-
Notifications
You must be signed in to change notification settings - Fork 366
/
verifier.go
713 lines (657 loc) · 27.6 KB
/
verifier.go
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
// Package kzg implements KZG polynomial commitment verification.
//
// KZG polynomial commitment allows for the prover to commit to a polynomial and
// then selectively prove evaluations of the said polynomial. The size of the
// commitment is a single G1 element and the size of the evaluation proof is
// also a single G1 element. However, KZG polynomial commitment scheme requires
// a trusted SRS.
//
// This package supersedes previous type-specific implementations and allows to
// use any implemented pairing-friendly curve implementation, being defined over
// a 2-chain (native implementation) or using field emulation.
package kzg
import (
"fmt"
bls12377 "github.com/consensys/gnark-crypto/ecc/bls12-377"
fr_bls12377 "github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
kzg_bls12377 "github.com/consensys/gnark-crypto/ecc/bls12-377/kzg"
bls12381 "github.com/consensys/gnark-crypto/ecc/bls12-381"
fr_bls12381 "github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
kzg_bls12381 "github.com/consensys/gnark-crypto/ecc/bls12-381/kzg"
bls24315 "github.com/consensys/gnark-crypto/ecc/bls24-315"
fr_bls24315 "github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
kzg_bls24315 "github.com/consensys/gnark-crypto/ecc/bls24-315/kzg"
"github.com/consensys/gnark-crypto/ecc/bn254"
fr_bn254 "github.com/consensys/gnark-crypto/ecc/bn254/fr"
kzg_bn254 "github.com/consensys/gnark-crypto/ecc/bn254/kzg"
bw6761 "github.com/consensys/gnark-crypto/ecc/bw6-761"
fr_bw6761 "github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
kzg_bw6761 "github.com/consensys/gnark-crypto/ecc/bw6-761/kzg"
"github.com/consensys/gnark/frontend"
"github.com/consensys/gnark/std/algebra"
"github.com/consensys/gnark/std/algebra/algopts"
"github.com/consensys/gnark/std/algebra/emulated/sw_bls12381"
"github.com/consensys/gnark/std/algebra/emulated/sw_bn254"
"github.com/consensys/gnark/std/algebra/emulated/sw_bw6761"
"github.com/consensys/gnark/std/algebra/native/sw_bls12377"
"github.com/consensys/gnark/std/algebra/native/sw_bls24315"
"github.com/consensys/gnark/std/math/bits"
"github.com/consensys/gnark/std/math/emulated"
"github.com/consensys/gnark/std/recursion"
)
// ValueOfScalar initializes a scalar in a witness from a native scalar (Fr) point.
// The scalars are always emulated.
func ValueOfScalar[FR emulated.FieldParams](scalar any) (emulated.Element[FR], error) {
var ret emulated.Element[FR]
switch s := any(&ret).(type) {
case *emulated.Element[sw_bn254.ScalarField]:
tScalar, ok := scalar.(fr_bn254.Element)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, tScalar)
}
*s = sw_bn254.NewScalar(tScalar)
case *emulated.Element[sw_bls12377.ScalarField]:
tScalar, ok := scalar.(fr_bls12377.Element)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, tScalar)
}
*s = sw_bls12377.NewScalar(tScalar)
case *emulated.Element[sw_bls12381.ScalarField]:
tScalar, ok := scalar.(fr_bls12381.Element)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, tScalar)
}
*s = sw_bls12381.NewScalar(tScalar)
case *emulated.Element[sw_bw6761.ScalarField]:
tScalar, ok := scalar.(fr_bw6761.Element)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, tScalar)
}
*s = sw_bw6761.NewScalar(tScalar)
case *emulated.Element[sw_bls24315.ScalarField]:
tScalar, ok := scalar.(fr_bls24315.Element)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, tScalar)
}
*s = sw_bls24315.NewScalar(tScalar)
default:
return ret, fmt.Errorf("unknown type parametrization")
}
return ret, nil
}
// Commitment is an KZG commitment to a polynomial. Use [ValueOfCommitment] to
// initialize a witness from the native commitment.
type Commitment[G1El algebra.G1ElementT] struct {
G1El G1El
}
// ValueOfCommitment initializes a KZG commitment witness from a native
// commitment. It returns an error if there is a conflict between the type
// parameters and provided native commitment type.
