over R, PolynomialField, that will be used inside the snarks operations
73var Utils = prepareUtils()
74
75func prepareUtils() utils {
76 bn, err := bn128.NewBn128()
77 if err != nil {
78 panic(err)
79 }
80 // new Finite Field
81 fqR := fields.NewFq(bn.R)
82 // new Polynomial Field
83 pf := r1csqap.NewPolynomialField(fqR)
84
85 return utils{
86 Bn: bn,
87 FqR: fqR,
88 PF: pf,
89 }
90}
91
92// GenerateTrustedSetup generates the Trusted Setup from a compiled Circuit. The Setup.Toxic sub data structure must be destroyed
93func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, alphas, betas, gammas [][]*big.Int, zx []*big.Int) (Setup, error) {
94 var setup Setup
95 var err error
96
97 // input soundness
98 for i := 0; i < len(alphas); i++ {
99 for j := 0; j < len(alphas[i]); j++ {
100 if j <= circuit.NPublic {
101 if bytes.Equal(alphas[i][j].Bytes(), Utils.Bn.Fq1.Zero().Bytes()) {
102 alphas[i][j] = Utils.Bn.Fq1.One()
103 }
104 }
105 }
106 }
107
108 // generate random t value
109 setup.Toxic.T, err = Utils.FqR.Rand()
110 if err != nil {
111 return Setup{}, err
112 }
113
114 // k for calculating pi' and Vk
115 setup.Toxic.Ka, err = Utils.FqR.Rand()
116 if err != nil {
117 return Setup{}, err
118 }
119 setup.Toxic.Kb, err = Utils.FqR.Rand()
120 if err != nil {
121 return Setup{}, err
122 }
123 setup.Toxic.Kc, err = Utils.FqR.Rand()
124 if err != nil {
125 return Setup{}, err
126 }
127
128 // generate Kβ (Kbeta) and Kγ (Kgamma)
129 setup.Toxic.Kbeta, err = Utils.FqR.Rand()
130 if err != nil {
131 return Setup{}, err
132 }
133 setup.Toxic.Kgamma, err = Utils.FqR.Rand()
134 if err != nil {
135 return Setup{}, err
136 }
137
138 // generate ρ (Rho): ρA, ρB, ρC
139 setup.Toxic.RhoA, err = Utils.FqR.Rand()
140 if err != nil {
141 return Setup{}, err
142 }
143 setup.Toxic.RhoB, err = Utils.FqR.Rand()
144 if err != nil {
145 return Setup{}, err
146 }
147 setup.Toxic.RhoC = Utils.FqR.Mul(setup.Toxic.RhoA, setup.Toxic.RhoB)
148
149 // encrypt t values with curve generators
150 var gt1 [][3]*big.Int
151 var gt2 [][3][2]*big.Int
152 gt1 = append(gt1, Utils.Bn.G1.G)
153 tEncr := setup.Toxic.T
154 for i := 1; i < witnessLength; i++ {
155 gt1 = append(gt1, Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, tEncr))
156 tEncr = Utils.Bn.Fq1.Mul(tEncr, setup.Toxic.T)
157 }
158 // for i := 0; i < witnessLength; i++ {
159 // tPow := Utils.FqR.Exp(setup.Toxic.T, big.NewInt(int64(i)))
160 // tEncr1 := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, tPow)
161 // gt1 = append(gt1, tEncr1)
162 // tEncr2 := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, tPow)
163 // gt2 = append(gt2, tEncr2)
164 // }
165 // gt1: g1, g1*t, g1*t^2, g1*t^3, ...
166 // gt2: g2, g2*t, g2*t^2, ...
