sonobe/folding-schemes/src/folding/hypernova/nimfs.rs
folding-schemes/src/folding/hypernova/nimfs.rsRaw
1use ark_crypto_primitives::sponge::Absorb;
2use ark_ec::{CurveGroup, Group};
3use ark_ff::{Field, PrimeField};
4use ark_poly::univariate::DensePolynomial;
5use ark_poly::{DenseUVPolynomial, Polynomial};
6use ark_std::{One, Zero};
7
8use super::cccs::{Witness, CCCS};
9use super::lcccs::LCCCS;
10use super::utils::{compute_c, compute_g, compute_sigmas_and_thetas};
11use crate::ccs::CCS;
12use crate::transcript::Transcript;
13use crate::utils::hypercube::BooleanHypercube;
14use crate::utils::sum_check::structs::IOPProof as SumCheckProof;
15use crate::utils::sum_check::{IOPSumCheck, SumCheck};
16use crate::utils::virtual_polynomial::VPAuxInfo;
17use crate::Error;
18
19use std::fmt::Debug;
20use std::marker::PhantomData;
21
22/// Proof defines a multifolding proof
23#[derive(Clone, Debug)]
24pub struct Proof<C: CurveGroup> {
25 pub sc_proof: SumCheckProof<C::ScalarField>,
26 pub sigmas_thetas: SigmasThetas<C::ScalarField>,
27}
28
29#[derive(Clone, Debug)]
30pub struct SigmasThetas<F: PrimeField>(pub Vec<Vec<F>>, pub Vec<Vec<F>>);
31
32#[derive(Debug)]
33/// Implements the Non-Interactive Multi Folding Scheme described in section 5 of
34/// [HyperNova](https://eprint.iacr.org/2023/573.pdf)
35pub struct NIMFS<C: CurveGroup, T: Transcript<C>> {
36 pub _c: PhantomData<C>,
37 pub _t: PhantomData<T>,
38}
39
40impl<C: CurveGroup, T: Transcript<C>> NIMFS<C, T>
41where
42 <C as Group>::ScalarField: Absorb,
43{
44 pub fn fold(
45 lcccs: &[LCCCS<C>],
46 cccs: &[CCCS<C>],
47 sigmas_thetas: &SigmasThetas<C::ScalarField>,
48 r_x_prime: Vec<C::ScalarField>,
49 rho: C::ScalarField,
50 ) -> LCCCS<C> {
51 let (sigmas, thetas) = (sigmas_thetas.0.clone(), sigmas_thetas.1.clone());
52 let mut C_folded = C::zero();
53 let mut u_folded = C::ScalarField::zero();
54 let mut x_folded: Vec<C::ScalarField> = vec![C::ScalarField::zero(); lcccs[0].x.len()];
55 let mut v_folded: Vec<C::ScalarField> = vec![C::ScalarField::zero(); sigmas[0].len()];
56
57 let mut rho_i = C::ScalarField::one();
58 for i in 0..(lcccs.len() + cccs.len()) {
59 let c: C;
60 let u: C::ScalarField;
61 let x: Vec<C::ScalarField>;
62 let v: Vec<C::ScalarField>;
63 if i < lcccs.len() {
64 c = lcccs[i].C;
65 u = lcccs[i].u;
66 x = lcccs[i].x.clone();
67 v = sigmas[i].clone();
68 } else {
69 c = cccs[i - lcccs.len()].C;
70 u = C::ScalarField::one();
71 x = cccs[i - lcccs.len()].x.clone();
72 v = thetas[i - lcccs.len()].clone();
73 }
74
75 C_folded += c.mul(rho_i);
76 u_folded += rho_i * u;
77 x_folded = x_folded
78 .iter()
79 .zip(
80 x.iter()
81 .map(|x_i| *x_i * rho_i)
82 .collect::<Vec<C::ScalarField>>(),
83 )
84 .map(|(a_i, b_i)| *a_i + b_i)
85 .collect();
86
87 v_folded = v_folded
88 .iter()
89 .zip(
90 v.iter()
91 .map(|x_i| *x_i * rho_i)
92 .collect::<Vec<C::ScalarField>>(),
93 )
94 .map(|(a_i, b_i)| *a_i + b_i)
95 .collect();
96
97 rho_i *= rho;
98 }
99
100 LCCCS::<C> {
101 C: C_folded,
102 u: u_folded,
103 x: x_folded,
104 r_x: r_x_prime,
105 v: v_folded,
106 }
107 }
108
109 pub fn fold_witness(
110 w_lcccs: &[Witness<C::ScalarField>],
111 w_cccs: &[Witness<C::ScalarField>],
112 rho: C::ScalarField,
113 ) -> Witness<C::ScalarField> {
