testudo/src/r1csproof.rs
src/r1csproof.rsRaw
1#![allow(clippy::too_many_arguments)]
2use crate::constraints::{VerifierCircuit, VerifierConfig};
3use crate::group::{Fq, Fr};
4use crate::math::Math;
5use crate::parameters::poseidon_params;
6use crate::poseidon_transcript::{AppendToPoseidon, PoseidonTranscript};
7use crate::sumcheck::SumcheckInstanceProof;
8use ark_bls12_377::Bls12_377 as I;
9use ark_bw6_761::BW6_761 as P;
10use ark_poly::MultilinearExtension;
11use ark_poly_commit::multilinear_pc::data_structures::{Commitment, Proof};
12use ark_poly_commit::multilinear_pc::MultilinearPC;
13
14use super::commitments::MultiCommitGens;
15use super::dense_mlpoly::{DensePolynomial, EqPolynomial, PolyCommitmentGens};
16use super::errors::ProofVerifyError;
17
18use super::r1csinstance::R1CSInstance;
19
20use super::scalar::Scalar;
21use super::sparse_mlpoly::{SparsePolyEntry, SparsePolynomial};
22use super::timer::Timer;
23use ark_crypto_primitives::{CircuitSpecificSetupSNARK, SNARK};
24
25use ark_groth16::Groth16;
26use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystem};
27use ark_serialize::*;
28use ark_std::{One, Zero};
29
30use std::time::Instant;
31
32#[derive(CanonicalSerialize, CanonicalDeserialize, Debug)]
33pub struct R1CSProof {
34 // The PST commitment to the multilinear extension of the witness.
35 comm: Commitment<I>,
36 sc_proof_phase1: SumcheckInstanceProof,
37 claims_phase2: (Scalar, Scalar, Scalar, Scalar),
38 sc_proof_phase2: SumcheckInstanceProof,
39 eval_vars_at_ry: Scalar,
40 proof_eval_vars_at_ry: Proof<I>,
41 rx: Vec<Scalar>,
42 ry: Vec<Scalar>,
43 // The transcript state after the satisfiability proof was computed.
44 pub transcript_sat_state: Scalar,
45}
46#[derive(Clone)]
47pub struct R1CSSumcheckGens {
48 gens_1: MultiCommitGens,
49 gens_3: MultiCommitGens,
50 gens_4: MultiCommitGens,
51}
52
53// TODO: fix passing gens_1_ref
54impl R1CSSumcheckGens {
55 pub fn new(label: &'static [u8], gens_1_ref: &MultiCommitGens) -> Self {
56 let gens_1 = gens_1_ref.clone();
57 let gens_3 = MultiCommitGens::new(3, label);
58 let gens_4 = MultiCommitGens::new(4, label);
59
60 R1CSSumcheckGens {
61 gens_1,
62 gens_3,
63 gens_4,
64 }
65 }
66}
67
68#[derive(Clone)]
69pub struct R1CSGens {
70 gens_sc: R1CSSumcheckGens,
71 gens_pc: PolyCommitmentGens,
72}
73
74impl R1CSGens {
75 pub fn new(label: &'static [u8], _num_cons: usize, num_vars: usize) -> Self {
76 let num_poly_vars = num_vars.log_2();
77 let gens_pc = PolyCommitmentGens::new(num_poly_vars, label);
78 let gens_sc = R1CSSumcheckGens::new(label, &gens_pc.gens.gens_1);
79 R1CSGens { gens_sc, gens_pc }
80 }
81}
82
83impl R1CSProof {
84 fn prove_phase_one(
85 num_rounds: usize,
86 evals_tau: &mut DensePolynomial,
87 evals_Az: &mut DensePolynomial,
88 evals_Bz: &mut DensePolynomial,
89 evals_Cz: &mut DensePolynomial,
90 transcript: &mut PoseidonTranscript,
91 ) -> (SumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>) {
92 let comb_func =
93 |poly_tau_comp: &Scalar,
94 poly_A_comp: &Scalar,
95 poly_B_comp: &Scalar,
96 poly_C_comp: &Scalar|
97 -> Scalar { (*poly_tau_comp) * ((*poly_A_comp) * poly_B_comp - poly_C_comp) };
98
99 let (sc_proof_phase_one, r, claims) = SumcheckInstanceProof::prove_cubic_with_additive_term(
100 &Scalar::zero(), // claim is zero
101 num_rounds,
102 evals_tau,
103 evals_Az,
104 evals_Bz,
105 evals_Cz,
106 comb_func,
107 transcript,
108 );
109
110 (sc_proof_phase_one, r, claims)
111 }
112
113 fn prove_phase_two(
114 num_rounds: usize,
115 claim: &Scalar,
116 evals_z: &mut DensePolynomial,
117 evals_ABC: &mut DensePolynomial,
118 transcript: &mut PoseidonTranscript,
