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 let timer_commit = Timer::new("polycommit");
156 let (poly_vars, comm_vars, blinds_vars) = {
157 // create a multilinear polynomial using the supplied assignment for variables
158 let poly_vars = DensePolynomial::new(vars.clone());
159
160 // produce a commitment to the satisfying assignment
161 let (comm_vars, blinds_vars) = poly_vars.commit(&gens.gens_pc, Some(random_tape));
162
163 // add the commitment to the prover's transcript
164 comm_vars.append_to_transcript(b"poly_commitment", transcript);
165 (poly_vars, comm_vars, blinds_vars)
166 };
167 timer_commit.stop();
168
169 let timer_sc_proof_phase1 = Timer::new("prove_sc_phase_one");
170
171 // append input to variables to create a single vector z
172 let z = {
173 let num_inputs = input.len();
174 let num_vars = vars.len();
175 let mut z = vars;
176 z.extend(&vec![Scalar::one()]); // add constant term in z
177 z.extend(input);
178 z.extend(&vec![Scalar::zero(); num_vars - num_inputs - 1]); // we will pad with zeros
179 z
180 };
181
182 // derive the verifier's challenge tau
183 let (num_rounds_x, num_rounds_y) =
184 (inst.get_num_cons().log2() as usize, z.len().log2() as usize);
185 let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
186 // compute the initial evaluation table for R(\tau, x)
187 let mut poly_tau = DensePolynomial::new(EqPolynomial::new(tau).evals());
188 let (mut poly_Az, mut poly_Bz, mut poly_Cz) =
189 inst.multiply_vec(inst.get_num_cons(), z.len(), &z);
190
191 let (sc_proof_phase1, rx, _claims_phase1, blind_claim_postsc1) = R1CSProof::prove_phase_one(
192 num_rounds_x,
193 &mut poly_tau,
194 &mut poly_Az,
195 &mut poly_Bz,
196 &mut poly_Cz,
197 &gens.gens_sc,
198 transcript,
199 random_tape,
200 );
201 assert_eq!(poly_tau.len(), 1);
202 assert_eq!(poly_Az.len(), 1);
203 assert_eq!(poly_Bz.len(), 1);
204 assert_eq!(poly_Cz.len(), 1);
205 timer_sc_proof_phase1.stop();
206
207 let (tau_claim, Az_claim, Bz_claim, Cz_claim) =
208 (&poly_tau[0], &poly_Az[0], &poly_Bz[0], &poly_Cz[0]);
209 let (Az_blind, Bz_blind, Cz_blind, prod_Az_Bz_blind) = (
210 random_tape.random_scalar(b"Az_blind"),
211 random_tape.random_scalar(b"Bz_blind"),
212 random_tape.random_scalar(b"Cz_blind"),
213 random_tape.random_scalar(b"prod_Az_Bz_blind"),
214 );
215
216 let (pok_Cz_claim, comm_Cz_claim) = {
217 KnowledgeProof::prove(
218 &gens.gens_sc.gens_1,
219 transcript,
220 random_tape,
221 Cz_claim,
222 &Cz_blind,
223 )
224 };
225
226 let (proof_prod, comm_Az_claim, comm_Bz_claim, comm_prod_Az_Bz_claims) = {
227 let prod = Az_claim * Bz_claim;
228 ProductProof::prove(
229 &gens.gens_sc.gens_1,
230 transcript,
231 random_tape,
232 Az_claim,
233 &Az_blind,
234 Bz_claim,
235 &Bz_blind,
236 &prod,
237 &prod_Az_Bz_blind,
238 )
239 };
240
241 comm_Az_claim.append_to_transcript(b"comm_Az_claim", transcript);
242 comm_Bz_claim.append_to_transcript(b"comm_Bz_claim", transcript);
243 comm_Cz_claim.append_to_transcript(b"comm_Cz_claim", transcript);
244 comm_prod_Az_Bz_claims.append_to_transcript(b"comm_prod_Az_Bz_claims", transcript);
245
246 // prove the final step of sum-check #1
247 let taus_bound_rx = tau_claim;
248 let blind_expected_claim_postsc1 = taus_bound_rx * (prod_Az_Bz_blind - Cz_blind);
249 let claim_post_phase1 = (Az_claim * Bz_claim - Cz_claim) * taus_bound_rx;
250 let (proof_eq_sc_phase1, _C1, _C2) = EqualityProof::prove(
251 &gens.gens_sc.gens_1,
252 transcript,
253 random_tape,
254 &claim_post_phase1,
255 &blind_expected_claim_postsc1,
256 &claim_post_phase1,
