testudo/src/r1csproof.rs
src/r1csproof.rsRaw
1#![allow(clippy::too_many_arguments)]
2use crate::group::CompressedGroup;
3use crate::sumcheck::SumcheckInstanceProof;
4
5use super::commitments::{Commitments, MultiCommitGens};
6use super::dense_mlpoly::{
7 DensePolynomial, EqPolynomial, PolyCommitment, PolyCommitmentGens, PolyEvalProof,
8};
9use super::errors::ProofVerifyError;
10use super::group::{
11 CompressGroupElement, DecompressGroupElement, GroupElement, VartimeMultiscalarMul,
12};
13use super::math::Math;
14use super::nizk::{EqualityProof, KnowledgeProof, ProductProof};
15use super::r1csinstance::R1CSInstance;
16use super::random::RandomTape;
17use super::scalar::Scalar;
18use super::sparse_mlpoly::{SparsePolyEntry, SparsePolynomial};
19use super::timer::Timer;
20use super::transcript::{AppendToTranscript, ProofTranscript};
21use ark_ec::ProjectiveCurve;
22use ark_ff::PrimeField;
23use ark_serialize::*;
24use ark_std::{One, Zero};
25use core::iter;
26use merlin::Transcript;
27
28#[derive(CanonicalSerialize, CanonicalDeserialize, Debug)]
29pub struct R1CSProof {
30 sc_proof_phase1: SumcheckInstanceProof,
31 claims_phase2: (Scalar, Scalar, Scalar, Scalar),
32 // pok_claims_phase2: (KnowledgeProof, ProductProof),
33 // proof_eq_sc_phase1: EqualityProof,
34 sc_proof_phase2: SumcheckInstanceProof,
35 eval_vars_at_ry: Scalar,
36 // proof_eval_vars_at_ry: PolyEvalProof,
37 // proof_eq_sc_phase2: EqualityProof,
38}
39
40pub struct R1CSSumcheckGens {
41 gens_1: MultiCommitGens,
42 gens_3: MultiCommitGens,
43 gens_4: MultiCommitGens,
44}
45
46// TODO: fix passing gens_1_ref
47impl R1CSSumcheckGens {
48 pub fn new(label: &'static [u8], gens_1_ref: &MultiCommitGens) -> Self {
49 let gens_1 = gens_1_ref.clone();
50 let gens_3 = MultiCommitGens::new(3, label);
51 let gens_4 = MultiCommitGens::new(4, label);
52
53 R1CSSumcheckGens {
54 gens_1,
55 gens_3,
56 gens_4,
57 }
58 }
59}
60
61pub struct R1CSGens {
62 gens_sc: R1CSSumcheckGens,
63 gens_pc: PolyCommitmentGens,
64}
65
66impl R1CSGens {
67 pub fn new(label: &'static [u8], _num_cons: usize, num_vars: usize) -> Self {
68 let num_poly_vars = num_vars.log_2();
69 let gens_pc = PolyCommitmentGens::new(num_poly_vars, label);
70 let gens_sc = R1CSSumcheckGens::new(label, &gens_pc.gens.gens_1);
71 R1CSGens { gens_sc, gens_pc }
72 }
73}
74
75impl R1CSProof {
76 fn prove_phase_one(
77 num_rounds: usize,
78 evals_tau: &mut DensePolynomial,
79 evals_Az: &mut DensePolynomial,
80 evals_Bz: &mut DensePolynomial,
81 evals_Cz: &mut DensePolynomial,
82 transcript: &mut PoseidonTranscript,
83 ) -> (SumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>) {
84 let comb_func =
85 |poly_tau_comp: &Scalar,
86 poly_A_comp: &Scalar,
87 poly_B_comp: &Scalar,
88 poly_C_comp: &Scalar|
89 -> Scalar { (*poly_tau_comp) * ((*poly_A_comp) * poly_B_comp - poly_C_comp) };
90
91 let (sc_proof_phase_one, r, claims) = SumcheckInstanceProof::prove_cubic_with_additive_term(
92 &Scalar::zero(), // claim is zero
93 num_rounds,
94 evals_tau,
95 evals_Az,
96 evals_Bz,
97 evals_Cz,
98 comb_func,
99 transcript,
100 );
101
102 (sc_proof_phase_one, r, claims)
103 }
104
105 fn prove_phase_two(