114 let mut w_folded: Vec<C::ScalarField> = vec![C::ScalarField::zero(); w_lcccs[0].w.len()];
115 let mut r_w_folded = C::ScalarField::zero();
116
117 for i in 0..(w_lcccs.len() + w_cccs.len()) {
118 let rho_i = rho.pow([i as u64]);
119 let w: Vec<C::ScalarField>;
120 let r_w: C::ScalarField;
121
122 if i < w_lcccs.len() {
123 w = w_lcccs[i].w.clone();
124 r_w = w_lcccs[i].r_w;
125 } else {
126 w = w_cccs[i - w_lcccs.len()].w.clone();
127 r_w = w_cccs[i - w_lcccs.len()].r_w;
128 }
129
130 w_folded = w_folded
131 .iter()
132 .zip(
133 w.iter()
134 .map(|x_i| *x_i * rho_i)
135 .collect::<Vec<C::ScalarField>>(),
136 )
137 .map(|(a_i, b_i)| *a_i + b_i)
138 .collect();
139
140 r_w_folded += rho_i * r_w;
141 }
142 Witness {
143 w: w_folded,
144 r_w: r_w_folded,
145 }
146 }
147
148 /// Performs the multifolding prover. Given μ LCCCS instances and ν CCS instances, fold them
149 /// into a single LCCCS instance. Since this is the prover, also fold their witness.
150 /// Returns the final folded LCCCS, the folded witness, and the multifolding proof, which
151 /// contains the sumcheck proof and the helper sumcheck claim sigmas and thetas.
152 #[allow(clippy::type_complexity)]
153 pub fn prove(
154 transcript: &mut impl Transcript<C>,
155 ccs: &CCS<C::ScalarField>,
156 running_instances: &[LCCCS<C>],
157 new_instances: &[CCCS<C>],
158 w_lcccs: &[Witness<C::ScalarField>],
159 w_cccs: &[Witness<C::ScalarField>],
160 ) -> Result<(Proof<C>, LCCCS<C>, Witness<C::ScalarField>), Error> {
161 // TODO appends to transcript
162
163 if running_instances.is_empty() {
164 return Err(Error::Empty);
165 }
166 if new_instances.is_empty() {
167 return Err(Error::Empty);
168 }
169
170 // construct the LCCCS z vector from the relaxation factor, public IO and witness
171 // XXX this deserves its own function in LCCCS
172 let mut z_lcccs = Vec::new();
173 for (i, running_instance) in running_instances.iter().enumerate() {
174 let z_1: Vec<C::ScalarField> = [
175 vec![running_instance.u],
176 running_instance.x.clone(),
177 w_lcccs[i].w.to_vec(),
178 ]
179 .concat();
180 z_lcccs.push(z_1);
181 }
182 // construct the CCCS z vector from the public IO and witness
183 let mut z_cccs = Vec::new();
184 for (i, new_instance) in new_instances.iter().enumerate() {
185 let z_2: Vec<C::ScalarField> = [
186 vec![C::ScalarField::one()],
187 new_instance.x.clone(),
188 w_cccs[i].w.to_vec(),
189 ]
190 .concat();
191 z_cccs.push(z_2);
192 }
193
194 // Step 1: Get some challenges
195 let gamma_scalar = C::ScalarField::from_le_bytes_mod_order(b"gamma");
196 let beta_scalar = C::ScalarField::from_le_bytes_mod_order(b"beta");
197 transcript.absorb(&gamma_scalar);
198 let gamma: C::ScalarField = transcript.get_challenge();
199 transcript.absorb(&beta_scalar);
200 let beta: Vec<C::ScalarField> = transcript.get_challenges(ccs.s);
201
202 // Compute g(x)
203 let g = compute_g(ccs, running_instances, &z_lcccs, &z_cccs, gamma, &beta);
204
205 // Step 3: Run the sumcheck prover
206 let sumcheck_proof = IOPSumCheck::<C, T>::prove(&g, transcript)
207 .map_err(|err| Error::SumCheckProveError(err.to_string()))?;
208
209 // Note: The following two "sanity checks" are done for this prototype, in a final version
210 // they should be removed.