257 &blind_claim_postsc1,
258 );
259
260 let timer_sc_proof_phase2 = Timer::new("prove_sc_phase_two");
261 // combine the three claims into a single claim
262 let r_A = transcript.challenge_scalar(b"challenege_Az");
263 let r_B = transcript.challenge_scalar(b"challenege_Bz");
264 let r_C = transcript.challenge_scalar(b"challenege_Cz");
265 let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;
266 let blind_claim_phase2 = r_A * Az_blind + r_B * Bz_blind + r_C * Cz_blind;
267
268 let evals_ABC = {
269 // compute the initial evaluation table for R(\tau, x)
270 let evals_rx = EqPolynomial::new(rx.clone()).evals();
271 let (evals_A, evals_B, evals_C) =
272 inst.compute_eval_table_sparse(inst.get_num_cons(), z.len(), &evals_rx);
273
274 assert_eq!(evals_A.len(), evals_B.len());
275 assert_eq!(evals_A.len(), evals_C.len());
276 (0..evals_A.len())
277 .map(|i| r_A * evals_A[i] + r_B * evals_B[i] + r_C * evals_C[i])
278 .collect::<Vec<Scalar>>()
279 };
280
281 // another instance of the sum-check protocol
282 let (sc_proof_phase2, ry, claims_phase2, blind_claim_postsc2) = R1CSProof::prove_phase_two(
283 num_rounds_y,
284 &claim_phase2,
285 &blind_claim_phase2,
286 &mut DensePolynomial::new(z),
287 &mut DensePolynomial::new(evals_ABC),
288 &gens.gens_sc,
289 transcript,
290 random_tape,
291 );
292 timer_sc_proof_phase2.stop();
293
294 let timer_polyeval = Timer::new("polyeval");
295 let eval_vars_at_ry = poly_vars.evaluate(&ry[1..].to_vec());
296 let blind_eval = random_tape.random_scalar(b"blind_eval");
297 let (proof_eval_vars_at_ry, comm_vars_at_ry) = PolyEvalProof::prove(
298 &poly_vars,
299 Some(&blinds_vars),
300 &ry[1..].to_vec(),
301 &eval_vars_at_ry,
302 Some(&blind_eval),
303 &gens.gens_pc,
304 transcript,
305 random_tape,
306 );
307 timer_polyeval.stop();
308
309 // prove the final step of sum-check #2
310 let blind_eval_Z_at_ry = (Scalar::one() - ry[0]) * blind_eval;
311 let blind_expected_claim_postsc2 = claims_phase2[1] * blind_eval_Z_at_ry;
312 let claim_post_phase2 = claims_phase2[0] * claims_phase2[1];
313 let (proof_eq_sc_phase2, _C1, _C2) = EqualityProof::prove(
314 &gens.gens_pc.gens.gens_1,
315 transcript,
316 random_tape,
317 &claim_post_phase2,
318 &blind_expected_claim_postsc2,
319 &claim_post_phase2,
320 &blind_claim_postsc2,
321 );
322
323 timer_prove.stop();
324
325 (
326 R1CSProof {
327 comm_vars,
328 sc_proof_phase1,
329 claims_phase2: (
330 comm_Az_claim,
331 comm_Bz_claim,
332 comm_Cz_claim,
333 comm_prod_Az_Bz_claims,
334 ),
335 pok_claims_phase2: (pok_Cz_claim, proof_prod),
336 proof_eq_sc_phase1,
337 sc_proof_phase2,
338 comm_vars_at_ry,
339 proof_eval_vars_at_ry,
340 proof_eq_sc_phase2,
341 },
342 rx,
343 ry,
344 )
345 }
346
347 pub fn verify(
348 &self,
349 num_vars: usize,
350 num_cons: usize,
351 input: &[Scalar],
352 evals: &(Scalar, Scalar, Scalar),
353 transcript: &mut Transcript,
354 gens: &R1CSGens,
355 ) -> Result<(Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
356 transcript.append_protocol_name(R1CSProof::protocol_name());
357
358 let n = num_vars;
359 // add the commitment to the verifier's transcript
360 self
361 .comm_vars
362 .append_to_transcript(b"poly_commitment", transcript);
363
364 let (num_rounds_x, num_rounds_y) = (num_cons.log2() as usize, (2 * num_vars).log2() as usize);
365
366 // derive the verifier's challenge tau
367 let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
368
369 // verify the first sum-check instance
370 let claim_phase1 = Scalar::zero()
371 .commit(&Scalar::zero(), &gens.gens_sc.gens_1)
