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, G1T == Pk.H
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 Z []*big.Int
41 }
42 Vk struct {
43 Vka [3][2]*big.Int
44 Vkb [3]*big.Int
45 Vkc [3][2]*big.Int
46 IC [][3]*big.Int
47 G1Kbg [3]*big.Int // g1 * Kbeta * Kgamma
48 G2Kbg [3][2]*big.Int // g2 * Kbeta * Kgamma
49 G2Kg [3][2]*big.Int // g2 * Kgamma
50 Vkz [3][2]*big.Int
51 }
52}
53
54// Proof contains the parameters to proof the zkSNARK
55type Proof struct {
56 PiA [3]*big.Int
57 PiAp [3]*big.Int
58 PiB [3][2]*big.Int
59 PiBp [3]*big.Int
60 PiC [3]*big.Int
61 PiCp [3]*big.Int
62 PiH [3]*big.Int
63 PiKp [3]*big.Int
64 // PublicSignals []*big.Int
65}
66
67type utils struct {
68 Bn bn128.Bn128
69 FqR fields.Fq
70 PF r1csqap.PolynomialField
71}
72
73// Utils is the data structure holding the BN128, FqR Finite Field over R, PolynomialField, that will be used inside the snarks operations
74var Utils = prepareUtils()
75
76func prepareUtils() utils {
77 bn, err := bn128.NewBn128()
78 if err != nil {
79 panic(err)
80 }
81 // new Finite Field
82 fqR := fields.NewFq(bn.R)
83 // new Polynomial Field
84 pf := r1csqap.NewPolynomialField(fqR)
85
86 return utils{
87 Bn: bn,
88 FqR: fqR,
89 PF: pf,
90 }
91}
92
93// GenerateTrustedSetup generates the Trusted Setup from a compiled Circuit. The Setup.Toxic sub data structure must be destroyed
94func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, alphas, betas, gammas [][]*big.Int) (Setup, error) {
95 var setup Setup
96 var err error
97
98 // input soundness
99 for i := 0; i < len(alphas); i++ {
100 for j := 0; j < len(alphas[i]); j++ {
101 if j <= circuit.NPublic {
102 if bytes.Equal(alphas[i][j].Bytes(), Utils.Bn.Fq1.Zero().Bytes()) {
103 alphas[i][j] = Utils.Bn.Fq1.One()
104 }
105 }
106 }
107 }
108
109 // generate random t value
110 setup.Toxic.T, err = Utils.FqR.Rand()
111 if err != nil {
112 return Setup{}, err
113 }
114
115 // k for calculating pi' and Vk
116 setup.Toxic.Ka, err = Utils.FqR.Rand()
117 if err != nil {
118 return Setup{}, err
119 }
120 setup.Toxic.Kb, err = Utils.FqR.Rand()
121 if err != nil {
122 return Setup{}, err
123 }
124 setup.Toxic.Kc, err = Utils.FqR.Rand()
125 if err != nil {
126 return Setup{}, err
127 }
128
129 // generate Kβ (Kbeta) and Kγ (Kgamma)
130 setup.Toxic.Kbeta, err = Utils.FqR.Rand()
131 if err != nil {
132 return Setup{}, err
133 }
134 setup.Toxic.Kgamma, err = Utils.FqR.Rand()
135 if err != nil {
136 return Setup{}, err
137 }
138
139 // generate ρ (Rho): ρA, ρB, ρC
140 setup.Toxic.RhoA, err = Utils.FqR.Rand()
141 if err != nil {
142 return Setup{}, err
143 }
144 setup.Toxic.RhoB, err = Utils.FqR.Rand()
145 if err != nil {
146 return Setup{}, err
147 }
148 setup.Toxic.RhoC = Utils.FqR.Mul(setup.Toxic.RhoA, setup.Toxic.RhoB)
149
150 // calculated more down
151 // for i := 0; i < witnessLength; i++ {
152 // tPow := Utils.FqR.Exp(setup.Toxic.T, big.NewInt(int64(i)))
153 // tEncr1 := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, tPow)
154 // gt1 = append(gt1, tEncr1)
155 // tEncr2 := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, tPow)
156 // gt2 = append(gt2, tEncr2)
157 // }
158 // gt1: g1, g1*t, g1*t^2, g1*t^3, ...
159 // gt2: g2, g2*t, g2*t^2, ...