func ValueOfCommitment[G1El algebra.G1ElementT](cmt any) (Commitment[G1El], error) {
var ret Commitment[G1El]
switch s := any(&ret).(type) {
case *Commitment[sw_bn254.G1Affine]:
tCmt, ok := cmt.(bn254.G1Affine)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, cmt)
}
s.G1El = sw_bn254.NewG1Affine(tCmt)
case *Commitment[sw_bls12377.G1Affine]:
tCmt, ok := cmt.(bls12377.G1Affine)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, cmt)
}
s.G1El = sw_bls12377.NewG1Affine(tCmt)
case *Commitment[sw_bls12381.G1Affine]:
tCmt, ok := cmt.(bls12381.G1Affine)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, cmt)
}
s.G1El = sw_bls12381.NewG1Affine(tCmt)
case *Commitment[sw_bw6761.G1Affine]:
tCmt, ok := cmt.(bw6761.G1Affine)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, cmt)
}
s.G1El = sw_bw6761.NewG1Affine(tCmt)
case *Commitment[sw_bls24315.G1Affine]:
tCmt, ok := cmt.(bls24315.G1Affine)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, cmt)
}
s.G1El = sw_bls24315.NewG1Affine(tCmt)
default:
return ret, fmt.Errorf("unknown type parametrization")
}
return ret, nil
}
// OpeningProof embeds the opening proof that polynomial evaluated at Point is
// equal to ClaimedValue. Use [ValueOfOpeningProof] to initialize a witness from
// a native opening proof.
type OpeningProof[FR emulated.FieldParams, G1El algebra.G1ElementT] struct {
Quotient G1El
ClaimedValue emulated.Element[FR]
}
// ValueOfOpeningProof initializes an opening proof from the given proof and
// point. It returns an error if there is a mismatch between the type parameters
// and types of the provided point and proof.
func ValueOfOpeningProof[FR emulated.FieldParams, G1El algebra.G1ElementT](proof any) (OpeningProof[FR, G1El], error) {
var ret OpeningProof[FR, G1El]
switch s := any(&ret).(type) {
case *OpeningProof[sw_bn254.ScalarField, sw_bn254.G1Affine]:
tProof, ok := proof.(kzg_bn254.OpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bn254.NewG1Affine(tProof.H)
s.ClaimedValue = sw_bn254.NewScalar(tProof.ClaimedValue)
case *OpeningProof[sw_bls12377.ScalarField, sw_bls12377.G1Affine]:
tProof, ok := proof.(kzg_bls12377.OpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bls12377.NewG1Affine(tProof.H)
s.ClaimedValue = sw_bls12377.NewScalar(tProof.ClaimedValue)
case *OpeningProof[sw_bls12381.ScalarField, sw_bls12381.G1Affine]:
tProof, ok := proof.(kzg_bls12381.OpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bls12381.NewG1Affine(tProof.H)
s.ClaimedValue = sw_bls12381.NewScalar(tProof.ClaimedValue)
case *OpeningProof[sw_bw6761.ScalarField, sw_bw6761.G1Affine]:
tProof, ok := proof.(kzg_bw6761.OpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bw6761.NewG1Affine(tProof.H)
s.ClaimedValue = sw_bw6761.NewScalar(tProof.ClaimedValue)
case *OpeningProof[sw_bls24315.ScalarField, sw_bls24315.G1Affine]:
tProof, ok := proof.(kzg_bls24315.OpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bls24315.NewG1Affine(tProof.H)
s.ClaimedValue = sw_bls24315.NewScalar(tProof.ClaimedValue)
default:
return ret, fmt.Errorf("unknown type parametrization")
}
return ret, nil
}
type BatchOpeningProof[FR emulated.FieldParams, G1El algebra.G1ElementT] struct {
Quotient G1El
ClaimedValues []emulated.Element[FR]
}
func ValueOfBatchOpeningProof[FR emulated.FieldParams, G1El any](proof any) (BatchOpeningProof[FR, G1El], error) {
var ret BatchOpeningProof[FR, G1El]
switch s := any(&ret).(type) {
case *BatchOpeningProof[sw_bn254.ScalarField, sw_bn254.G1Affine]:
tProof, ok := proof.(kzg_bn254.BatchOpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bn254.NewG1Affine(tProof.H)