211 //
212 // Sanity check 1: evaluate g(x) over x \in {0,1} (the boolean hypercube), and check that
213 // its sum is equal to the extracted_sum from the SumCheck.
214 //////////////////////////////////////////////////////////////////////
215 let mut g_over_bhc = C::ScalarField::zero();
216 for x in BooleanHypercube::new(ccs.s) {
217 g_over_bhc += g.evaluate(&x)?;
218 }
219
220 // note: this is the sum of g(x) over the whole boolean hypercube
221 let extracted_sum = IOPSumCheck::<C, T>::extract_sum(&sumcheck_proof);
222
223 if extracted_sum != g_over_bhc {
224 return Err(Error::NotEqual);
225 }
226 // Sanity check 2: expect \sum v_j * gamma^j to be equal to the sum of g(x) over the
227 // boolean hypercube (and also equal to the extracted_sum from the SumCheck).
228 let mut sum_v_j_gamma = C::ScalarField::zero();
229 for (i, running_instance) in running_instances.iter().enumerate() {
230 for j in 0..running_instance.v.len() {
231 let gamma_j = gamma.pow([(i * ccs.t + j) as u64]);
232 sum_v_j_gamma += running_instance.v[j] * gamma_j;
233 }
234 }
235 if g_over_bhc != sum_v_j_gamma {
236 return Err(Error::NotEqual);
237 }
238 if extracted_sum != sum_v_j_gamma {
239 return Err(Error::NotEqual);
240 }
241 //////////////////////////////////////////////////////////////////////
242
243 // Step 2: dig into the sumcheck and extract r_x_prime
244 let r_x_prime = sumcheck_proof.point.clone();
245
246 // Step 4: compute sigmas and thetas
247 let sigmas_thetas = compute_sigmas_and_thetas(ccs, &z_lcccs, &z_cccs, &r_x_prime);
248
249 // Step 6: Get the folding challenge
250 let rho_scalar = C::ScalarField::from_le_bytes_mod_order(b"rho");
251 transcript.absorb(&rho_scalar);
252 let rho: C::ScalarField = transcript.get_challenge();
253
254 // Step 7: Create the folded instance
255 let folded_lcccs = Self::fold(
256 running_instances,
257 new_instances,
258 &sigmas_thetas,
259 r_x_prime,
260 rho,
261 );
262
263 // Step 8: Fold the witnesses
264 let folded_witness = Self::fold_witness(w_lcccs, w_cccs, rho);
265
266 Ok((
267 Proof::<C> {
268 sc_proof: sumcheck_proof,
269 sigmas_thetas,
270 },
271 folded_lcccs,
272 folded_witness,
273 ))
274 }
275
276 /// Performs the multifolding verifier. Given μ LCCCS instances and ν CCS instances, fold them
277 /// into a single LCCCS instance.
278 /// Returns the folded LCCCS instance.
