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::{BigInteger, Field, PrimeField};
4use ark_poly::univariate::DensePolynomial;
5use ark_poly::{DenseUVPolynomial, Polynomial};
6use ark_std::{One, Zero};
7
8use super::{
9 cccs::CCCS,
10 lcccs::LCCCS,
11 utils::{compute_c, compute_g, compute_sigmas_thetas},
12 Witness,
13};
14use crate::ccs::CCS;
15use crate::constants::N_BITS_RO;
16use crate::folding::circuits::nonnative::affine::nonnative_affine_to_field_elements;
17use crate::transcript::Transcript;
18use crate::utils::sum_check::structs::{IOPProof as SumCheckProof, IOPProverMessage};
19use crate::utils::sum_check::{IOPSumCheck, SumCheck};
20use crate::utils::virtual_polynomial::VPAuxInfo;
21use crate::Error;
22
23use std::fmt::Debug;
24use std::marker::PhantomData;
25
26/// NIMFSProof defines a multifolding proof
27#[derive(Clone, Debug)]
28pub struct NIMFSProof<C: CurveGroup> {
29 pub sc_proof: SumCheckProof<C::ScalarField>,
30 pub sigmas_thetas: SigmasThetas<C::ScalarField>,
31}
32
33impl<C: CurveGroup> NIMFSProof<C> {
34 pub fn dummy(ccs: &CCS<C::ScalarField>, mu: usize, nu: usize) -> Self {
35 // use 'C::ScalarField::one()' instead of 'zero()' to enforce the NIMFSProof to have the
36 // same in-circuit representation to match the number of constraints of an actual proof.
37 NIMFSProof::<C> {
38 sc_proof: SumCheckProof::<C::ScalarField> {
39 point: vec![C::ScalarField::one(); ccs.s],
40 proofs: vec![
41 IOPProverMessage {
42 coeffs: vec![C::ScalarField::one(); ccs.t + 1]
43 };
44 ccs.s
45 ],
46 },
47 sigmas_thetas: SigmasThetas(
48 vec![vec![C::ScalarField::one(); ccs.t]; mu],
49 vec![vec![C::ScalarField::one(); ccs.t]; nu],
50 ),
51 }
52 }
53}
54
55#[derive(Clone, Debug)]
56pub struct SigmasThetas<F: PrimeField>(pub Vec<Vec<F>>, pub Vec<Vec<F>>);
57
58#[derive(Debug)]
59/// Implements the Non-Interactive Multi Folding Scheme described in section 5 of
60/// [HyperNova](https://eprint.iacr.org/2023/573.pdf)
61pub struct NIMFS<C: CurveGroup, T: Transcript<C>> {
62 pub _c: PhantomData<C>,
63 pub _t: PhantomData<T>,
64}
65
66impl<C: CurveGroup, T: Transcript<C>> NIMFS<C, T>
67where
68 <C as Group>::ScalarField: Absorb,
69 C::BaseField: PrimeField,
70{
71 pub fn fold(
72 lcccs: &[LCCCS<C>],
73 cccs: &[CCCS<C>],
74 sigmas_thetas: &SigmasThetas<C::ScalarField>,
75 r_x_prime: Vec<C::ScalarField>,
76 rho: C::ScalarField,
77 ) -> LCCCS<C> {
78 let (sigmas, thetas) = (sigmas_thetas.0.clone(), sigmas_thetas.1.clone());
79 let mut C_folded = C::zero();
80 let mut u_folded = C::ScalarField::zero();
81 let mut x_folded: Vec<C::ScalarField> = vec![C::ScalarField::zero(); lcccs[0].x.len()];
82 let mut v_folded: Vec<C::ScalarField> = vec![C::ScalarField::zero(); sigmas[0].len()];
83
84 let mut rho_i = C::ScalarField::one();
85 for i in 0..(lcccs.len() + cccs.len()) {
86 let c: C;
87 let u: C::ScalarField;
88 let x: Vec<C::ScalarField>;
89 let v: Vec<C::ScalarField>;
90 if i < lcccs.len() {
91 c = lcccs[i].C;
92 u = lcccs[i].u;
93 x = lcccs[i].x.clone();
94 v = sigmas[i].clone();
95 } else {
96 c = cccs[i - lcccs.len()].C;
97 u = C::ScalarField::one();
98 x = cccs[i - lcccs.len()].x.clone();
99 v = thetas[i - lcccs.len()].clone();
100 }
101
102 C_folded += c.mul(rho_i);
103 u_folded += rho_i * u;
104 x_folded = x_folded
105 .iter()
106 .zip(
107 x.iter()
108 .map(|x_i| *x_i * rho_i)
109 .collect::<Vec<C::ScalarField>>(),
110 )
111 .map(|(a_i, b_i)| *a_i + b_i)
112 .collect();
113
114 v_folded = v_folded
115 .iter()
116 .zip(
117 v.iter()
118 .map(|x_i| *x_i * rho_i)
119 .collect::<Vec<C::ScalarField>>(),
120 )