106 num_rounds: usize,
107 claim: &Scalar,
108 evals_z: &mut DensePolynomial,
109 evals_ABC: &mut DensePolynomial,
110 transcript: &mut PoseidonTranscript,
111 ) -> (SumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>) {
112 let comb_func =
113 |poly_A_comp: &Scalar, poly_B_comp: &Scalar| -> Scalar { (*poly_A_comp) * poly_B_comp };
114 let (sc_proof_phase_two, r, claims) = SumcheckInstanceProof::prove_quad(
115 claim, num_rounds, evals_z, evals_ABC, comb_func, transcript,
116 );
117
118 (sc_proof_phase_two, r, claims)
119 }
120
121 fn protocol_name() -> &'static [u8] {
122 b"R1CS proof"
123 }
124
125 pub fn prove(
126 inst: &R1CSInstance,
127 vars: Vec<Scalar>,
128 input: &[Scalar],
129 gens: &R1CSGens,
130 transcript: &mut PoseidonTranscript,
131 random_tape: &mut RandomTape,
132 ) -> (R1CSProof, Vec<Scalar>, Vec<Scalar>) {
133 let timer_prove = Timer::new("R1CSProof::prove");
134 // we currently require the number of |inputs| + 1 to be at most number of vars
135 assert!(input.len() < vars.len());
136
137 transcript.append_scalar_vector(&input.to_vec());
138
139 let poly_vars = DensePolynomial::new(vars.clone());
140
141 let timer_sc_proof_phase1 = Timer::new("prove_sc_phase_one");
142
143 // append input to variables to create a single vector z
144 let z = {
145 let num_inputs = input.len();
146 let num_vars = vars.len();
147 let mut z = vars;
148 z.extend(&vec![Scalar::one()]); // add constant term in z
149 z.extend(input);
150 z.extend(&vec![Scalar::zero(); num_vars - num_inputs - 1]); // we will pad with zeros
151 z
152 };
153
154 // derive the verifier's challenge tau
155 let (num_rounds_x, num_rounds_y) =
156 (inst.get_num_cons().log2() as usize, z.len().log2() as usize);
157 let tau = transcript.challenge_vector(num_rounds_x);
158 // compute the initial evaluation table for R(\tau, x)
159 let mut poly_tau = DensePolynomial::new(EqPolynomial::new(tau).evals());
160 let (mut poly_Az, mut poly_Bz, mut poly_Cz) =
161 inst.multiply_vec(inst.get_num_cons(), z.len(), &z);
162
163 let (sc_proof_phase1, rx, _claims_phase1) = R1CSProof::prove_phase_one(
164 num_rounds_x,
165 &mut poly_tau,
166 &mut poly_Az,
167 &mut poly_Bz,
168 &mut poly_Cz,
169 transcript,
170 );
171 assert_eq!(poly_tau.len(), 1);
172 assert_eq!(poly_Az.len(), 1);
173 assert_eq!(poly_Bz.len(), 1);
174 assert_eq!(poly_Cz.len(), 1);
175 timer_sc_proof_phase1.stop();
176
177 let (tau_claim, Az_claim, Bz_claim, Cz_claim) =
178 (&poly_tau[0], &poly_Az[0], &poly_Bz[0], &poly_Cz[0]);
179 let prod_Az_Bz_claims = (*Az_claim) * Bz_claim;
180
181 // prove the final step of sum-check #1
182 let taus_bound_rx = tau_claim;
183 let claim_post_phase1 = ((*Az_claim) * Bz_claim - Cz_claim) * taus_bound_rx;
184
185 let timer_sc_proof_phase2 = Timer::new("prove_sc_phase_two");
186 // combine the three claims into a single claim
187 let r_A = transcript.challenge_scalar();
188 let r_B = transcript.challenge_scalar();
189 let r_C = transcript.challenge_scalar();
190 let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;
191
192 let evals_ABC = {
193 // compute the initial evaluation table for R(\tau, x)