279 pub fn verify(
280 transcript: &mut impl Transcript<C>,
281 ccs: &CCS<C::ScalarField>,
282 running_instances: &[LCCCS<C>],
283 new_instances: &[CCCS<C>],
284 proof: Proof<C>,
285 ) -> Result<LCCCS<C>, Error> {
286 // TODO appends to transcript
287
288 if running_instances.is_empty() {
289 return Err(Error::Empty);
290 }
291 if new_instances.is_empty() {
292 return Err(Error::Empty);
293 }
294
295 // Step 1: Get some challenges
296 let gamma_scalar = C::ScalarField::from_le_bytes_mod_order(b"gamma");
297 transcript.absorb(&gamma_scalar);
298 let gamma: C::ScalarField = transcript.get_challenge();
299
300 let beta_scalar = C::ScalarField::from_le_bytes_mod_order(b"beta");
301 transcript.absorb(&beta_scalar);
302 let beta: Vec<C::ScalarField> = transcript.get_challenges(ccs.s);
303
304 let vp_aux_info = VPAuxInfo::<C::ScalarField> {
305 max_degree: ccs.d + 1,
306 num_variables: ccs.s,
307 phantom: PhantomData::<C::ScalarField>,
308 };
309
310 // Step 3: Start verifying the sumcheck
311 // First, compute the expected sumcheck sum: \sum gamma^j v_j
312 let mut sum_v_j_gamma = C::ScalarField::zero();
313 for (i, running_instance) in running_instances.iter().enumerate() {
314 for j in 0..running_instance.v.len() {
315 let gamma_j = gamma.pow([(i * ccs.t + j) as u64]);
316 sum_v_j_gamma += running_instance.v[j] * gamma_j;
317 }
318 }
319
320 // Verify the interactive part of the sumcheck
321 let sumcheck_subclaim =
322 IOPSumCheck::<C, T>::verify(sum_v_j_gamma, &proof.sc_proof, &vp_aux_info, transcript)
323 .map_err(|err| Error::SumCheckVerifyError(err.to_string()))?;
324
325 // Step 2: Dig into the sumcheck claim and extract the randomness used
326 let r_x_prime = sumcheck_subclaim.point.clone();
327
328 // Step 5: Finish verifying sumcheck (verify the claim c)
329 let c = compute_c(
330 ccs,
331 &proof.sigmas_thetas,
332 gamma,
333 &beta,
334 &running_instances
335 .iter()
336 .map(|lcccs| lcccs.r_x.clone())
337 .collect(),
338 &r_x_prime,
339 );
340
341 // check that the g(r_x') from the sumcheck proof is equal to the computed c from sigmas&thetas
342 if c != sumcheck_subclaim.expected_evaluation {
343 return Err(Error::NotEqual);
344 }
345
346 // Sanity check: we can also compute g(r_x') from the proof last evaluation value, and
347 // should be equal to the previously obtained values.
348 let g_on_rxprime_from_sumcheck_last_eval =
349 DensePolynomial::from_coefficients_slice(&proof.sc_proof.proofs.last().unwrap().coeffs)
350 .evaluate(r_x_prime.last().unwrap());
351 if g_on_rxprime_from_sumcheck_last_eval != c {
352 return Err(Error::NotEqual);
353 }
354 if g_on_rxprime_from_sumcheck_last_eval != sumcheck_subclaim.expected_evaluation {
355 return Err(Error::NotEqual);
356 }
357
358 // Step 6: Get the folding challenge
359 let rho_scalar = C::ScalarField::from_le_bytes_mod_order(b"rho");
360 transcript.absorb(&rho_scalar);
361 let rho: C::ScalarField = transcript.get_challenge();
362
363 // Step 7: Compute the folded instance
364 Ok(Self::fold(
365 running_instances,
366 new_instances,
367 &proof.sigmas_thetas,
368 r_x_prime,
369 rho,
370 ))
371 }
372}
373
374#[cfg(test)]
375pub mod tests {
376 use super::*;
377 use crate::ccs::tests::{get_test_ccs, get_test_z};
378 use crate::transcript::poseidon::poseidon_canonical_config;
379 use crate::transcript::poseidon::PoseidonTranscript;
380 use ark_std::test_rng;
381 use ark_std::UniformRand;
382
383 use crate::commitment::{pedersen::Pedersen, CommitmentScheme};
384 use ark_pallas::{Fr, Projective};
385
386 #[test]
387 fn test_fold() {
388 let ccs = get_test_ccs();
389 let z1 = get_test_z::<Fr>(3);
390 let z2 = get_test_z::<Fr>(4);
391 ccs.check_relation(&z1).unwrap();
392 ccs.check_relation(&z2).unwrap();
393
394 let mut rng = test_rng();
395 let r_x_prime: Vec<Fr> = (0..ccs.s).map(|_| Fr::rand(&mut rng)).collect();
396
397 let sigmas_thetas =
398 compute_sigmas_and_thetas(&ccs, &[z1.clone()], &[z2.clone()], &r_x_prime);