s.ClaimedValues = make([]emulated.Element[sw_bn254.ScalarField], len(tProof.ClaimedValues))
for i := 0; i < len(s.ClaimedValues); i++ {
s.ClaimedValues[i] = sw_bn254.NewScalar(tProof.ClaimedValues[i])
}
case *BatchOpeningProof[sw_bls12377.ScalarField, sw_bls12377.G1Affine]:
tProof, ok := proof.(kzg_bls12377.BatchOpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bls12377.NewG1Affine(tProof.H)
s.ClaimedValues = make([]emulated.Element[sw_bls12377.ScalarField], len(tProof.ClaimedValues))
for i := 0; i < len(s.ClaimedValues); i++ {
s.ClaimedValues[i] = sw_bls12377.NewScalar(tProof.ClaimedValues[i])
}
case *BatchOpeningProof[sw_bls12381.ScalarField, sw_bls12381.G1Affine]:
tProof, ok := proof.(kzg_bls12381.BatchOpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bls12381.NewG1Affine(tProof.H)
s.ClaimedValues = make([]emulated.Element[sw_bls12381.ScalarField], len(tProof.ClaimedValues))
for i := 0; i < len(s.ClaimedValues); i++ {
s.ClaimedValues[i] = sw_bls12381.NewScalar(tProof.ClaimedValues[i])
}
case *BatchOpeningProof[sw_bw6761.ScalarField, sw_bw6761.G1Affine]:
tProof, ok := proof.(kzg_bw6761.BatchOpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bw6761.NewG1Affine(tProof.H)
s.ClaimedValues = make([]emulated.Element[sw_bw6761.ScalarField], len(tProof.ClaimedValues))
for i := 0; i < len(s.ClaimedValues); i++ {
s.ClaimedValues[i] = sw_bw6761.NewScalar(tProof.ClaimedValues[i])
}
case *BatchOpeningProof[sw_bls24315.ScalarField, sw_bls24315.G1Affine]:
tProof, ok := proof.(kzg_bls24315.BatchOpeningProof)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, proof)
}
s.Quotient = sw_bls24315.NewG1Affine(tProof.H)
s.ClaimedValues = make([]emulated.Element[sw_bls24315.ScalarField], len(tProof.ClaimedValues))
for i := 0; i < len(s.ClaimedValues); i++ {
s.ClaimedValues[i] = sw_bls24315.NewScalar(tProof.ClaimedValues[i])
}
default:
return ret, fmt.Errorf("unknown type parametrization")
}
return ret, nil
}
// VerifyingKey is the trusted setup for KZG polynomial commitment scheme. Use
// [ValueOfVerifyingKey] to initialize a witness from the native VerifyingKey.
type VerifyingKey[G1El algebra.G1ElementT, G2El algebra.G2ElementT] struct {
G2 [2]G2El
G1 G1El
}
// PlaceholderVerifyingKey returns a placeholder value for the verifying key for
// compiling if the witness is going to be in precomputed form using [ValueOfVerifyingKeyFixed].
func PlaceholderVerifyingKey[G1El algebra.G1ElementT, G2El algebra.G2ElementT]() VerifyingKey[G1El, G2El] {
var ret VerifyingKey[G1El, G2El]
switch s := any(&ret).(type) {
case *VerifyingKey[sw_bn254.G1Affine, sw_bn254.G2Affine]:
s.G2[0] = sw_bn254.NewG2AffineFixedPlaceholder()
s.G2[1] = sw_bn254.NewG2AffineFixedPlaceholder()
case *VerifyingKey[sw_bls12377.G1Affine, sw_bls12377.G2Affine]:
s.G2[0] = sw_bls12377.NewG2AffineFixedPlaceholder()
s.G2[1] = sw_bls12377.NewG2AffineFixedPlaceholder()
case *VerifyingKey[sw_bls12381.G1Affine, sw_bls12381.G2Affine]:
s.G2[0] = sw_bls12381.NewG2AffineFixedPlaceholder()
s.G2[1] = sw_bls12381.NewG2AffineFixedPlaceholder()
case *VerifyingKey[sw_bw6761.G1Affine, sw_bw6761.G2Affine]:
s.G2[0] = sw_bw6761.NewG2AffineFixedPlaceholder()
s.G2[1] = sw_bw6761.NewG2AffineFixedPlaceholder()
case *VerifyingKey[sw_bls24315.G1Affine, sw_bls24315.G2Affine]:
s.G2[0] = sw_bls24315.NewG2AffineFixedPlaceholder()
s.G2[1] = sw_bls24315.NewG2AffineFixedPlaceholder()
default:
panic("not supported")
}
return ret
}
// ValueOfVerifyingKey initializes verifying key witness from the native
// verifying key. It returns an error if there is a mismatch between the type
// parameters and the provided verifying key type.