119 ) -> (SumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>) {
120 let comb_func =
121 |poly_A_comp: &Scalar, poly_B_comp: &Scalar| -> Scalar { (*poly_A_comp) * poly_B_comp };
122 let (sc_proof_phase_two, r, claims) = SumcheckInstanceProof::prove_quad(
123 claim, num_rounds, evals_z, evals_ABC, comb_func, transcript,
124 );
125
126 (sc_proof_phase_two, r, claims)
127 }
128
129 fn protocol_name() -> &'static [u8] {
130 b"R1CS proof"
131 }
132
133 pub fn prove(
134 inst: &R1CSInstance,
135 vars: Vec<Scalar>,
136 input: &[Scalar],
137 gens: &R1CSGens,
138 transcript: &mut PoseidonTranscript,
139 ) -> (R1CSProof, Vec<Scalar>, Vec<Scalar>) {
140 let timer_prove = Timer::new("R1CSProof::prove");
141 // we currently require the number of |inputs| + 1 to be at most number of vars
142 assert!(input.len() < vars.len());
143
144 // create the multilinear witness polynomial from the satisfying assiment
145 let poly_vars = DensePolynomial::new(vars.clone());
146
147 let timer_commit = Timer::new("polycommit");
148 // commitment to the satisfying witness polynomial
149 let comm = MultilinearPC::<I>::commit(&gens.gens_pc.ck, &poly_vars);
150 comm.append_to_poseidon(transcript);
151 timer_commit.stop();
152
153 let c = transcript.challenge_scalar();
154 transcript.new_from_state(&c);
155
156 transcript.append_scalar_vector(input);
157
158 let timer_sc_proof_phase1 = Timer::new("prove_sc_phase_one");
159
160 // append input to variables to create a single vector z
161 let z = {
162 let num_inputs = input.len();
163 let num_vars = vars.len();
164 let mut z = vars;
165 z.extend(&vec![Scalar::one()]); // add constant term in z
166 z.extend(input);
167 z.extend(&vec![Scalar::zero(); num_vars - num_inputs - 1]); // we will pad with zeros
168 z
169 };
170
171 // derive the verifier's challenge tau
172 let (num_rounds_x, num_rounds_y) = (inst.get_num_cons().log_2(), z.len().log_2());
173 let tau = transcript.challenge_vector(num_rounds_x);
174 // compute the initial evaluation table for R(\tau, x)
175 let mut poly_tau = DensePolynomial::new(EqPolynomial::new(tau).evals());
176 let (mut poly_Az, mut poly_Bz, mut poly_Cz) =
177 inst.multiply_vec(inst.get_num_cons(), z.len(), &z);
178
179 let (sc_proof_phase1, rx, _claims_phase1) = R1CSProof::prove_phase_one(
180 num_rounds_x,
181 &mut poly_tau,
182 &mut poly_Az,
183 &mut poly_Bz,
184 &mut poly_Cz,
185 transcript,
186 );
187 assert_eq!(poly_tau.len(), 1);
188 assert_eq!(poly_Az.len(), 1);
189 assert_eq!(poly_Bz.len(), 1);
190 assert_eq!(poly_Cz.len(), 1);
191 timer_sc_proof_phase1.stop();
192
193 let (tau_claim, Az_claim, Bz_claim, Cz_claim) =
194 (&poly_tau[0], &poly_Az[0], &poly_Bz[0], &poly_Cz[0]);
195 let prod_Az_Bz_claims = (*Az_claim) * Bz_claim;
196
197 // prove the final step of sum-check #1
198 let taus_bound_rx = tau_claim;
199 let _claim_post_phase1 = ((*Az_claim) * Bz_claim - Cz_claim) * taus_bound_rx;
200
201 let timer_sc_proof_phase2 = Timer::new("prove_sc_phase_two");
202 // combine the three claims into a single claim
203 let r_A = transcript.challenge_scalar();
204 let r_B = transcript.challenge_scalar();
205 let r_C = transcript.challenge_scalar();
206 let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;
207
208 let evals_ABC = {
209 // compute the initial evaluation table for R(\tau, x)
210 let evals_rx = EqPolynomial::new(rx.clone()).evals();
211 let (evals_A, evals_B, evals_C) =
212 inst.compute_eval_table_sparse(inst.get_num_cons(), z.len(), &evals_rx);
213
214 assert_eq!(evals_A.len(), evals_B.len());
215 assert_eq!(evals_A.len(), evals_C.len());
216 (0..evals_A.len())
217 .map(|i| r_A * evals_A[i] + r_B * evals_B[i] + r_C * evals_C[i])
218 .collect::<Vec<Scalar>>()
