testudo/src/r1csproof.rs
src/r1csproof.rsRaw
1#![allow(clippy::too_many_arguments)]
2use super::commitments::{Commitments, MultiCommitGens};
3use super::dense_mlpoly::{
4 DensePolynomial, EqPolynomial, PolyCommitment, PolyCommitmentGens, PolyEvalProof,
5};
6use super::errors::ProofVerifyError;
7use super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul};
8use super::nizk::{EqualityProof, KnowledgeProof, ProductProof};
9use super::r1csinstance::R1CSInstance;
10use super::random::RandomTape;
11use super::scalar::Scalar;
12use super::sparse_mlpoly::{SparsePolyEntry, SparsePolynomial};
13use super::sumcheck::ZKSumcheckInstanceProof;
14use super::timer::Timer;
15use super::transcript::{AppendToTranscript, ProofTranscript};
16use core::iter;
17use merlin::Transcript;
18use serde::{Deserialize, Serialize};
19
20#[derive(Serialize, Deserialize, Debug)]
21pub struct R1CSProof {
22 comm_vars: PolyCommitment,
23 sc_proof_phase1: ZKSumcheckInstanceProof,
24 claims_phase2: (
25 CompressedGroup,
26 CompressedGroup,
27 CompressedGroup,
28 CompressedGroup,
29 ),
30 pok_claims_phase2: (KnowledgeProof, ProductProof),
31 proof_eq_sc_phase1: EqualityProof,
32 sc_proof_phase2: ZKSumcheckInstanceProof,
33 comm_vars_at_ry: CompressedGroup,
34 proof_eval_vars_at_ry: PolyEvalProof,
35 proof_eq_sc_phase2: EqualityProof,
36}
37
38pub struct R1CSSumcheckGens {
39 gens_1: MultiCommitGens,
40 gens_3: MultiCommitGens,
41 gens_4: MultiCommitGens,
42}
43
44// TODO: fix passing gens_1_ref
45impl R1CSSumcheckGens {
46 pub fn new(label: &'static [u8], gens_1_ref: &MultiCommitGens) -> Self {
47 let gens_1 = gens_1_ref.clone();
48 let gens_3 = MultiCommitGens::new(3, label);
49 let gens_4 = MultiCommitGens::new(4, label);
50
51 R1CSSumcheckGens {
52 gens_1,
53 gens_3,
54 gens_4,
55 }
56 }
57}
58
59pub struct R1CSGens {
60 gens_sc: R1CSSumcheckGens,
61 gens_pc: PolyCommitmentGens,
62}
63
64impl R1CSGens {
65 pub fn new(label: &'static [u8], _num_cons: usize, num_vars: usize) -> Self {
66 let num_poly_vars = num_vars.log2() as usize;
67 let gens_pc = PolyCommitmentGens::new(num_poly_vars, label);
68 let gens_sc = R1CSSumcheckGens::new(label, &gens_pc.gens.gens_1);
69 R1CSGens { gens_sc, gens_pc }
70 }
71}
72
73impl R1CSProof {
74 fn prove_phase_one(
75 num_rounds: usize,
76 evals_tau: &mut DensePolynomial,
77 evals_Az: &mut DensePolynomial,
78 evals_Bz: &mut DensePolynomial,
79 evals_Cz: &mut DensePolynomial,
80 gens: &R1CSSumcheckGens,
81 transcript: &mut Transcript,
82 random_tape: &mut RandomTape,
83 ) -> (ZKSumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>, Scalar) {
84 let comb_func = |poly_A_comp: &Scalar,
85 poly_B_comp: &Scalar,
86 poly_C_comp: &Scalar,
87 poly_D_comp: &Scalar|
88 -> Scalar { poly_A_comp * (poly_B_comp * poly_C_comp - poly_D_comp) };
89
90 let (sc_proof_phase_one, r, claims, blind_claim_postsc) =
91 ZKSumcheckInstanceProof::prove_cubic_with_additive_term(
92 &Scalar::zero(), // claim is zero
93 &Scalar::zero(), // blind for claim is also zero
94 num_rounds,
95 evals_tau,
96 evals_Az,
97 evals_Bz,
98 evals_Cz,
99 comb_func,
100 &gens.gens_1,
101 &gens.gens_4,