func ValueOfVerifyingKey[G1El algebra.G1ElementT, G2El algebra.G2ElementT](vk any) (VerifyingKey[G1El, G2El], error) {
var ret VerifyingKey[G1El, G2El]
switch s := any(&ret).(type) {
case *VerifyingKey[sw_bn254.G1Affine, sw_bn254.G2Affine]:
tVk, ok := vk.(kzg_bn254.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bn254.NewG1Affine(tVk.G1)
s.G2[0] = sw_bn254.NewG2Affine(tVk.G2[0])
s.G2[1] = sw_bn254.NewG2Affine(tVk.G2[1])
case *VerifyingKey[sw_bls12377.G1Affine, sw_bls12377.G2Affine]:
tVk, ok := vk.(kzg_bls12377.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bls12377.NewG1Affine(tVk.G1)
s.G2[0] = sw_bls12377.NewG2Affine(tVk.G2[0])
s.G2[1] = sw_bls12377.NewG2Affine(tVk.G2[1])
case *VerifyingKey[sw_bls12381.G1Affine, sw_bls12381.G2Affine]:
tVk, ok := vk.(kzg_bls12381.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bls12381.NewG1Affine(tVk.G1)
s.G2[0] = sw_bls12381.NewG2Affine(tVk.G2[0])
s.G2[1] = sw_bls12381.NewG2Affine(tVk.G2[1])
case *VerifyingKey[sw_bw6761.G1Affine, sw_bw6761.G2Affine]:
tVk, ok := vk.(kzg_bw6761.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bw6761.NewG1Affine(tVk.G1)
s.G2[0] = sw_bw6761.NewG2Affine(tVk.G2[0])
s.G2[1] = sw_bw6761.NewG2Affine(tVk.G2[1])
case *VerifyingKey[sw_bls24315.G1Affine, sw_bls24315.G2Affine]:
tVk, ok := vk.(kzg_bls24315.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bls24315.NewG1Affine(tVk.G1)
s.G2[0] = sw_bls24315.NewG2Affine(tVk.G2[0])
s.G2[1] = sw_bls24315.NewG2Affine(tVk.G2[1])
default:
return ret, fmt.Errorf("unknown type parametrization")
}
return ret, nil
}
// ValueOfVerifyingKeyFixed initializes verifying key witness from the native
// verifying key and perform pre-computations for G2 elements. It returns an
// error if there is a mismatch between the type parameters and the provided
// verifying key type. Such witness is significantly larger than without
// precomputations. If witness size is important, then use [ValueOfVerifyingKey]
// instead.