372 .compress();
373 let (comm_claim_post_phase1, rx) = self.sc_proof_phase1.verify(
374 &claim_phase1,
375 num_rounds_x,
376 3,
377 &gens.gens_sc.gens_1,
378 &gens.gens_sc.gens_4,
379 transcript,
380 )?;
381 // perform the intermediate sum-check test with claimed Az, Bz, and Cz
382 let (comm_Az_claim, comm_Bz_claim, comm_Cz_claim, comm_prod_Az_Bz_claims) = &self.claims_phase2;
383 let (pok_Cz_claim, proof_prod) = &self.pok_claims_phase2;
384
385 pok_Cz_claim.verify(&gens.gens_sc.gens_1, transcript, comm_Cz_claim)?;
386 proof_prod.verify(
387 &gens.gens_sc.gens_1,
388 transcript,
389 comm_Az_claim,
390 comm_Bz_claim,
391 comm_prod_Az_Bz_claims,
392 )?;
393
394 comm_Az_claim.append_to_transcript(b"comm_Az_claim", transcript);
395 comm_Bz_claim.append_to_transcript(b"comm_Bz_claim", transcript);
396 comm_Cz_claim.append_to_transcript(b"comm_Cz_claim", transcript);
397 comm_prod_Az_Bz_claims.append_to_transcript(b"comm_prod_Az_Bz_claims", transcript);
398
399 let taus_bound_rx: Scalar = (0..rx.len())
400 .map(|i| rx[i] * tau[i] + (Scalar::one() - rx[i]) * (Scalar::one() - tau[i]))
401 .product();
402 let expected_claim_post_phase1 = (taus_bound_rx
403 * (comm_prod_Az_Bz_claims.decompress().unwrap() - comm_Cz_claim.decompress().unwrap()))
404 .compress();
405
406 // verify proof that expected_claim_post_phase1 == claim_post_phase1
407 self.proof_eq_sc_phase1.verify(
408 &gens.gens_sc.gens_1,
409 transcript,
410 &expected_claim_post_phase1,
411 &comm_claim_post_phase1,
412 )?;
413
414 // derive three public challenges and then derive a joint claim
415 let r_A = transcript.challenge_scalar(b"challenege_Az");
416 let r_B = transcript.challenge_scalar(b"challenege_Bz");
417 let r_C = transcript.challenge_scalar(b"challenege_Cz");
418
419 // r_A * comm_Az_claim + r_B * comm_Bz_claim + r_C * comm_Cz_claim;
420 let comm_claim_phase2 = GroupElement::vartime_multiscalar_mul(
421 iter::once(&r_A)
422 .chain(iter::once(&r_B))
423 .chain(iter::once(&r_C)),
424 iter::once(&comm_Az_claim)
425 .chain(iter::once(&comm_Bz_claim))
426 .chain(iter::once(&comm_Cz_claim))
427 .map(|pt| pt.decompress().unwrap())
428 .collect::<Vec<GroupElement>>(),
429 )
430 .compress();
431
432 // verify the joint claim with a sum-check protocol
433 let (comm_claim_post_phase2, ry) = self.sc_proof_phase2.verify(
434 &comm_claim_phase2,
435 num_rounds_y,
436 2,
437 &gens.gens_sc.gens_1,
438 &gens.gens_sc.gens_3,
439 transcript,
440 )?;
441
442 // verify Z(ry) proof against the initial commitment
443 self.proof_eval_vars_at_ry.verify(
444 &gens.gens_pc,
445 transcript,
446 &ry[1..].to_vec(),
447 &self.comm_vars_at_ry,
448 &self.comm_vars,
449 )?;
450
451 let poly_input_eval = {
452 // constant term
453 let mut input_as_sparse_poly_entries = vec![SparsePolyEntry::new(0, Scalar::one())];
454 //remaining inputs
455 input_as_sparse_poly_entries.extend(
456 (0..input.len())
457 .map(|i| SparsePolyEntry::new(i + 1, input[i]))
458 .collect::<Vec<SparsePolyEntry>>(),
459 );
460 SparsePolynomial::new(n.log2() as usize, input_as_sparse_poly_entries)
461 .evaluate(&ry[1..].to_vec())
462 };
463
464 // compute commitment to eval_Z_at_ry = (Scalar::one() - ry[0]) * self.eval_vars_at_ry + ry[0] * poly_input_eval
465 let comm_eval_Z_at_ry = GroupElement::vartime_multiscalar_mul(
466 iter::once(Scalar::one() - ry[0]).chain(iter::once(ry[0])),
467 iter::once(&self.comm_vars_at_ry.decompress().unwrap()).chain(iter::once(
468 &poly_input_eval.commit(&Scalar::zero(), &gens.gens_pc.gens.gens_1),
469 )),
470 );