102 transcript,
103 random_tape,
104 );
105
106 (sc_proof_phase_one, r, claims, blind_claim_postsc)
107 }
108
109 fn prove_phase_two(
110 num_rounds: usize,
111 claim: &Scalar,
112 blind_claim: &Scalar,
113 evals_z: &mut DensePolynomial,
114 evals_ABC: &mut DensePolynomial,
115 gens: &R1CSSumcheckGens,
116 transcript: &mut Transcript,
117 random_tape: &mut RandomTape,
118 ) -> (ZKSumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>, Scalar) {
119 let comb_func =
120 |poly_A_comp: &Scalar, poly_B_comp: &Scalar| -> Scalar { poly_A_comp * poly_B_comp };
121 let (sc_proof_phase_two, r, claims, blind_claim_postsc) = ZKSumcheckInstanceProof::prove_quad(
122 claim,
123 blind_claim,
124 num_rounds,
125 evals_z,
126 evals_ABC,
127 comb_func,
128 &gens.gens_1,
129 &gens.gens_3,
130 transcript,
131 random_tape,
132 );
133
134 (sc_proof_phase_two, r, claims, blind_claim_postsc)
135 }
136
137 fn protocol_name() -> &'static [u8] {
138 b"R1CS proof"
139 }
140
141 pub fn prove(
142 inst: &R1CSInstance,
143 vars: Vec<Scalar>,
144 input: &[Scalar],
145 gens: &R1CSGens,
146 transcript: &mut Transcript,
147 random_tape: &mut RandomTape,
148 ) -> (R1CSProof, Vec<Scalar>, Vec<Scalar>) {
149 let timer_prove = Timer::new("R1CSProof::prove");
150 transcript.append_protocol_name(R1CSProof::protocol_name());
151
152 // we currently require the number of |inputs| + 1 to be at most number of vars
153 assert!(input.len() < vars.len());
154
155 input.append_to_transcript(b"input", transcript);
156
157 let timer_commit = Timer::new("polycommit");
158 let (poly_vars, comm_vars, blinds_vars) = {
159 // create a multilinear polynomial using the supplied assignment for variables
160 let poly_vars = DensePolynomial::new(vars.clone());
161
162 // produce a commitment to the satisfying assignment
163 let (comm_vars, blinds_vars) = poly_vars.commit(&gens.gens_pc, Some(random_tape));
164
165 // add the commitment to the prover's transcript
166 comm_vars.append_to_transcript(b"poly_commitment", transcript);
167 (poly_vars, comm_vars, blinds_vars)
168 };
169 timer_commit.stop();
170
171 let timer_sc_proof_phase1 = Timer::new("prove_sc_phase_one");
172
173 // append input to variables to create a single vector z
174 let z = {
175 let num_inputs = input.len();
176 let num_vars = vars.len();
177 let mut z = vars;
178 z.extend(&vec![Scalar::one()]); // add constant term in z
179 z.extend(input);
180 z.extend(&vec![Scalar::zero(); num_vars - num_inputs - 1]); // we will pad with zeros
181 z
182 };
183
184 // derive the verifier's challenge tau
185 let (num_rounds_x, num_rounds_y) =
186 (inst.get_num_cons().log2() as usize, z.len().log2() as usize);
187 let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
188 // compute the initial evaluation table for R(\tau, x)
189 let mut poly_tau = DensePolynomial::new(EqPolynomial::new(tau).evals());
190 let (mut poly_Az, mut poly_Bz, mut poly_Cz) =
191 inst.multiply_vec(inst.get_num_cons(), z.len(), &z);
192
193 let (sc_proof_phase1, rx, _claims_phase1, blind_claim_postsc1) = R1CSProof::prove_phase_one(
194 num_rounds_x,
195 &mut poly_tau,
196 &mut poly_Az,
197 &mut poly_Bz,