func ValueOfVerifyingKeyFixed[G1El algebra.G1ElementT, G2El algebra.G2ElementT](vk any) (VerifyingKey[G1El, G2El], error) {
var ret VerifyingKey[G1El, G2El]
switch s := any(&ret).(type) {
case *VerifyingKey[sw_bn254.G1Affine, sw_bn254.G2Affine]:
tVk, ok := vk.(kzg_bn254.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bn254.NewG1Affine(tVk.G1)
s.G2[0] = sw_bn254.NewG2AffineFixed(tVk.G2[0])
s.G2[1] = sw_bn254.NewG2AffineFixed(tVk.G2[1])
case *VerifyingKey[sw_bls12377.G1Affine, sw_bls12377.G2Affine]:
tVk, ok := vk.(kzg_bls12377.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bls12377.NewG1Affine(tVk.G1)
s.G2[0] = sw_bls12377.NewG2AffineFixed(tVk.G2[0])
s.G2[1] = sw_bls12377.NewG2AffineFixed(tVk.G2[1])
case *VerifyingKey[sw_bls12381.G1Affine, sw_bls12381.G2Affine]:
tVk, ok := vk.(kzg_bls12381.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bls12381.NewG1Affine(tVk.G1)
s.G2[0] = sw_bls12381.NewG2AffineFixed(tVk.G2[0])
s.G2[1] = sw_bls12381.NewG2AffineFixed(tVk.G2[1])
case *VerifyingKey[sw_bw6761.G1Affine, sw_bw6761.G2Affine]:
tVk, ok := vk.(kzg_bw6761.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bw6761.NewG1Affine(tVk.G1)
s.G2[0] = sw_bw6761.NewG2AffineFixed(tVk.G2[0])
s.G2[1] = sw_bw6761.NewG2AffineFixed(tVk.G2[1])
case *VerifyingKey[sw_bls24315.G1Affine, sw_bls24315.G2Affine]:
tVk, ok := vk.(kzg_bls24315.VerifyingKey)
if !ok {
return ret, fmt.Errorf("mismatching types %T %T", ret, vk)
}
s.G1 = sw_bls24315.NewG1Affine(tVk.G1)
s.G2[0] = sw_bls24315.NewG2AffineFixed(tVk.G2[0])
s.G2[1] = sw_bls24315.NewG2AffineFixed(tVk.G2[1])
default:
return ret, fmt.Errorf("precomputation not supported")
}
return ret, nil
}
// Verifier allows verifying KZG opening proofs.
type Verifier[FR emulated.FieldParams, G1El algebra.G1ElementT, G2El algebra.G2ElementT, GtEl algebra.G2ElementT] struct {
api frontend.API
scalarApi *emulated.Field[FR]
curve algebra.Curve[FR, G1El]
pairing algebra.Pairing[G1El, G2El, GtEl]
}
// NewVerifier initializes a new Verifier instance.
func NewVerifier[FR emulated.FieldParams, G1El algebra.G1ElementT, G2El algebra.G2ElementT, GtEl algebra.G2ElementT](api frontend.API) (*Verifier[FR, G1El, G2El, GtEl], error) {
curve, err := algebra.GetCurve[FR, G1El](api)
if err != nil {
return nil, err
}
scalarApi, err := emulated.NewField[FR](api)
if err != nil {
return nil, err
}
pairing, err := algebra.GetPairing[G1El, G2El, GtEl](api)
if err != nil {
return nil, err
}
return &Verifier[FR, G1El, G2El, GtEl]{
api: api,
scalarApi: scalarApi,
curve: curve,
pairing: pairing,
}, nil
}
// CheckOpeningProof asserts the validity of the opening proof for the given
// commitment at point.
func (v *Verifier[FR, G1El, G2El, GTEl]) CheckOpeningProof(commitment Commitment[G1El], proof OpeningProof[FR, G1El], point emulated.Element[FR], vk VerifyingKey[G1El, G2El]) error {
// [f(a)]G1 + [-a]([H(α)]G₁) = [f(a) - a*H(α)]G₁
pointNeg := v.scalarApi.Neg(&point)
totalG1, err := v.curve.MultiScalarMul([]*G1El{&vk.G1, &proof.Quotient}, []*emulated.Element[FR]{&proof.ClaimedValue, pointNeg})
if err != nil {
return fmt.Errorf("check opening proof: %w", err)
}
// [f(a) - a*H(α)]G₁ + [-f(α)]G₁ = [f(a) - f(α) - a*H(α)]G₁
commitmentNeg := v.curve.Neg(&commitment.G1El)
totalG1 = v.curve.Add(totalG1, commitmentNeg)
// e([f(a)-f(α)-a*H(α)]G₁], G₂).e([H(α)]G₁, [α]G₂) == 1
if err := v.pairing.PairingCheck(
[]*G1El{totalG1, &proof.Quotient},
[]*G2El{&vk.G2[0], &vk.G2[1]},
); err != nil {
return fmt.Errorf("pairing check: %w", err)
}
return nil
}
// BatchVerifySinglePoint verifies multiple opening proofs at a single point.