194 let evals_rx = EqPolynomial::new(rx.clone()).evals();
195 let (evals_A, evals_B, evals_C) =
196 inst.compute_eval_table_sparse(inst.get_num_cons(), z.len(), &evals_rx);
197
198 assert_eq!(evals_A.len(), evals_B.len());
199 assert_eq!(evals_A.len(), evals_C.len());
200 (0..evals_A.len())
201 .map(|i| r_A * evals_A[i] + r_B * evals_B[i] + r_C * evals_C[i])
202 .collect::<Vec<Scalar>>()
203 };
204
205 // another instance of the sum-check protocol
206 let (sc_proof_phase2, ry, claims_phase2) = R1CSProof::prove_phase_two(
207 num_rounds_y,
208 &claim_phase2,
209 &mut DensePolynomial::new(z),
210 &mut DensePolynomial::new(evals_ABC),
211 transcript,
212 );
213 timer_sc_proof_phase2.stop();
214
215 let timer_polyeval = Timer::new("polyeval");
216 let eval_vars_at_ry = poly_vars.evaluate(&ry[1..].to_vec());
217 timer_polyeval.stop();
218
219 timer_prove.stop();
220
221 (
222 R1CSProof {
223 sc_proof_phase1,
224 claims_phase2: (*Az_claim, *Bz_claim, *Cz_claim, prod_Az_Bz_claims),
225 sc_proof_phase2,
226 eval_vars_at_ry,
227 },
228 rx,
229 ry,
230 )
231 }
232
233 pub fn verify(
234 &self,
235 num_vars: usize,
236 num_cons: usize,
237 input: &[Scalar],
238 evals: &(Scalar, Scalar, Scalar),
239 transcript: &mut PoseidonTranscript,
240 gens: &R1CSGens,
241 ) -> Result<(Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
242 // transcript.append_protocol_name(R1CSProof::protocol_name());
243
244 for i in 0..input.len() {
245 transcript.append_scalar(&input[i]);
246 }
247
248 let n = num_vars;
249
250 let (num_rounds_x, num_rounds_y) = (num_cons.log_2(), (2 * num_vars).log_2());
251
252 // derive the verifier's challenge tau
253 let tau = transcript.challenge_vector(num_rounds_x);
254
255 // verify the first sum-check instance
256 let claim_phase1 = Scalar::zero();
257 let (claim_post_phase1, rx) =
258 self
259 .sc_proof_phase1
260 .verify(claim_phase1, num_rounds_x, 3, transcript)?;
261
262 // perform the intermediate sum-check test with claimed Az, Bz, and Cz
263 let (Az_claim, Bz_claim, Cz_claim, prod_Az_Bz_claims) = &self.claims_phase2;
264
265 let taus_bound_rx: Scalar = (0..rx.len())
266 .map(|i| rx[i] * tau[i] + (Scalar::one() - rx[i]) * (Scalar::one() - tau[i]))
267 .product();
268
269 let expected_claim_post_phase1 = (*prod_Az_Bz_claims - *Cz_claim) * (taus_bound_rx);
270
271 assert_eq!(claim_post_phase1, expected_claim_post_phase1);
272
273 // derive three public challenges and then derive a joint claim
274 let r_A = transcript.challenge_scalar();
275 let r_B = transcript.challenge_scalar();
276 let r_C = transcript.challenge_scalar();
277
278 let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;
279
280 // verify the joint claim with a sum-check protocol
281 let (claim_post_phase2, ry) =
282 self
283 .sc_proof_phase2
284 .verify(claim_phase2, num_rounds_y, 2, transcript)?;
285
286 let poly_input_eval = {
287 // constant term
288 let mut input_as_sparse_poly_entries = vec![SparsePolyEntry::new(0, Scalar::one())];
289 //remaining inputs
290 input_as_sparse_poly_entries.extend(
291 (0..input.len())
292 .map(|i| SparsePolyEntry::new(i + 1, input[i]))
293 .collect::<Vec<SparsePolyEntry>>(),
294 );