219 };
220
221 // another instance of the sum-check protocol
222 let (sc_proof_phase2, ry, _claims_phase2) = R1CSProof::prove_phase_two(
223 num_rounds_y,
224 &claim_phase2,
225 &mut DensePolynomial::new(z),
226 &mut DensePolynomial::new(evals_ABC),
227 transcript,
228 );
229 timer_sc_proof_phase2.stop();
230
231 // TODO: modify the polynomial evaluation in Spartan to be consistent
232 // with the evaluation in ark-poly-commit so that reversing is not needed
233 // anymore
234 let timmer_opening = Timer::new("polyopening");
235 let mut dummy = ry[1..].to_vec().clone();
236 dummy.reverse();
237 let proof_eval_vars_at_ry = MultilinearPC::<I>::open(&gens.gens_pc.ck, &poly_vars, &dummy);
238 println!(
239 "proof size (no of quotients): {:?}",
240 proof_eval_vars_at_ry.proofs.len()
241 );
242 timmer_opening.stop();
243
244 let timer_polyeval = Timer::new("polyeval");
245 let eval_vars_at_ry = poly_vars.evaluate(&ry[1..]);
246 timer_polyeval.stop();
247
248 timer_prove.stop();
249
250 let c = transcript.challenge_scalar();
251
252 (
253 R1CSProof {
254 comm,
255 sc_proof_phase1,
256 claims_phase2: (*Az_claim, *Bz_claim, *Cz_claim, prod_Az_Bz_claims),
257 sc_proof_phase2,
258 eval_vars_at_ry,
259 proof_eval_vars_at_ry,
260 rx: rx.clone(),
261 ry: ry.clone(),
262 transcript_sat_state: c,
263 },
264 rx,
265 ry,
266 )
267 }
268
269 pub fn verify_groth16(
270 &self,
271 num_vars: usize,
272 num_cons: usize,
273 input: &[Scalar],
274 evals: &(Scalar, Scalar, Scalar),
275 transcript: &mut PoseidonTranscript,
276 gens: &R1CSGens,
277 ) -> Result<(u128, u128, u128), ProofVerifyError> {
278 self.comm.append_to_poseidon(transcript);
279
280 let c = transcript.challenge_scalar();
281
282 let mut input_as_sparse_poly_entries = vec![SparsePolyEntry::new(0, Scalar::one())];
283 //remaining inputs
284 input_as_sparse_poly_entries.extend(
285 (0..input.len())
286 .map(|i| SparsePolyEntry::new(i + 1, input[i]))
287 .collect::<Vec<SparsePolyEntry>>(),
288 );
289
290 let n = num_vars;
291 let input_as_sparse_poly =
292 SparsePolynomial::new(n.log_2() as usize, input_as_sparse_poly_entries);
293
294 let config = VerifierConfig {
295 num_vars,
296 num_cons,
297 input: input.to_vec(),
298 evals: *evals,
299 params: poseidon_params(),
300 prev_challenge: c,
301 claims_phase2: self.claims_phase2,
302 polys_sc1: self.sc_proof_phase1.polys.clone(),
303 polys_sc2: self.sc_proof_phase2.polys.clone(),
304 eval_vars_at_ry: self.eval_vars_at_ry,
305 input_as_sparse_poly,
306 // rx: self.rx.clone(),
307 ry: self.ry.clone(),
308 transcript_sat_state: self.transcript_sat_state,
309 };
310
311 let mut rng = ark_std::test_rng();
312
313 let prove_inner = Timer::new("proveinnercircuit");
314 let start = Instant::now();
315 let circuit = VerifierCircuit::new(&config, &mut rng).unwrap();
316 let dp1 = start.elapsed().as_millis();
317 prove_inner.stop();
318
319 let start = Instant::now();
320 let (pk, vk) = Groth16::<P>::setup(circuit.clone(), &mut rng).unwrap();
321 let ds = start.elapsed().as_millis();
322
323 let prove_outer = Timer::new("proveoutercircuit");
324 let start = Instant::now();
325 let proof = Groth16::<P>::prove(&pk, circuit, &mut rng).unwrap();
326 let dp2 = start.elapsed().as_millis();
327 prove_outer.stop();
328
329 let start = Instant::now();
330 let is_verified = Groth16::<P>::verify(&vk, &[], &proof).unwrap();
331 assert!(is_verified);
332
333 let timer_verification = Timer::new("commitverification");
334 let mut dummy = self.ry[1..].to_vec();
335 // TODO: ensure ark-poly-commit and Spartan produce consistent results
336 // when evaluating a polynomial at a given point so this reverse is not
337 // needed.