func (v *Verifier[FR, G1El, G2El, GTEl]) BatchVerifySinglePoint(digests []Commitment[G1El], batchOpeningProof BatchOpeningProof[FR, G1El], point emulated.Element[FR], vk VerifyingKey[G1El, G2El], dataTranscript ...emulated.Element[FR]) error {
// fold the proof
foldedProof, foldedDigest, err := v.FoldProof(digests, batchOpeningProof, point, dataTranscript...)
if err != nil {
return fmt.Errorf("fold proofs: %w", err)
}
// verify the foldedProof against the foldedDigest
err = v.CheckOpeningProof(foldedDigest, foldedProof, point, vk)
if err != nil {
return fmt.Errorf("check opening proof: %w", err)
}
return nil
}
// FoldProofsMultiPoint folds multiple proofs with openings at multiple points.
// Used for batch verification of different opening proofs. See also
// [Verifier.BatchVerifyMultiPoints].
func (v *Verifier[FR, G1El, G2El, GTEl]) FoldProofsMultiPoint(digests []Commitment[G1El], proofs []OpeningProof[FR, G1El], points []emulated.Element[FR], vk VerifyingKey[G1El, G2El]) (*G1El, *G1El, error) {
var fr FR
// check consistency nb proogs vs nb digests
if len(digests) != len(proofs) {
return nil, nil, fmt.Errorf("number of commitments doesn't match number of proofs")
}
if len(digests) != len(points) {
return nil, nil, fmt.Errorf("number of commitments doesn't match number of points ")
}
// len(digests) should be nonzero because of randomNumbers
if len(digests) == 0 {
return nil, nil, fmt.Errorf("number of digests should be nonzero")
}
// sample random numbers λᵢ for sampling
randomNumbers := make([]*emulated.Element[FR], len(digests))
randomNumbers[0] = v.scalarApi.One()
whSnark, err := recursion.NewHash(v.api, fr.Modulus(), true)
if err != nil {
return nil, nil, err
}
for i := 0; i < len(digests); i++ {
marshalledG1 := v.curve.MarshalG1(digests[i].G1El)
whSnark.Write(marshalledG1...)
marshalledG1 = v.curve.MarshalG1(proofs[i].Quotient)
whSnark.Write(marshalledG1...)
marshalledScalar := v.curve.MarshalScalar(proofs[i].ClaimedValue)
whSnark.Write(marshalledScalar...)
marshalledScalar = v.curve.MarshalScalar(points[i])
whSnark.Write(marshalledScalar...)
}
seed := whSnark.Sum()
binSeed := bits.ToBinary(v.api, seed, bits.WithNbDigits(fr.Modulus().BitLen()))
randomNumbers[1] = v.scalarApi.FromBits(binSeed...)
for i := 2; i < len(randomNumbers); i++ {
// TODO: we can also use random number from the higher level transcript
// instead of computing it from the inputs. Currently it is inefficient
// as it computes hash of something for which we already have a hash.