198 &mut poly_Cz,
199 &gens.gens_sc,
200 transcript,
201 random_tape,
202 );
203 assert_eq!(poly_tau.len(), 1);
204 assert_eq!(poly_Az.len(), 1);
205 assert_eq!(poly_Bz.len(), 1);
206 assert_eq!(poly_Cz.len(), 1);
207 timer_sc_proof_phase1.stop();
208
209 let (tau_claim, Az_claim, Bz_claim, Cz_claim) =
210 (&poly_tau[0], &poly_Az[0], &poly_Bz[0], &poly_Cz[0]);
211 let (Az_blind, Bz_blind, Cz_blind, prod_Az_Bz_blind) = (
212 random_tape.random_scalar(b"Az_blind"),
213 random_tape.random_scalar(b"Bz_blind"),
214 random_tape.random_scalar(b"Cz_blind"),
215 random_tape.random_scalar(b"prod_Az_Bz_blind"),
216 );
217
218 let (pok_Cz_claim, comm_Cz_claim) = {
219 KnowledgeProof::prove(
220 &gens.gens_sc.gens_1,
221 transcript,
222 random_tape,
223 Cz_claim,
224 &Cz_blind,
225 )
226 };
227
228 let (proof_prod, comm_Az_claim, comm_Bz_claim, comm_prod_Az_Bz_claims) = {
229 let prod = Az_claim * Bz_claim;
230 ProductProof::prove(
231 &gens.gens_sc.gens_1,
232 transcript,
233 random_tape,
234 Az_claim,
235 &Az_blind,
236 Bz_claim,
237 &Bz_blind,
238 &prod,
239 &prod_Az_Bz_blind,
240 )
241 };
242
243 comm_Az_claim.append_to_transcript(b"comm_Az_claim", transcript);
244 comm_Bz_claim.append_to_transcript(b"comm_Bz_claim", transcript);
245 comm_Cz_claim.append_to_transcript(b"comm_Cz_claim", transcript);
246 comm_prod_Az_Bz_claims.append_to_transcript(b"comm_prod_Az_Bz_claims", transcript);
247
248 // prove the final step of sum-check #1
249 let taus_bound_rx = tau_claim;
250 let blind_expected_claim_postsc1 = taus_bound_rx * (prod_Az_Bz_blind - Cz_blind);
251 let claim_post_phase1 = (Az_claim * Bz_claim - Cz_claim) * taus_bound_rx;
252 let (proof_eq_sc_phase1, _C1, _C2) = EqualityProof::prove(
253 &gens.gens_sc.gens_1,
254 transcript,
255 random_tape,
256 &claim_post_phase1,
257 &blind_expected_claim_postsc1,
258 &claim_post_phase1,
259 &blind_claim_postsc1,
260 );
261
262 let timer_sc_proof_phase2 = Timer::new("prove_sc_phase_two");
263 // combine the three claims into a single claim
264 let r_A = transcript.challenge_scalar(b"challenege_Az");
265 let r_B = transcript.challenge_scalar(b"challenege_Bz");
266 let r_C = transcript.challenge_scalar(b"challenege_Cz");
267 let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;
268 let blind_claim_phase2 = r_A * Az_blind + r_B * Bz_blind + r_C * Cz_blind;
269
270 let evals_ABC = {
271 // compute the initial evaluation table for R(\tau, x)
272 let evals_rx = EqPolynomial::new(rx.clone()).evals();
273 let (evals_A, evals_B, evals_C) =
274 inst.compute_eval_table_sparse(inst.get_num_cons(), z.len(), &evals_rx);
275
276 assert_eq!(evals_A.len(), evals_B.len());
277 assert_eq!(evals_A.len(), evals_C.len());
278 (0..evals_A.len())
279 .map(|i| r_A * evals_A[i] + r_B * evals_B[i] + r_C * evals_C[i])
280 .collect::<Vec<Scalar>>()
281 };
282
283 // another instance of the sum-check protocol
284 let (sc_proof_phase2, ry, claims_phase2, blind_claim_postsc2) = R1CSProof::prove_phase_two(
285 num_rounds_y,
286 &claim_phase2,
287 &blind_claim_phase2,
288 &mut DensePolynomial::new(z),
289 &mut DensePolynomial::new(evals_ABC),
290 &gens.gens_sc,
