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