// Maybe add an option to provide the folding coefficient? See issue
// https://github.com/Consensys/gnark/issues/1108
randomNumbers[i] = v.scalarApi.Mul(randomNumbers[1], randomNumbers[i-1])
}
randomPointNumbers := make([]*emulated.Element[FR], len(randomNumbers))
randomPointNumbers[0] = &points[0]
for i := 1; i < len(randomPointNumbers); i++ {
randomPointNumbers[i] = v.scalarApi.Mul(randomNumbers[i], &points[i])
}
// fold the committed quotients compute ∑ᵢλᵢ[Hᵢ(α)]G₁ and
// ∑ᵢλᵢ[p_i]([Hᵢ(α)]G₁)
quotients := make([]*G1El, len(proofs))
for i := 0; i < len(randomNumbers); i++ {
quotients[i] = &proofs[i].Quotient
}
foldedQuotients, err := v.curve.MultiScalarMul(quotients[1:], randomNumbers[1:])
if err != nil {
return nil, nil, fmt.Errorf("fold quotients: %w", err)
}
foldedQuotients = v.curve.Add(foldedQuotients, quotients[0])
foldedPointsQuotients, err := v.curve.MultiScalarMul(quotients, randomPointNumbers)
if err != nil {
return nil, nil, fmt.Errorf("fold point quotients: %w", err)
}
// fold digests and evals
evals := make([]emulated.Element[FR], len(digests))
// fold the digests: ∑ᵢλᵢ[f_i(α)]G₁
// fold the evals : ∑ᵢλᵢfᵢ(aᵢ)
for i := 0; i < len(digests); i++ {
evals[i] = proofs[i].ClaimedValue
}
foldedDigests, foldedEvals, err := v.fold(digests, evals, randomNumbers)
if err != nil {
return nil, nil, fmt.Errorf("fold: %w", err)
}
// compute commitment to folded Eval [∑ᵢλᵢfᵢ(aᵢ)]G₁
foldedEvalsCommit := v.curve.ScalarMul(&vk.G1, foldedEvals)
// compute foldedDigests = ∑ᵢλᵢ[fᵢ(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁
tmp := v.curve.Neg(foldedEvalsCommit)
var foldedDigest *G1El
foldedDigest = v.curve.Add(&foldedDigests.G1El, tmp)
// ∑ᵢλᵢ[f_i(α)]G₁ - [∑ᵢλᵢfᵢ(aᵢ)]G₁ + ∑ᵢλᵢ[p_i]([Hᵢ(α)]G₁)
// = [∑ᵢλᵢf_i(α) - ∑ᵢλᵢfᵢ(aᵢ) + ∑ᵢλᵢpᵢHᵢ(α)]G₁
foldedDigest = v.curve.Add(foldedDigest, foldedPointsQuotients)
// -∑ᵢλᵢ[Qᵢ(α)]G₁
// foldedQuotients.Neg(&foldedQuotients)
foldedQuotients = v.curve.Neg(foldedQuotients)
return foldedDigest, foldedQuotients, nil
}
// BatchVerifyMultiPoints verifies multiple opening proofs at different points.
func (v *Verifier[FR, G1El, G2El, GTEl]) BatchVerifyMultiPoints(digests []Commitment[G1El], proofs []OpeningProof[FR, G1El], points []emulated.Element[FR], vk VerifyingKey[G1El, G2El]) error {
// if only one proof go to base case
if len(digests) == 1 {
return v.CheckOpeningProof(digests[0], proofs[0], points[0], vk)
}
// fold the proofs
foldedDigest, foldedQuotients, err := v.FoldProofsMultiPoint(digests, proofs, points, vk)
if err != nil {
return err
}
// pairing check
err = v.pairing.PairingCheck(
[]*G1El{foldedDigest, foldedQuotients},
[]*G2El{&vk.G2[0], &vk.G2[1]},
)
if err != nil {
return fmt.Errorf("pairingcheck: %w", err)
}
return err
}
// FoldProof folds multiple commitments and a batch opening proof for a single opening check.
func (v *Verifier[FR, G1El, G2El, GTEl]) FoldProof(digests []Commitment[G1El], batchOpeningProof BatchOpeningProof[FR, G1El], point emulated.Element[FR], dataTranscript ...emulated.Element[FR]) (OpeningProof[FR, G1El], Commitment[G1El], error) {
var retP OpeningProof[FR, G1El]
var retC Commitment[G1El]
// we assume the short hash output size is full byte fitting into the modulus length.
nbDigests := len(digests)
// check consistency between numbers of claims vs number of digests
if nbDigests != len(batchOpeningProof.ClaimedValues) {
return retP, retC, fmt.Errorf("length mismatch for digests and claimed values")
}
// derive the challenge γ, binded to the point and the commitments
gamma, err := v.deriveGamma(point, digests, batchOpeningProof.ClaimedValues, dataTranscript...)