338 dummy.reverse();
339
340 // Verifies the proof of opening against the result of evaluating the
341 // witness polynomial at point ry.
342 let res = MultilinearPC::<I>::check(
343 &gens.gens_pc.vk,
344 &self.comm,
345 &dummy,
346 self.eval_vars_at_ry,
347 &self.proof_eval_vars_at_ry,
348 );
349
350 timer_verification.stop();
351 assert!(res == true);
352 let dv = start.elapsed().as_millis();
353
354 Ok((ds, dp1 + dp2, dv))
355 }
356
357 // Helper function to find the number of constraint in the circuit which
358 // requires executing it.
359 pub fn circuit_size(
360 &self,
361 num_vars: usize,
362 num_cons: usize,
363 input: &[Scalar],
364 evals: &(Scalar, Scalar, Scalar),
365 transcript: &mut PoseidonTranscript,
366 _gens: &R1CSGens,
367 ) -> Result<usize, ProofVerifyError> {
368 self.comm.append_to_poseidon(transcript);
369
370 let c = transcript.challenge_scalar();
371
372 let mut input_as_sparse_poly_entries = vec![SparsePolyEntry::new(0, Scalar::one())];
373 //remaining inputs
374 input_as_sparse_poly_entries.extend(
375 (0..input.len())
376 .map(|i| SparsePolyEntry::new(i + 1, input[i]))
377 .collect::<Vec<SparsePolyEntry>>(),
378 );
379
380 let n = num_vars;
381 let input_as_sparse_poly =
382 SparsePolynomial::new(n.log_2() as usize, input_as_sparse_poly_entries);
383
384 let config = VerifierConfig {
385 num_vars,
386 num_cons,
387 input: input.to_vec(),
388 evals: *evals,
389 params: poseidon_params(),
390 prev_challenge: c,
391 claims_phase2: self.claims_phase2,
392 polys_sc1: self.sc_proof_phase1.polys.clone(),
393 polys_sc2: self.sc_proof_phase2.polys.clone(),
394 eval_vars_at_ry: self.eval_vars_at_ry,
395 input_as_sparse_poly,
396 // rx: self.rx.clone(),
397 ry: self.ry.clone(),
398 transcript_sat_state: self.transcript_sat_state,
399 };
400
401 let mut rng = ark_std::test_rng();
402 let circuit = VerifierCircuit::new(&config, &mut rng).unwrap();
403
404 let nc_inner = verify_constraints_inner(circuit.clone(), &num_cons);
405
406 let nc_outer = verify_constraints_outer(circuit, &num_cons);
407 Ok(nc_inner + nc_outer)
408 }
409}
410
411fn verify_constraints_outer(circuit: VerifierCircuit, _num_cons: &usize) -> usize {
412 let cs = ConstraintSystem::<Fq>::new_ref();
413 circuit.generate_constraints(cs.clone()).unwrap();
414 assert!(cs.is_satisfied().unwrap());
415 cs.num_constraints()
416}
417
418fn verify_constraints_inner(circuit: VerifierCircuit, _num_cons: &usize) -> usize {
419 let cs = ConstraintSystem::<Fr>::new_ref();
420 circuit
421 .inner_circuit
422 .generate_constraints(cs.clone())
423 .unwrap();
424 assert!(cs.is_satisfied().unwrap());
425 cs.num_constraints()
426}
427
428#[cfg(test)]
429mod tests {
430 use crate::parameters::poseidon_params;
431
432 use super::*;
433
434 use ark_std::UniformRand;
435
436 fn produce_tiny_r1cs() -> (R1CSInstance, Vec<Scalar>, Vec<Scalar>) {
437 // three constraints over five variables Z1, Z2, Z3, Z4, and Z5