160
161 setup.Vk.Vka = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Ka)
162 setup.Vk.Vkb = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, setup.Toxic.Kb)
163 setup.Vk.Vkc = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kc)
164
165 /*
166 Verification keys:
167 - Vk_betagamma1: setup.G1Kbg = g1 * Kbeta*Kgamma
168 - Vk_betagamma2: setup.G2Kbg = g2 * Kbeta*Kgamma
169 - Vk_gamma: setup.G2Kg = g2 * Kgamma
170 */
171 kbg := Utils.FqR.Mul(setup.Toxic.Kbeta, setup.Toxic.Kgamma)
172 setup.Vk.G1Kbg = Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kbg)
173 setup.Vk.G2Kbg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, kbg)
174 setup.Vk.G2Kg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kgamma)
175
176 // for i := 0; i < circuit.NVars; i++ {
177 for i := 0; i < len(circuit.Signals); i++ {
178 at := Utils.PF.Eval(alphas[i], setup.Toxic.T)
179 rhoAat := Utils.Bn.Fq1.Mul(setup.Toxic.RhoA, at)
180 a := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoAat)
181 setup.Pk.A = append(setup.Pk.A, a)
182 if i <= circuit.NPublic {
183 setup.Vk.IC = append(setup.Vk.IC, a)
184 }
185
186 bt := Utils.PF.Eval(betas[i], setup.Toxic.T)
187 rhoBbt := Utils.Bn.Fq1.Mul(setup.Toxic.RhoB, bt)
188 bg1 := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoBbt)
189 bg2 := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, rhoBbt)
190 setup.Pk.B = append(setup.Pk.B, bg2)
191
192 ct := Utils.PF.Eval(gammas[i], setup.Toxic.T)
193 rhoCct := Utils.Bn.Fq1.Mul(setup.Toxic.RhoC, ct)
194 c := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoCct)
195 setup.Pk.C = append(setup.Pk.C, c)
196
197 kt := Utils.FqR.Add(Utils.FqR.Add(rhoAat, rhoBbt), rhoCct)
198 k := Utils.Bn.G1.Affine(Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kt))
199
200 ktest := Utils.Bn.G1.Affine(Utils.Bn.G1.Add(Utils.Bn.G1.Add(a, bg1), c))
201 if !Utils.Bn.Fq2.Equal(k, ktest) {
202 os.Exit(1)
203 return setup, err
204 }
205
206 setup.Pk.Ap = append(setup.Pk.Ap, Utils.Bn.G1.MulScalar(a, setup.Toxic.Ka))
207 setup.Pk.Bp = append(setup.Pk.Bp, Utils.Bn.G1.MulScalar(bg1, setup.Toxic.Kb))
208 setup.Pk.Cp = append(setup.Pk.Cp, Utils.Bn.G1.MulScalar(c, setup.Toxic.Kc))
209 k_ := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, kt)
210 setup.Pk.Kp = append(setup.Pk.Kp, Utils.Bn.G1.MulScalar(k_, setup.Toxic.Kbeta))
211 }
212
213 // z pol
214 zpol := []*big.Int{big.NewInt(int64(1))}
215 // for i := 1; i < len(circuit.Constraints); i++ {
216 for i := 1; i <= circuit.NPublic; i++ { // circuit.NPublic == d
217 zpol = Utils.PF.Mul(
218 zpol,
219 []*big.Int{
220 Utils.FqR.Neg( // neg over R
221 big.NewInt(int64(i))),
222 big.NewInt(int64(1)),
223 })
224 }
225 setup.Pk.Z = zpol
226
227 zt := Utils.PF.Eval(zpol, setup.Toxic.T)
228 rhoCzt := Utils.Bn.Fq1.Mul(setup.Toxic.RhoC, zt)
229 setup.Vk.Vkz = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, rhoCzt)
230
231 // encrypt t values with curve generators
232 var gt1 [][3]*big.Int
233 gt1 = append(gt1, Utils.Bn.G1.G) // the first is t**0 * G1 = 1 * G1 = G1
234 tEncr := setup.Toxic.T
235 for i := 1; i < len(zpol); i++ { //should be G1T = pkH = (tau**i * G1) from i=0 to d, where d is degree of pol Z(x)
236 gt1 = append(gt1, Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, tEncr))
237 tEncr = Utils.Bn.Fq1.Mul(tEncr, setup.Toxic.T)
238 }
239 fmt.Println("len(G1T)", len(gt1))
240 setup.G1T = gt1
241
242 return setup, nil
243}
244
245// GenerateProofs generates all the parameters to proof the zkSNARK from the Circuit, Setup and the Witness
246func GenerateProofs(circuit circuitcompiler.Circuit, setup Setup, w []*big.Int, px []*big.Int) (Proof, error) {
247 var proof Proof
248 proof.PiA = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
249 proof.PiAp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
250 proof.PiB = Utils.Bn.Fq6.Zero()
251 proof.PiBp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
252 proof.PiC = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