291 transcript,
292 random_tape,
293 );
294 timer_sc_proof_phase2.stop();
295
296 let timer_polyeval = Timer::new("polyeval");
297 let eval_vars_at_ry = poly_vars.evaluate(&ry[1..].to_vec());
298 let blind_eval = random_tape.random_scalar(b"blind_eval");
299 let (proof_eval_vars_at_ry, comm_vars_at_ry) = PolyEvalProof::prove(
300 &poly_vars,
301 Some(&blinds_vars),
302 &ry[1..].to_vec(),
303 &eval_vars_at_ry,
304 Some(&blind_eval),
305 &gens.gens_pc,
306 transcript,
307 random_tape,
308 );
309 timer_polyeval.stop();
310
311 // prove the final step of sum-check #2
312 let blind_eval_Z_at_ry = (Scalar::one() - ry[0]) * blind_eval;
313 let blind_expected_claim_postsc2 = claims_phase2[1] * blind_eval_Z_at_ry;
314 let claim_post_phase2 = claims_phase2[0] * claims_phase2[1];
315 let (proof_eq_sc_phase2, _C1, _C2) = EqualityProof::prove(
316 &gens.gens_pc.gens.gens_1,
317 transcript,
318 random_tape,
319 &claim_post_phase2,
320 &blind_expected_claim_postsc2,
321 &claim_post_phase2,
322 &blind_claim_postsc2,
323 );
324
325 timer_prove.stop();
326
327 (
328 R1CSProof {
329 comm_vars,
330 sc_proof_phase1,
331 claims_phase2: (
332 comm_Az_claim,
333 comm_Bz_claim,
334 comm_Cz_claim,
335 comm_prod_Az_Bz_claims,
336 ),
337 pok_claims_phase2: (pok_Cz_claim, proof_prod),
338 proof_eq_sc_phase1,
339 sc_proof_phase2,
340 comm_vars_at_ry,
341 proof_eval_vars_at_ry,
342 proof_eq_sc_phase2,
343 },
344 rx,
345 ry,
346 )
347 }
348
349 pub fn verify(
350 &self,
351 num_vars: usize,
352 num_cons: usize,
353 input: &[Scalar],
354 evals: &(Scalar, Scalar, Scalar),
355 transcript: &mut Transcript,
356 gens: &R1CSGens,
357 ) -> Result<(Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
358 transcript.append_protocol_name(R1CSProof::protocol_name());
359
360 input.append_to_transcript(b"input", transcript);
361
362 let n = num_vars;
363 // add the commitment to the verifier's transcript
364 self
365 .comm_vars
366 .append_to_transcript(b"poly_commitment", transcript);
367
368 let (num_rounds_x, num_rounds_y) = (num_cons.log2() as usize, (2 * num_vars).log2() as usize);
369
370 // derive the verifier's challenge tau
371 let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
372
373 // verify the first sum-check instance
374 let claim_phase1 = Scalar::zero()
375 .commit(&Scalar::zero(), &gens.gens_sc.gens_1)
376 .compress();
377 let (comm_claim_post_phase1, rx) = self.sc_proof_phase1.verify(
378 &claim_phase1,
379 num_rounds_x,
380 3,
381 &gens.gens_sc.gens_1,
382 &gens.gens_sc.gens_4,
383 transcript,
384 )?;
385 // perform the intermediate sum-check test with claimed Az, Bz, and Cz
386 let (comm_Az_claim, comm_Bz_claim, comm_Cz_claim, comm_prod_Az_Bz_claims) = &self.claims_phase2;
387 let (pok_Cz_claim, proof_prod) = &self.pok_claims_phase2;
388
389 pok_Cz_claim.verify(&gens.gens_sc.gens_1, transcript, comm_Cz_claim)?;
390 proof_prod.verify(
391 &gens.gens_sc.gens_1,
392 transcript,
393 comm_Az_claim,
394 comm_Bz_claim,
395 comm_prod_Az_Bz_claims,
396 )?;
397
398 comm_Az_claim.append_to_transcript(b"comm_Az_claim", transcript);
399 comm_Bz_claim.append_to_transcript(b"comm_Bz_claim", transcript);