167 setup.G1T = gt1
168 setup.G2T = gt2
169
170 setup.Vk.Vka = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Ka)
171 setup.Vk.Vkb = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, setup.Toxic.Kb)
172 setup.Vk.Vkc = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kc)
173
174 /*
175 Verification keys:
176 - Vk_betagamma1: setup.G1Kbg = g1 * Kbeta*Kgamma
177 - Vk_betagamma2: setup.G2Kbg = g2 * Kbeta*Kgamma
178 - Vk_gamma: setup.G2Kg = g2 * Kgamma
179 */
180 kbg := Utils.FqR.Mul(setup.Toxic.Kbeta, setup.Toxic.Kgamma)
181 setup.Vk.G1Kbg = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kbg)
182 setup.Vk.G2Kbg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, kbg)
183 setup.Vk.G2Kg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kgamma)
184
185 for i := 0; i < circuit.NVars; i++ {
186 at := Utils.PF.Eval(alphas[i], setup.Toxic.T)
187 rhoAat := Utils.Bn.Fq1.Mul(setup.Toxic.RhoA, at)
188 a := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoAat)
189 setup.Pk.A = append(setup.Pk.A, a)
190 if i <= circuit.NPublic {
191 setup.Vk.IC = append(setup.Vk.IC, a)
192 }
193
194 bt := Utils.PF.Eval(betas[i], setup.Toxic.T)
195 rhoBbt := Utils.Bn.Fq1.Mul(setup.Toxic.RhoB, bt)
196 bg1 := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoBbt)
197 bg2 := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, rhoBbt)
198 setup.Pk.B = append(setup.Pk.B, bg2)
199
200 ct := Utils.PF.Eval(gammas[i], setup.Toxic.T)
201 rhoCct := Utils.Bn.Fq1.Mul(setup.Toxic.RhoC, ct)
202 c := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoCct)
203 setup.Pk.C = append(setup.Pk.C, c)
204
205 kt := Utils.FqR.Add(Utils.FqR.Add(rhoAat, rhoBbt), rhoCct)
206 k := Utils.Bn.G1.Affine(Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kt))
207
208 ktest := Utils.Bn.G1.Affine(Utils.Bn.G1.Add(Utils.Bn.G1.Add(a, bg1), c))
209 if !Utils.Bn.Fq2.Equal(k, ktest) {
210 os.Exit(1)
211 return setup, err
212 }
213
214 setup.Pk.Ap = append(setup.Pk.Ap, Utils.Bn.G1.MulScalar(a, setup.Toxic.Ka))
215 setup.Pk.Bp = append(setup.Pk.Bp, Utils.Bn.G1.MulScalar(bg1, setup.Toxic.Kb))
216 setup.Pk.Cp = append(setup.Pk.Cp, Utils.Bn.G1.MulScalar(c, setup.Toxic.Kc))
217 k_ := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kt)
218 setup.Pk.Kp = append(setup.Pk.Kp, Utils.Bn.G1.MulScalar(k_, setup.Toxic.Kbeta))
219 }
220 zt := Utils.PF.Eval(zx, setup.Toxic.T)
221 rhoCzt := Utils.Bn.Fq1.Mul(setup.Toxic.RhoC, zt)
222 setup.Vk.Vkz = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, rhoCzt)
223
224 return setup, nil
225}
226
227// GenerateProofs generates all the parameters to proof the zkSNARK from the Circuit, Setup and the Witness
228func GenerateProofs(circuit circuitcompiler.Circuit, setup Setup, hx []*big.Int, w []*big.Int) (Proof, error) {
229 var proof Proof
230 proof.PiA = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
231 proof.PiAp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
232 proof.PiB = Utils.Bn.Fq6.Zero()
233 proof.PiBp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
234 proof.PiC = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
235 proof.PiCp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
236 proof.PiH = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
237 proof.PiKp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
238
239 for i := circuit.NPublic + 1; i < circuit.NVars; i++ {
240 proof.PiA = Utils.Bn.G1.Add(proof.PiA, Utils.Bn.G1.MulScalar(setup.Pk.A[i], w[i]))