471
472 // perform the final check in the second sum-check protocol
473 let (eval_A_r, eval_B_r, eval_C_r) = evals;
474 let expected_claim_post_phase2 =
475 ((r_A * eval_A_r + r_B * eval_B_r + r_C * eval_C_r) * comm_eval_Z_at_ry).compress();
476 // verify proof that expected_claim_post_phase1 == claim_post_phase1
477 self.proof_eq_sc_phase2.verify(
478 &gens.gens_sc.gens_1,
479 transcript,
480 &expected_claim_post_phase2,
481 &comm_claim_post_phase2,
482 )?;
483
484 Ok((rx, ry))
485 }
486}
487
488#[cfg(test)]
489mod tests {
490 use super::*;
491 use rand::rngs::OsRng;
492
493 fn produce_tiny_r1cs() -> (R1CSInstance, Vec<Scalar>, Vec<Scalar>) {
494 // three constraints over five variables Z1, Z2, Z3, Z4, and Z5
495 // rounded to the nearest power of two
496 let num_cons = 128;
497 let num_vars = 256;
498 let num_inputs = 2;
499
500 // encode the above constraints into three matrices
501 let mut A: Vec<(usize, usize, Scalar)> = Vec::new();
502 let mut B: Vec<(usize, usize, Scalar)> = Vec::new();
503 let mut C: Vec<(usize, usize, Scalar)> = Vec::new();
504
505 let one = Scalar::one();
506 // constraint 0 entries
507 // (Z1 + Z2) * I0 - Z3 = 0;
508 A.push((0, 0, one));
509 A.push((0, 1, one));
510 B.push((0, num_vars + 1, one));
511 C.push((0, 2, one));
512
513 // constraint 1 entries
514 // (Z1 + I1) * (Z3) - Z4 = 0
515 A.push((1, 0, one));
516 A.push((1, num_vars + 2, one));
517 B.push((1, 2, one));
518 C.push((1, 3, one));
519 // constraint 3 entries
520 // Z5 * 1 - 0 = 0
521 A.push((2, 4, one));
522 B.push((2, num_vars, one));
523
524 let inst = R1CSInstance::new(num_cons, num_vars, num_inputs, &A, &B, &C);
525
526 // compute a satisfying assignment
527 let mut csprng: OsRng = OsRng;
528 let i0 = Scalar::random(&mut csprng);
529 let i1 = Scalar::random(&mut csprng);
530 let z1 = Scalar::random(&mut csprng);
531 let z2 = Scalar::random(&mut csprng);
532 let z3 = (z1 + z2) * i0; // constraint 1: (Z1 + Z2) * I0 - Z3 = 0;
533 let z4 = (z1 + i1) * z3; // constraint 2: (Z1 + I1) * (Z3) - Z4 = 0
534 let z5 = Scalar::zero(); //constraint 3
535
536 let mut vars = vec![Scalar::zero(); num_vars];
537 vars[0] = z1;
538 vars[1] = z2;
539 vars[2] = z3;
540 vars[3] = z4;
541 vars[4] = z5;
542
543 let mut input = vec![Scalar::zero(); num_inputs];
544 input[0] = i0;
545 input[1] = i1;
546
547 (inst, vars, input)
548 }
549
550 #[test]
551 fn test_tiny_r1cs() {
552 let (inst, vars, input) = tests::produce_tiny_r1cs();
553 let is_sat = inst.is_sat(&vars, &input);
554 assert!(is_sat);
555 }
556
557 #[test]
558 fn test_synthetic_r1cs() {
559 let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(1024, 1024, 10);
560 let is_sat = inst.is_sat(&vars, &input);
561 assert!(is_sat);
562 }
563
564 #[test]
565 pub fn check_r1cs_proof() {
566 let num_vars = 1024;
567 let num_cons = num_vars;
568 let num_inputs = 10;
569 let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
570
571 let gens = R1CSGens::new(b"test-m", num_cons, num_vars);
572
573 let mut random_tape = RandomTape::new(b"proof");
574 let mut prover_transcript = Transcript::new(b"example");
575 let (proof, rx, ry) = R1CSProof::prove(
576 &inst,
577 vars,
578 &input,
579 &gens,
580 &mut prover_transcript,
581 &mut random_tape,
582 );
583
584 let inst_evals = inst.evaluate(&rx, &ry);
585
586 let mut verifier_transcript = Transcript::new(b"example");
587 assert!(proof
588 .verify(
589 inst.get_num_vars(),
590 inst.get_num_cons(),
591 &input,
592 &inst_evals,
593 &mut verifier_transcript,
594 &gens,
595 )
596 .is_ok());
597 }
598}