121 .map(|(a_i, b_i)| *a_i + b_i)
122 .collect();
123
124 rho_i *= rho;
125 }
126
127 LCCCS::<C> {
128 C: C_folded,
129 u: u_folded,
130 x: x_folded,
131 r_x: r_x_prime,
132 v: v_folded,
133 }
134 }
135
136 pub fn fold_witness(
137 w_lcccs: &[Witness<C::ScalarField>],
138 w_cccs: &[Witness<C::ScalarField>],
139 rho: C::ScalarField,
140 ) -> Witness<C::ScalarField> {
141 let mut w_folded: Vec<C::ScalarField> = vec![C::ScalarField::zero(); w_lcccs[0].w.len()];
142 let mut r_w_folded = C::ScalarField::zero();
143
144 for i in 0..(w_lcccs.len() + w_cccs.len()) {
145 let rho_i = rho.pow([i as u64]);
146 let w: Vec<C::ScalarField>;
147 let r_w: C::ScalarField;
148
149 if i < w_lcccs.len() {
150 w = w_lcccs[i].w.clone();
151 r_w = w_lcccs[i].r_w;
152 } else {
153 w = w_cccs[i - w_lcccs.len()].w.clone();
154 r_w = w_cccs[i - w_lcccs.len()].r_w;
155 }
156
157 w_folded = w_folded
158 .iter()
159 .zip(
160 w.iter()
161 .map(|x_i| *x_i * rho_i)
162 .collect::<Vec<C::ScalarField>>(),
163 )
164 .map(|(a_i, b_i)| *a_i + b_i)
165 .collect();
166
167 r_w_folded += rho_i * r_w;
168 }
169 Witness {
170 w: w_folded,
171 r_w: r_w_folded,
172 }
173 }
174
175 /// Performs the multifolding prover. Given μ LCCCS instances and ν CCS instances, fold them
176 /// into a single LCCCS instance. Since this is the prover, also fold their witness.
177 /// Returns the final folded LCCCS, the folded witness, and the multifolding proof, which
178 /// contains the sumcheck proof and the helper sumcheck claim sigmas and thetas.
179 #[allow(clippy::type_complexity)]
180 pub fn prove(
181 transcript: &mut impl Transcript<C>,
182 ccs: &CCS<C::ScalarField>,
183 running_instances: &[LCCCS<C>],
184 new_instances: &[CCCS<C>],
185 w_lcccs: &[Witness<C::ScalarField>],
186 w_cccs: &[Witness<C::ScalarField>],
187 ) -> Result<(NIMFSProof<C>, LCCCS<C>, Witness<C::ScalarField>, Vec<bool>), Error> {
188 // absorb instances to transcript
189 for U_i in running_instances {
190 let (C_x, C_y) = nonnative_affine_to_field_elements::<C>(U_i.C)?;
191 let v = [
192 C_x,
193 C_y,
194 vec![U_i.u],
195 U_i.x.clone(),
196 U_i.r_x.clone(),
197 U_i.v.clone(),
198 ]
199 .concat();
200 transcript.absorb_vec(&v);
201 }
202 for u_i in new_instances {
203 let (C_x, C_y) = nonnative_affine_to_field_elements::<C>(u_i.C)?;
204 let v = [C_x, C_y, u_i.x.clone()].concat();
205 transcript.absorb_vec(&v);
206 }
207
208 if running_instances.is_empty() {
209 return Err(Error::Empty);
210 }
211 if new_instances.is_empty() {
212 return Err(Error::Empty);
213 }
214
215 // construct the LCCCS z vector from the relaxation factor, public IO and witness
216 let mut z_lcccs = Vec::new();
217 for (i, running_instance) in running_instances.iter().enumerate() {
218 let z_1: Vec<C::ScalarField> = [
219 vec![running_instance.u],
220 running_instance.x.clone(),
221 w_lcccs[i].w.to_vec(),
222 ]
223 .concat();
224 z_lcccs.push(z_1);
225 }
226 // construct the CCCS z vector from the public IO and witness
227 let mut z_cccs = Vec::new();
228 for (i, new_instance) in new_instances.iter().enumerate() {
229 let z_2: Vec<C::ScalarField> = [
230 vec![C::ScalarField::one()],
231 new_instance.x.clone(),
232 w_cccs[i].w.to_vec(),
233 ]
234 .concat();
235 z_cccs.push(z_2);
236 }
237
238 // Step 1: Get some challenges
239 let gamma_scalar = C::ScalarField::from_le_bytes_mod_order(b"gamma");
240 let beta_scalar = C::ScalarField::from_le_bytes_mod_order(b"beta");
241 transcript.absorb(&gamma_scalar);
242 let gamma: C::ScalarField = transcript.get_challenge();
243 transcript.absorb(&beta_scalar);