438 // rounded to the nearest power of two
439 let num_cons = 128;
440 let num_vars = 256;
441 let num_inputs = 2;
442
443 // encode the above constraints into three matrices
444 let mut A: Vec<(usize, usize, Scalar)> = Vec::new();
445 let mut B: Vec<(usize, usize, Scalar)> = Vec::new();
446 let mut C: Vec<(usize, usize, Scalar)> = Vec::new();
447
448 let one = Scalar::one();
449 // constraint 0 entries
450 // (Z1 + Z2) * I0 - Z3 = 0;
451 A.push((0, 0, one));
452 A.push((0, 1, one));
453 B.push((0, num_vars + 1, one));
454 C.push((0, 2, one));
455
456 // constraint 1 entries
457 // (Z1 + I1) * (Z3) - Z4 = 0
458 A.push((1, 0, one));
459 A.push((1, num_vars + 2, one));
460 B.push((1, 2, one));
461 C.push((1, 3, one));
462 // constraint 3 entries
463 // Z5 * 1 - 0 = 0
464 A.push((2, 4, one));
465 B.push((2, num_vars, one));
466
467 let inst = R1CSInstance::new(num_cons, num_vars, num_inputs, &A, &B, &C);
468
469 // compute a satisfying assignment
470 let mut rng = ark_std::rand::thread_rng();
471 let i0 = Scalar::rand(&mut rng);
472 let i1 = Scalar::rand(&mut rng);
473 let z1 = Scalar::rand(&mut rng);
474 let z2 = Scalar::rand(&mut rng);
475 let z3 = (z1 + z2) * i0; // constraint 1: (Z1 + Z2) * I0 - Z3 = 0;
476 let z4 = (z1 + i1) * z3; // constraint 2: (Z1 + I1) * (Z3) - Z4 = 0
477 let z5 = Scalar::zero(); //constraint 3
478
479 let mut vars = vec![Scalar::zero(); num_vars];
480 vars[0] = z1;
481 vars[1] = z2;
482 vars[2] = z3;
483 vars[3] = z4;
484 vars[4] = z5;
485
486 let mut input = vec![Scalar::zero(); num_inputs];
487 input[0] = i0;
488 input[1] = i1;
489
490 (inst, vars, input)
491 }
492
493 #[test]
494 fn test_tiny_r1cs() {
495 let (inst, vars, input) = tests::produce_tiny_r1cs();
496 let is_sat = inst.is_sat(&vars, &input);
497 assert!(is_sat);
498 }
499
500 #[test]
501 fn test_synthetic_r1cs() {
502 let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(1024, 1024, 10);
503 let is_sat = inst.is_sat(&vars, &input);
504 assert!(is_sat);
505 }
506
507 #[test]
508 pub fn check_r1cs_proof() {
509 let num_vars = 1024;
510 let num_cons = num_vars;
511 let num_inputs = 10;
512 let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
513
514 let gens = R1CSGens::new(b"test-m", num_cons, num_vars);
515
516 let params = poseidon_params();
517 // let mut random_tape = RandomTape::new(b"proof");
518
519 let mut prover_transcript = PoseidonTranscript::new(¶ms);
520 let (proof, rx, ry) = R1CSProof::prove(&inst, vars, &input, &gens, &mut prover_transcript);
521
522 let inst_evals = inst.evaluate(&rx, &ry);
523
524 let mut verifier_transcript = PoseidonTranscript::new(¶ms);
525
526 // if you want to check the test fails
527 // input[0] = Scalar::zero();
528
529 assert!(proof
530 .verify_groth16(
531 inst.get_num_vars(),
532 inst.get_num_cons(),
533 &input,
534 &inst_evals,
535 &mut verifier_transcript,
536 &gens,
537 )
538 .is_ok());
539 }
540}