399
400 let (pedersen_params, _) =
401 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
402
403 let (lcccs, w1) = ccs.to_lcccs(&mut rng, &pedersen_params, &z1).unwrap();
404 let (cccs, w2) = ccs.to_cccs(&mut rng, &pedersen_params, &z2).unwrap();
405
406 lcccs.check_relation(&pedersen_params, &ccs, &w1).unwrap();
407 cccs.check_relation(&pedersen_params, &ccs, &w2).unwrap();
408
409 let mut rng = test_rng();
410 let rho = Fr::rand(&mut rng);
411
412 let folded = NIMFS::<Projective, PoseidonTranscript<Projective>>::fold(
413 &[lcccs],
414 &[cccs],
415 &sigmas_thetas,
416 r_x_prime,
417 rho,
418 );
419
420 let w_folded =
421 NIMFS::<Projective, PoseidonTranscript<Projective>>::fold_witness(&[w1], &[w2], rho);
422
423 // check lcccs relation
424 folded
425 .check_relation(&pedersen_params, &ccs, &w_folded)
426 .unwrap();
427 }
428
429 /// Perform multifolding of an LCCCS instance with a CCCS instance (as described in the paper)
430 #[test]
431 pub fn test_basic_multifolding() {
432 let mut rng = test_rng();
433
434 // Create a basic CCS circuit
435 let ccs = get_test_ccs::<Fr>();
436 let (pedersen_params, _) =
437 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
438
439 // Generate a satisfying witness
440 let z_1 = get_test_z(3);
441 // Generate another satisfying witness
442 let z_2 = get_test_z(4);
443
444 // Create the LCCCS instance out of z_1
445 let (running_instance, w1) = ccs.to_lcccs(&mut rng, &pedersen_params, &z_1).unwrap();
446 // Create the CCCS instance out of z_2
447 let (new_instance, w2) = ccs.to_cccs(&mut rng, &pedersen_params, &z_2).unwrap();
448
449 // Prover's transcript
450 let poseidon_config = poseidon_canonical_config::<Fr>();
451 let mut transcript_p: PoseidonTranscript<Projective> =
452 PoseidonTranscript::<Projective>::new(&poseidon_config);
453 transcript_p.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
454
455 // Run the prover side of the multifolding
456 let (proof, folded_lcccs, folded_witness) =
457 NIMFS::<Projective, PoseidonTranscript<Projective>>::prove(
458 &mut transcript_p,
459 &ccs,
460 &[running_instance.clone()],
461 &[new_instance.clone()],
462 &[w1],
463 &[w2],
464 )
465 .unwrap();
466
467 // Verifier's transcript
468 let mut transcript_v: PoseidonTranscript<Projective> =
469 PoseidonTranscript::<Projective>::new(&poseidon_config);
470 transcript_v.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
471
472 // Run the verifier side of the multifolding
473 let folded_lcccs_v = NIMFS::<Projective, PoseidonTranscript<Projective>>::verify(
474 &mut transcript_v,
475 &ccs,
476 &[running_instance.clone()],
477 &[new_instance.clone()],
478 proof,
479 )
480 .unwrap();
481 assert_eq!(folded_lcccs, folded_lcccs_v);
482
483 // Check that the folded LCCCS instance is a valid instance with respect to the folded witness
484 folded_lcccs
485 .check_relation(&pedersen_params, &ccs, &folded_witness)
486 .unwrap();
487 }
488
489 /// Perform multiple steps of multifolding of an LCCCS instance with a CCCS instance
490 #[test]
491 pub fn test_multifolding_two_instances_multiple_steps() {
492 let mut rng = test_rng();
493
494 let ccs = get_test_ccs::<Fr>();
495
496 let (pedersen_params, _) =
497 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
498
499 // LCCCS witness
500 let z_1 = get_test_z(2);
501 let (mut running_instance, mut w1) =
502 ccs.to_lcccs(&mut rng, &pedersen_params, &z_1).unwrap();
503
504 let poseidon_config = poseidon_canonical_config::<Fr>();
505
506 let mut transcript_p: PoseidonTranscript<Projective> =
507 PoseidonTranscript::<Projective>::new(&poseidon_config);
508 transcript_p.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
509
510 let mut transcript_v: PoseidonTranscript<Projective> =
511 PoseidonTranscript::<Projective>::new(&poseidon_config);
512 transcript_v.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
513
514 let n: usize = 10;