if err != nil {
return retP, retC, fmt.Errorf("derive gamma: %w", err)
}
// gammai = [1,γ,γ²,..,γⁿ⁻¹]
gammai := make([]*emulated.Element[FR], nbDigests)
gammai[0] = v.scalarApi.One()
if nbDigests > 1 {
gammai[1] = gamma
}
for i := 2; i < nbDigests; i++ {
gammai[i] = v.scalarApi.Mul(gammai[i-1], gamma)
}
// fold the claimed values and digests
// compute ∑ᵢ γ^i C_i = C_0 + γ(C_1 + γ(C2 ...)), allowing to bound the scalar multiplication iterations
digestsP := make([]*G1El, len(digests))
for i := range digestsP {
digestsP[i] = &digests[i].G1El
}
foldedDigests, err := v.curve.MultiScalarMul(digestsP[1:], gammai[1:])
if err != nil {
return retP, retC, fmt.Errorf("multi scalar mul: %w", err)
}
foldedDigests = v.curve.Add(foldedDigests, digestsP[0])
foldedEvaluations := &batchOpeningProof.ClaimedValues[0]
for i := 1; i < nbDigests; i++ {
tmp := v.scalarApi.Mul(&batchOpeningProof.ClaimedValues[i], gammai[i])
foldedEvaluations = v.scalarApi.Add(foldedEvaluations, tmp)
}
return OpeningProof[FR, G1El]{
Quotient: batchOpeningProof.Quotient,
ClaimedValue: *foldedEvaluations,
}, Commitment[G1El]{
G1El: *foldedDigests,
}, nil
}
// deriveGamma derives a challenge using Fiat Shamir to fold proofs.
// dataTranscript are supposed to be bits.
func (v *Verifier[FR, G1El, G2El, GTEl]) deriveGamma(point emulated.Element[FR], digests []Commitment[G1El], claimedValues []emulated.Element[FR], dataTranscript ...emulated.Element[FR]) (*emulated.Element[FR], error) {
var fr FR
fs, err := recursion.NewTranscript(v.api, fr.Modulus(), []string{"gamma"})
if err != nil {
return nil, fmt.Errorf("new transcript: %w", err)
}
if err := fs.Bind("gamma", v.curve.MarshalScalar(point)); err != nil {
return nil, fmt.Errorf("bind point: %w", err)
}
for i := range digests {
if err := fs.Bind("gamma", v.curve.MarshalG1(digests[i].G1El)); err != nil {
return nil, fmt.Errorf("bind %d-th commitment: %w", i, err)
}
}
for i := range claimedValues {
if err := fs.Bind("gamma", v.curve.MarshalScalar(claimedValues[i])); err != nil {
return nil, fmt.Errorf("bing %d-th claimed value: %w", i, err)
}
}
for i := range dataTranscript {
if err := fs.Bind("gamma", v.curve.MarshalScalar(dataTranscript[i])); err != nil {
return nil, fmt.Errorf("bind %d-ith data transcript: %w", i, err)
}
}
gamma, err := fs.ComputeChallenge("gamma")
if err != nil {
return nil, fmt.Errorf("compute challenge: %w", err)
}
bGamma := bits.ToBinary(v.api, gamma, bits.WithNbDigits(fr.Modulus().BitLen()))
gammaS := v.scalarApi.FromBits(bGamma...)
return gammaS, nil
}
func (v *Verifier[FR, G1El, G2El, GTEl]) fold(digests []Commitment[G1El], fai []emulated.Element[FR], ci []*emulated.Element[FR], algopts ...algopts.AlgebraOption) (Commitment[G1El], *emulated.Element[FR], error) {
// length inconsistency between digests and evaluations should have been done before calling this function
nbDigests := len(digests)
// fold the claimed values ∑ᵢcᵢf(aᵢ)
var tmp *emulated.Element[FR]
foldedEvaluations := &fai[0]
for i := 1; i < nbDigests; i++ {
tmp = v.scalarApi.Mul(&fai[i], ci[i])
foldedEvaluations = v.scalarApi.Add(foldedEvaluations, tmp)
}
// fold the digests ∑ᵢ[cᵢ]([fᵢ(α)]G₁)
digestPoints := make([]*G1El, len(digests))
for i := range digestPoints {
digestPoints[i] = &digests[i].G1El
}
foldedDigest, err := v.curve.MultiScalarMul(digestPoints[1:], ci[1:])
if err != nil {
return Commitment[G1El]{}, nil, fmt.Errorf("fold digests: %w", err)
}
foldedDigest = v.curve.Add(foldedDigest, digestPoints[0])
// folding done
return Commitment[G1El]{
G1El: *foldedDigest,
}, foldedEvaluations, nil
}