253 proof.PiCp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
254 proof.PiH = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
255 proof.PiKp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
256
257 for i := circuit.NPublic + 1; i < circuit.NVars; i++ {
258 proof.PiA = Utils.Bn.G1.Add(proof.PiA, Utils.Bn.G1.MulScalar(setup.Pk.A[i], w[i]))
259 proof.PiAp = Utils.Bn.G1.Add(proof.PiAp, Utils.Bn.G1.MulScalar(setup.Pk.Ap[i], w[i]))
260 }
261
262 for i := 0; i < circuit.NVars; i++ {
263 proof.PiB = Utils.Bn.G2.Add(proof.PiB, Utils.Bn.G2.MulScalar(setup.Pk.B[i], w[i]))
264 proof.PiBp = Utils.Bn.G1.Add(proof.PiBp, Utils.Bn.G1.MulScalar(setup.Pk.Bp[i], w[i]))
265
266 proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(setup.Pk.C[i], w[i]))
267 proof.PiCp = Utils.Bn.G1.Add(proof.PiCp, Utils.Bn.G1.MulScalar(setup.Pk.Cp[i], w[i]))
268
269 proof.PiKp = Utils.Bn.G1.Add(proof.PiKp, Utils.Bn.G1.MulScalar(setup.Pk.Kp[i], w[i]))
270 }
271
272 hx := Utils.PF.DivisorPolynomial(px, setup.Pk.Z) // maybe move this calculation to a previous step
273
274 // piH = pkH,0 + sum ( hi * pk H,i ), where pkH = G1T, hi=hx
275 proof.PiH = Utils.Bn.G1.Add(proof.PiH, setup.G1T[0])
276 for i := 1; i < len(setup.Pk.Z); i++ {
277 proof.PiH = Utils.Bn.G1.Add(proof.PiH, Utils.Bn.G1.MulScalar(setup.G1T[i], hx[i]))
278 }
279
280 return proof, nil
281}
282
283// VerifyProof verifies over the BN128 the Pairings of the Proof
284func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof, publicSignals []*big.Int, debug bool) bool {
285 // e(piA, Va) == e(piA', g2)
286 pairingPiaVa := Utils.Bn.Pairing(proof.PiA, setup.Vk.Vka)
287 pairingPiapG2 := Utils.Bn.Pairing(proof.PiAp, Utils.Bn.G2.G)
288 if !Utils.Bn.Fq12.Equal(pairingPiaVa, pairingPiapG2) {
289 return false
290 }
291 if debug {
292 fmt.Println("✓ e(piA, Va) == e(piA', g2), valid knowledge commitment for A")
293 }
294
295 // e(Vb, piB) == e(piB', g2)
296 pairingVbPib := Utils.Bn.Pairing(setup.Vk.Vkb, proof.PiB)
297 pairingPibpG2 := Utils.Bn.Pairing(proof.PiBp, Utils.Bn.G2.G)
298 if !Utils.Bn.Fq12.Equal(pairingVbPib, pairingPibpG2) {
299 return false
300 }
301 if debug {
302 fmt.Println("✓ e(Vb, piB) == e(piB', g2), valid knowledge commitment for B")
303 }
304
305 // e(piC, Vc) == e(piC', g2)
306 pairingPicVc := Utils.Bn.Pairing(proof.PiC, setup.Vk.Vkc)
307 pairingPicpG2 := Utils.Bn.Pairing(proof.PiCp, Utils.Bn.G2.G)
308 if !Utils.Bn.Fq12.Equal(pairingPicVc, pairingPicpG2) {
309 return false
310 }
311 if debug {
312 fmt.Println("✓ e(piC, Vc) == e(piC', g2), valid knowledge commitment for C")
313 }
314
315 // Vkx, to then calculate Vkx+piA
316 vkxpia := setup.Vk.IC[0]
317 for i := 0; i < len(publicSignals); i++ {
318 fmt.Println("pub sig", publicSignals[i])
319 vkxpia = Utils.Bn.G1.Add(vkxpia, Utils.Bn.G1.MulScalar(setup.Vk.IC[i+1], publicSignals[i]))
320 }
321
322 // e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2)
323 if !Utils.Bn.Fq12.Equal(
324 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
325 Utils.Bn.Fq12.Mul(
326 Utils.Bn.Pairing(proof.PiH, setup.Vk.Vkz),
327 Utils.Bn.Pairing(proof.PiC, Utils.Bn.G2.G))) {
328 return false
329 }
330 if debug {
331 fmt.Println("✓ e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2), QAP disibility checked")
332 }
333
334 // e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB)
335 // == e(piK, g2Kgamma)
336 piApiC := Utils.Bn.G1.Add(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiC)
337 pairingPiACG2Kbg := Utils.Bn.Pairing(piApiC, setup.Vk.G2Kbg)
338 pairingG1KbgPiB := Utils.Bn.Pairing(setup.Vk.G1Kbg, proof.PiB)
339 pairingL := Utils.Bn.Fq12.Mul(pairingPiACG2Kbg, pairingG1KbgPiB)
340 pairingR := Utils.Bn.Pairing(proof.PiKp, setup.Vk.G2Kg)
341 if !Utils.Bn.Fq12.Equal(pairingL, pairingR) {
342 return false
343 }
344 if debug {
345 fmt.Println("✓ e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB) == e(piK, g2Kgamma)")
346 }
347
348 return true
349}