515 for i in 3..n {
516 println!("\niteration: i {}", i); // DBG
517
518 // CCS witness
519 let z_2 = get_test_z(i);
520 println!("z_2 {:?}", z_2); // DBG
521
522 let (new_instance, w2) = ccs.to_cccs(&mut rng, &pedersen_params, &z_2).unwrap();
523
524 // run the prover side of the multifolding
525 let (proof, folded_lcccs, folded_witness) =
526 NIMFS::<Projective, PoseidonTranscript<Projective>>::prove(
527 &mut transcript_p,
528 &ccs,
529 &[running_instance.clone()],
530 &[new_instance.clone()],
531 &[w1],
532 &[w2],
533 )
534 .unwrap();
535
536 // run the verifier side of the multifolding
537 let folded_lcccs_v = NIMFS::<Projective, PoseidonTranscript<Projective>>::verify(
538 &mut transcript_v,
539 &ccs,
540 &[running_instance.clone()],
541 &[new_instance.clone()],
542 proof,
543 )
544 .unwrap();
545 assert_eq!(folded_lcccs, folded_lcccs_v);
546
547 // check that the folded instance with the folded witness holds the LCCCS relation
548 println!("check_relation {}", i);
549 folded_lcccs
550 .check_relation(&pedersen_params, &ccs, &folded_witness)
551 .unwrap();
552
553 running_instance = folded_lcccs;
554 w1 = folded_witness;
555 }
556 }
557
558 /// Test that generates mu>1 and nu>1 instances, and folds them in a single multifolding step.
559 #[test]
560 pub fn test_multifolding_mu_nu_instances() {
561 let mut rng = test_rng();
562
563 // Create a basic CCS circuit
564 let ccs = get_test_ccs::<Fr>();
565 let (pedersen_params, _) =
566 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
567
568 let mu = 10;
569 let nu = 15;
570
571 // Generate a mu LCCCS & nu CCCS satisfying witness
572 let mut z_lcccs = Vec::new();
573 for i in 0..mu {
574 let z = get_test_z(i + 3);
575 z_lcccs.push(z);
576 }
577 let mut z_cccs = Vec::new();
578 for i in 0..nu {
579 let z = get_test_z(nu + i + 3);
580 z_cccs.push(z);
581 }
582
583 // Create the LCCCS instances out of z_lcccs
584 let mut lcccs_instances = Vec::new();
585 let mut w_lcccs = Vec::new();
586 for z_i in z_lcccs.iter() {
587 let (running_instance, w) = ccs.to_lcccs(&mut rng, &pedersen_params, z_i).unwrap();
588 lcccs_instances.push(running_instance);
589 w_lcccs.push(w);
590 }
591 // Create the CCCS instance out of z_cccs
592 let mut cccs_instances = Vec::new();
593 let mut w_cccs = Vec::new();
594 for z_i in z_cccs.iter() {
595 let (new_instance, w) = ccs.to_cccs(&mut rng, &pedersen_params, z_i).unwrap();
596 cccs_instances.push(new_instance);
597 w_cccs.push(w);
598 }
599
600 // Prover's transcript
601 let poseidon_config = poseidon_canonical_config::<Fr>();
602 let mut transcript_p: PoseidonTranscript<Projective> =
603 PoseidonTranscript::<Projective>::new(&poseidon_config);
604 transcript_p.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
605
606 // Run the prover side of the multifolding
607 let (proof, folded_lcccs, folded_witness) =
608 NIMFS::<Projective, PoseidonTranscript<Projective>>::prove(
609 &mut transcript_p,
610 &ccs,
611 &lcccs_instances,
612 &cccs_instances,
613 &w_lcccs,
614 &w_cccs,
615 )
616 .unwrap();
617
618 // Verifier's transcript
619 let mut transcript_v: PoseidonTranscript<Projective> =
620 PoseidonTranscript::<Projective>::new(&poseidon_config);
621 transcript_v.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
622
623 // Run the verifier side of the multifolding
624 let folded_lcccs_v = NIMFS::<Projective, PoseidonTranscript<Projective>>::verify(
625 &mut transcript_v,
626 &ccs,
627 &lcccs_instances,
628 &cccs_instances,
629 proof,
630 )
631 .unwrap();
632 assert_eq!(folded_lcccs, folded_lcccs_v);
633
634 // Check that the folded LCCCS instance is a valid instance with respect to the folded witness
635 folded_lcccs
636 .check_relation(&pedersen_params, &ccs, &folded_witness)
637 .unwrap();
638 }
639
640 /// Test that generates mu>1 and nu>1 instances, and folds them in a single multifolding step
641 /// and repeats the process doing multiple steps.