400 comm_Cz_claim.append_to_transcript(b"comm_Cz_claim", transcript);
401 comm_prod_Az_Bz_claims.append_to_transcript(b"comm_prod_Az_Bz_claims", transcript);
402
403 let taus_bound_rx: Scalar = (0..rx.len())
404 .map(|i| rx[i] * tau[i] + (Scalar::one() - rx[i]) * (Scalar::one() - tau[i]))
405 .product();
406 let expected_claim_post_phase1 = (taus_bound_rx
407 * (comm_prod_Az_Bz_claims.decompress().unwrap() - comm_Cz_claim.decompress().unwrap()))
408 .compress();
409
410 // verify proof that expected_claim_post_phase1 == claim_post_phase1
411 self.proof_eq_sc_phase1.verify(
412 &gens.gens_sc.gens_1,
413 transcript,
414 &expected_claim_post_phase1,
415 &comm_claim_post_phase1,
416 )?;
417
418 // derive three public challenges and then derive a joint claim
419 let r_A = transcript.challenge_scalar(b"challenege_Az");
420 let r_B = transcript.challenge_scalar(b"challenege_Bz");
421 let r_C = transcript.challenge_scalar(b"challenege_Cz");
422
423 // r_A * comm_Az_claim + r_B * comm_Bz_claim + r_C * comm_Cz_claim;
424 let comm_claim_phase2 = GroupElement::vartime_multiscalar_mul(
425 iter::once(&r_A)
426 .chain(iter::once(&r_B))
427 .chain(iter::once(&r_C)),
428 iter::once(&comm_Az_claim)
429 .chain(iter::once(&comm_Bz_claim))
430 .chain(iter::once(&comm_Cz_claim))
431 .map(|pt| pt.decompress().unwrap())
432 .collect::<Vec<GroupElement>>(),
433 )
434 .compress();
435
436 // verify the joint claim with a sum-check protocol
437 let (comm_claim_post_phase2, ry) = self.sc_proof_phase2.verify(
438 &comm_claim_phase2,
439 num_rounds_y,
440 2,
441 &gens.gens_sc.gens_1,
442 &gens.gens_sc.gens_3,
443 transcript,
444 )?;
445
446 // verify Z(ry) proof against the initial commitment
447 self.proof_eval_vars_at_ry.verify(
448 &gens.gens_pc,
449 transcript,
450 &ry[1..].to_vec(),
451 &self.comm_vars_at_ry,
452 &self.comm_vars,
453 )?;
454
455 let poly_input_eval = {
456 // constant term
457 let mut input_as_sparse_poly_entries = vec![SparsePolyEntry::new(0, Scalar::one())];
458 //remaining inputs
459 input_as_sparse_poly_entries.extend(
460 (0..input.len())
461 .map(|i| SparsePolyEntry::new(i + 1, input[i]))
462 .collect::<Vec<SparsePolyEntry>>(),
463 );
464 SparsePolynomial::new(n.log2() as usize, input_as_sparse_poly_entries)
465 .evaluate(&ry[1..].to_vec())
466 };
467
468 // compute commitment to eval_Z_at_ry = (Scalar::one() - ry[0]) * self.eval_vars_at_ry + ry[0] * poly_input_eval
469 let comm_eval_Z_at_ry = GroupElement::vartime_multiscalar_mul(
470 iter::once(Scalar::one() - ry[0]).chain(iter::once(ry[0])),
471 iter::once(&self.comm_vars_at_ry.decompress().unwrap()).chain(iter::once(
472 &poly_input_eval.commit(&Scalar::zero(), &gens.gens_pc.gens.gens_1),
473 )),
474 );
475
476 // perform the final check in the second sum-check protocol
477 let (eval_A_r, eval_B_r, eval_C_r) = evals;
478 let expected_claim_post_phase2 =
479 ((r_A * eval_A_r + r_B * eval_B_r + r_C * eval_C_r) * comm_eval_Z_at_ry).compress();
480 // verify proof that expected_claim_post_phase1 == claim_post_phase1
481 self.proof_eq_sc_phase2.verify(
482 &gens.gens_sc.gens_1,
483 transcript,