241 proof.PiAp = Utils.Bn.G1.Add(proof.PiAp, Utils.Bn.G1.MulScalar(setup.Pk.Ap[i], w[i]))
242 }
243
244 for i := 0; i < circuit.NVars; i++ {
245 proof.PiB = Utils.Bn.G2.Add(proof.PiB, Utils.Bn.G2.MulScalar(setup.Pk.B[i], w[i]))
246 proof.PiBp = Utils.Bn.G1.Add(proof.PiBp, Utils.Bn.G1.MulScalar(setup.Pk.Bp[i], w[i]))
247
248 proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(setup.Pk.C[i], w[i]))
249 proof.PiCp = Utils.Bn.G1.Add(proof.PiCp, Utils.Bn.G1.MulScalar(setup.Pk.Cp[i], w[i]))
250
251 proof.PiKp = Utils.Bn.G1.Add(proof.PiKp, Utils.Bn.G1.MulScalar(setup.Pk.Kp[i], w[i]))
252 }
253
254 for i := 0; i < len(hx); i++ {
255 proof.PiH = Utils.Bn.G1.Add(proof.PiH, Utils.Bn.G1.MulScalar(setup.G1T[i], hx[i]))
256 }
257
258 return proof, nil
259}
260
261// VerifyProof verifies over the BN128 the Pairings of the Proof
262func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof, publicSignals []*big.Int, printVer bool) bool {
263 // e(piA, Va) == e(piA', g2)
264 pairingPiaVa := Utils.Bn.Pairing(proof.PiA, setup.Vk.Vka)
265 pairingPiapG2 := Utils.Bn.Pairing(proof.PiAp, Utils.Bn.G2.G)
266 if !Utils.Bn.Fq12.Equal(pairingPiaVa, pairingPiapG2) {
267 return false
268 }
269 if printVer {
270 fmt.Println("✓ e(piA, Va) == e(piA', g2), valid knowledge commitment for A")
271 }
272
273 // e(Vb, piB) == e(piB', g2)
274 pairingVbPib := Utils.Bn.Pairing(setup.Vk.Vkb, proof.PiB)
275 pairingPibpG2 := Utils.Bn.Pairing(proof.PiBp, Utils.Bn.G2.G)
276 if !Utils.Bn.Fq12.Equal(pairingVbPib, pairingPibpG2) {
277 return false
278 }
279 if printVer {
280 fmt.Println("✓ e(Vb, piB) == e(piB', g2), valid knowledge commitment for B")
281 }
282
283 // e(piC, Vc) == e(piC', g2)
284 pairingPicVc := Utils.Bn.Pairing(proof.PiC, setup.Vk.Vkc)
285 pairingPicpG2 := Utils.Bn.Pairing(proof.PiCp, Utils.Bn.G2.G)
286 if !Utils.Bn.Fq12.Equal(pairingPicVc, pairingPicpG2) {
287 return false
288 }
289 if printVer {
290 fmt.Println("✓ e(piC, Vc) == e(piC', g2), valid knowledge commitment for C")
291 }
292
293 // Vkx, to then calculate Vkx+piA
294 vkxpia := setup.Vk.IC[0]
295 for i := 0; i < len(publicSignals); i++ {
296 vkxpia = Utils.Bn.G1.Add(vkxpia, Utils.Bn.G1.MulScalar(setup.Vk.IC[i+1], publicSignals[i]))
297 }
298
299 // e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2)
300 if !Utils.Bn.Fq12.Equal(
301 Utils.Bn.Pairing(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiB), // TODO Add(vkxpia, proof.PiA) can go outside in order to save computation, as is reused later
302 Utils.Bn.Fq12.Mul(
303 Utils.Bn.Pairing(proof.PiH, setup.Vk.Vkz),
304 Utils.Bn.Pairing(proof.PiC, Utils.Bn.G2.G))) {
305 return false
306 }
307 if printVer {
308 fmt.Println("✓ e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2), QAP disibility checked")
309 }
310
311 // e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB)
312 // == e(piK, g2Kgamma)
313 piApiC := Utils.Bn.G1.Add(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiC)
314 pairingPiACG2Kbg := Utils.Bn.Pairing(piApiC, setup.Vk.G2Kbg)
315 pairingG1KbgPiB := Utils.Bn.Pairing(setup.Vk.G1Kbg, proof.PiB)
316 pairingL := Utils.Bn.Fq12.Mul(pairingPiACG2Kbg, pairingG1KbgPiB)
317 pairingR := Utils.Bn.Pairing(proof.PiKp, setup.Vk.G2Kg)
318 if !Utils.Bn.Fq12.Equal(pairingL, pairingR) {
319 return false
320 }
321 if printVer {
322 fmt.Println("✓ e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB) == e(piK, g2Kgamma)")
323 }
324
325 return true
326}