642 #[test]
643 pub fn test_multifolding_mu_nu_instances_multiple_steps() {
644 let mut rng = test_rng();
645
646 // Create a basic CCS circuit
647 let ccs = get_test_ccs::<Fr>();
648 let (pedersen_params, _) =
649 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
650
651 let poseidon_config = poseidon_canonical_config::<Fr>();
652 // Prover's transcript
653 let mut transcript_p: PoseidonTranscript<Projective> =
654 PoseidonTranscript::<Projective>::new(&poseidon_config);
655 transcript_p.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
656
657 // Verifier's transcript
658 let mut transcript_v: PoseidonTranscript<Projective> =
659 PoseidonTranscript::<Projective>::new(&poseidon_config);
660 transcript_v.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
661
662 let n_steps = 3;
663
664 // number of LCCCS & CCCS instances in each multifolding step
665 let mu = 10;
666 let nu = 15;
667
668 // Generate a mu LCCCS & nu CCCS satisfying witness, for each step
669 for step in 0..n_steps {
670 let mut z_lcccs = Vec::new();
671 for i in 0..mu {
672 let z = get_test_z(step + i + 3);
673 z_lcccs.push(z);
674 }
675 let mut z_cccs = Vec::new();
676 for i in 0..nu {
677 let z = get_test_z(nu + i + 3);
678 z_cccs.push(z);
679 }
680
681 // Create the LCCCS instances out of z_lcccs
682 let mut lcccs_instances = Vec::new();
683 let mut w_lcccs = Vec::new();
684 for z_i in z_lcccs.iter() {
685 let (running_instance, w) = ccs.to_lcccs(&mut rng, &pedersen_params, z_i).unwrap();
686 lcccs_instances.push(running_instance);
687 w_lcccs.push(w);
688 }
689 // Create the CCCS instance out of z_cccs
690 let mut cccs_instances = Vec::new();
691 let mut w_cccs = Vec::new();
692 for z_i in z_cccs.iter() {
693 let (new_instance, w) = ccs.to_cccs(&mut rng, &pedersen_params, z_i).unwrap();
694 cccs_instances.push(new_instance);
695 w_cccs.push(w);
696 }
697
698 // Run the prover side of the multifolding
699 let (proof, folded_lcccs, folded_witness) =
700 NIMFS::<Projective, PoseidonTranscript<Projective>>::prove(
701 &mut transcript_p,
702 &ccs,
703 &lcccs_instances,
704 &cccs_instances,
705 &w_lcccs,
706 &w_cccs,
707 )
708 .unwrap();
709
710 // Run the verifier side of the multifolding
711 let folded_lcccs_v = NIMFS::<Projective, PoseidonTranscript<Projective>>::verify(
712 &mut transcript_v,
713 &ccs,
714 &lcccs_instances,
715 &cccs_instances,
716 proof,
717 )
718 .unwrap();
719
720 assert_eq!(folded_lcccs, folded_lcccs_v);
721
722 // Check that the folded LCCCS instance is a valid instance with respect to the folded witness
723 folded_lcccs
724 .check_relation(&pedersen_params, &ccs, &folded_witness)
725 .unwrap();
726 }
727 }
728}