484 &expected_claim_post_phase2,
485 &comm_claim_post_phase2,
486 )?;
487
488 Ok((rx, ry))
489 }
490}
491
492#[cfg(test)]
493mod tests {
494 use super::*;
495 use rand::rngs::OsRng;
496
497 fn produce_tiny_r1cs() -> (R1CSInstance, Vec<Scalar>, Vec<Scalar>) {
498 // three constraints over five variables Z1, Z2, Z3, Z4, and Z5
499 // rounded to the nearest power of two
500 let num_cons = 128;
501 let num_vars = 256;
502 let num_inputs = 2;
503
504 // encode the above constraints into three matrices
505 let mut A: Vec<(usize, usize, Scalar)> = Vec::new();
506 let mut B: Vec<(usize, usize, Scalar)> = Vec::new();
507 let mut C: Vec<(usize, usize, Scalar)> = Vec::new();
508
509 let one = Scalar::one();
510 // constraint 0 entries
511 // (Z1 + Z2) * I0 - Z3 = 0;
512 A.push((0, 0, one));
513 A.push((0, 1, one));
514 B.push((0, num_vars + 1, one));
515 C.push((0, 2, one));
516
517 // constraint 1 entries
518 // (Z1 + I1) * (Z3) - Z4 = 0
519 A.push((1, 0, one));
520 A.push((1, num_vars + 2, one));
521 B.push((1, 2, one));
522 C.push((1, 3, one));
523 // constraint 3 entries
524 // Z5 * 1 - 0 = 0
525 A.push((2, 4, one));
526 B.push((2, num_vars, one));
527
528 let inst = R1CSInstance::new(num_cons, num_vars, num_inputs, &A, &B, &C);
529
530 // compute a satisfying assignment
531 let mut csprng: OsRng = OsRng;
532 let i0 = Scalar::random(&mut csprng);
533 let i1 = Scalar::random(&mut csprng);
534 let z1 = Scalar::random(&mut csprng);
535 let z2 = Scalar::random(&mut csprng);
536 let z3 = (z1 + z2) * i0; // constraint 1: (Z1 + Z2) * I0 - Z3 = 0;
537 let z4 = (z1 + i1) * z3; // constraint 2: (Z1 + I1) * (Z3) - Z4 = 0
538 let z5 = Scalar::zero(); //constraint 3
539
540 let mut vars = vec![Scalar::zero(); num_vars];
541 vars[0] = z1;
542 vars[1] = z2;
543 vars[2] = z3;
544 vars[3] = z4;
545 vars[4] = z5;
546
547 let mut input = vec![Scalar::zero(); num_inputs];
548 input[0] = i0;
549 input[1] = i1;
550
551 (inst, vars, input)
552 }
553
554 #[test]
555 fn test_tiny_r1cs() {
556 let (inst, vars, input) = tests::produce_tiny_r1cs();
557 let is_sat = inst.is_sat(&vars, &input);
558 assert!(is_sat);
559 }
560
561 #[test]
562 fn test_synthetic_r1cs() {
563 let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(1024, 1024, 10);
564 let is_sat = inst.is_sat(&vars, &input);
565 assert!(is_sat);
566 }
567
568 #[test]
569 pub fn check_r1cs_proof() {
570 let num_vars = 1024;
571 let num_cons = num_vars;
572 let num_inputs = 10;
573 let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
574
575 let gens = R1CSGens::new(b"test-m", num_cons, num_vars);
576
577 let mut random_tape = RandomTape::new(b"proof");
578 let mut prover_transcript = Transcript::new(b"example");
579 let (proof, rx, ry) = R1CSProof::prove(
580 &inst,
581 vars,
582 &input,
583 &gens,
584 &mut prover_transcript,
585 &mut random_tape,
586 );
587
588 let inst_evals = inst.evaluate(&rx, &ry);
589
590 let mut verifier_transcript = Transcript::new(b"example");
591 assert!(proof
592 .verify(
593 inst.get_num_vars(),
594 inst.get_num_cons(),
595 &input,
596 &inst_evals,
597 &mut verifier_transcript,
598 &gens,
599 )
600 .is_ok());
601 }
602}