295 SparsePolynomial::new(n.log_2(), input_as_sparse_poly_entries).evaluate(&ry[1..])
296 };
297
298 let eval_Z_at_ry = (Scalar::one() - ry[0]) * self.eval_vars_at_ry + ry[0] * poly_input_eval;
299
300 // perform the final check in the second sum-check protocol
301 let (eval_A_r, eval_B_r, eval_C_r) = evals;
302 let scalar = r_A * eval_A_r + r_B * eval_B_r + r_C * eval_C_r;
303 let expected_claim_post_phase2 = eval_Z_at_ry * scalar;
304
305 assert_eq!(expected_claim_post_phase2, claim_post_phase2);
306
307 Ok((rx, ry))
308 }
309}
310
311#[cfg(test)]
312mod tests {
313 use crate::parameters::poseidon_params;
314
315 use super::*;
316 use ark_std::UniformRand;
317 use test::Bencher;
318
319 fn produce_tiny_r1cs() -> (R1CSInstance, Vec<Scalar>, Vec<Scalar>) {
320 // three constraints over five variables Z1, Z2, Z3, Z4, and Z5
321 // rounded to the nearest power of two
322 let num_cons = 128;
323 let num_vars = 256;
324 let num_inputs = 2;
325
326 // encode the above constraints into three matrices
327 let mut A: Vec<(usize, usize, Scalar)> = Vec::new();
328 let mut B: Vec<(usize, usize, Scalar)> = Vec::new();
329 let mut C: Vec<(usize, usize, Scalar)> = Vec::new();
330
331 let one = Scalar::one();
332 // constraint 0 entries
333 // (Z1 + Z2) * I0 - Z3 = 0;
334 A.push((0, 0, one));
335 A.push((0, 1, one));
336 B.push((0, num_vars + 1, one));
337 C.push((0, 2, one));
338
339 // constraint 1 entries
340 // (Z1 + I1) * (Z3) - Z4 = 0
341 A.push((1, 0, one));
342 A.push((1, num_vars + 2, one));
343 B.push((1, 2, one));
344 C.push((1, 3, one));
345 // constraint 3 entries
346 // Z5 * 1 - 0 = 0
347 A.push((2, 4, one));
348 B.push((2, num_vars, one));
349
350 let inst = R1CSInstance::new(num_cons, num_vars, num_inputs, &A, &B, &C);
351
352 // compute a satisfying assignment
353 let mut rng = ark_std::rand::thread_rng();
354 let i0 = Scalar::rand(&mut rng);
355 let i1 = Scalar::rand(&mut rng);
356 let z1 = Scalar::rand(&mut rng);
357 let z2 = Scalar::rand(&mut rng);
358 let z3 = (z1 + z2) * i0; // constraint 1: (Z1 + Z2) * I0 - Z3 = 0;
359 let z4 = (z1 + i1) * z3; // constraint 2: (Z1 + I1) * (Z3) - Z4 = 0
360 let z5 = Scalar::zero(); //constraint 3
361
362 let mut vars = vec![Scalar::zero(); num_vars];
363 vars[0] = z1;
364 vars[1] = z2;
365 vars[2] = z3;
366 vars[3] = z4;
367 vars[4] = z5;
368
369 let mut input = vec![Scalar::zero(); num_inputs];
370 input[0] = i0;
371 input[1] = i1;
372
373 (inst, vars, input)
374 }
375
376 #[test]
377 fn test_tiny_r1cs() {
378 let (inst, vars, input) = tests::produce_tiny_r1cs();
379 let is_sat = inst.is_sat(&vars, &input);
380 assert!(is_sat);
381 }
382
383 #[test]
384 fn test_synthetic_r1cs() {
385 let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(1024, 1024, 10);
386 let is_sat = inst.is_sat(&vars, &input);
387 assert!(is_sat);
388 }
389
390 #[test]
391 pub fn check_r1cs_proof() {
392 let num_vars = 1024;
393 let num_cons = num_vars;
394 let num_inputs = 10;
395 let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
396
397 let gens = R1CSGens::new(b"test-m", num_cons, num_vars);
398
399 let params = poseidon_params();
400 let mut random_tape = RandomTape::new(b"proof");
401 // let mut prover_transcript = PoseidonTranscript::new(¶ms);
402 let mut prover_transcript = PoseidonTranscript::new(¶ms);
403 let (proof, rx, ry) = R1CSProof::prove(
404 &inst,
405 vars,
406 &input,
407 &gens,
408 &mut prover_transcript,
409 &mut random_tape,
410 );
411
412 let inst_evals = inst.evaluate(&rx, &ry);
413
414 // let mut verifier_transcript = PoseidonTranscript::new(¶ms);
415 let mut verifier_transcript = PoseidonTranscript::new(¶ms);
416 assert!(proof
417 .verify(
418 inst.get_num_vars(),
419 inst.get_num_cons(),
420 &input,
421 &inst_evals,
422 &mut verifier_transcript,
423 &gens,
424 )
425 .is_ok());
426 }
427
428 #[bench]
429 fn bench_r1cs_proof(b: &mut Bencher) {
430 b.iter(|| check_r1cs_proof());
431 }
432}