244 let beta: Vec<C::ScalarField> = transcript.get_challenges(ccs.s);
245
246 // Compute g(x)
247 let g = compute_g(ccs, running_instances, &z_lcccs, &z_cccs, gamma, &beta)?;
248
249 // Step 3: Run the sumcheck prover
250 let sumcheck_proof = IOPSumCheck::<C, T>::prove(&g, transcript)
251 .map_err(|err| Error::SumCheckProveError(err.to_string()))?;
252
253 // Step 2: dig into the sumcheck and extract r_x_prime
254 let r_x_prime = sumcheck_proof.point.clone();
255
256 // Step 4: compute sigmas and thetas
257 let sigmas_thetas = compute_sigmas_thetas(ccs, &z_lcccs, &z_cccs, &r_x_prime)?;
258
259 // Step 6: Get the folding challenge
260 let rho_scalar = C::ScalarField::from_le_bytes_mod_order(b"rho");
261 transcript.absorb(&rho_scalar);
262 let rho_bits: Vec<bool> = transcript.get_challenge_nbits(N_BITS_RO);
263 let rho: C::ScalarField =
264 C::ScalarField::from_bigint(BigInteger::from_bits_le(&rho_bits)).unwrap();
265
266 // Step 7: Create the folded instance
267 let folded_lcccs = Self::fold(
268 running_instances,
269 new_instances,
270 &sigmas_thetas,
271 r_x_prime,
272 rho,
273 );
274
275 // Step 8: Fold the witnesses
276 let folded_witness = Self::fold_witness(w_lcccs, w_cccs, rho);
277
278 Ok((
279 NIMFSProof::<C> {
280 sc_proof: sumcheck_proof,
281 sigmas_thetas,
282 },
283 folded_lcccs,
284 folded_witness,
285 rho_bits,
286 ))
287 }
288
289 /// Performs the multifolding verifier. Given μ LCCCS instances and ν CCS instances, fold them
290 /// into a single LCCCS instance.
291 /// Returns the folded LCCCS instance.
292 pub fn verify(
293 transcript: &mut impl Transcript<C>,
294 ccs: &CCS<C::ScalarField>,
295 running_instances: &[LCCCS<C>],
296 new_instances: &[CCCS<C>],
297 proof: NIMFSProof<C>,
298 ) -> Result<LCCCS<C>, Error> {
299 // absorb instances to transcript
300 for U_i in running_instances {
301 let (C_x, C_y) = nonnative_affine_to_field_elements::<C>(U_i.C)?;
302 let v = [
303 C_x,
304 C_y,
305 vec![U_i.u],
306 U_i.x.clone(),
307 U_i.r_x.clone(),
308 U_i.v.clone(),
309 ]
310 .concat();
311 transcript.absorb_vec(&v);
312 }
313 for u_i in new_instances {
314 let (C_x, C_y) = nonnative_affine_to_field_elements::<C>(u_i.C)?;
315 let v = [C_x, C_y, u_i.x.clone()].concat();
316 transcript.absorb_vec(&v);
317 }
318
319 if running_instances.is_empty() {
320 return Err(Error::Empty);
321 }
322 if new_instances.is_empty() {
323 return Err(Error::Empty);
324 }
325
326 // Step 1: Get some challenges
327 let gamma_scalar = C::ScalarField::from_le_bytes_mod_order(b"gamma");
328 transcript.absorb(&gamma_scalar);
329 let gamma: C::ScalarField = transcript.get_challenge();
330
331 let beta_scalar = C::ScalarField::from_le_bytes_mod_order(b"beta");
332 transcript.absorb(&beta_scalar);
333 let beta: Vec<C::ScalarField> = transcript.get_challenges(ccs.s);
334
335 let vp_aux_info = VPAuxInfo::<C::ScalarField> {
336 max_degree: ccs.d + 1,
337 num_variables: ccs.s,
338 phantom: PhantomData::<C::ScalarField>,
339 };
340
341 // Step 3: Start verifying the sumcheck
342 // First, compute the expected sumcheck sum: \sum gamma^j v_j
343 let mut sum_v_j_gamma = C::ScalarField::zero();
344 for (i, running_instance) in running_instances.iter().enumerate() {
345 for j in 0..running_instance.v.len() {
346 let gamma_j = gamma.pow([(i * ccs.t + j) as u64]);
347 sum_v_j_gamma += running_instance.v[j] * gamma_j;
348 }
349 }
350
351 // Verify the interactive part of the sumcheck
352 let sumcheck_subclaim =
353 IOPSumCheck::<C, T>::verify(sum_v_j_gamma, &proof.sc_proof, &vp_aux_info, transcript)
354 .map_err(|err| Error::SumCheckVerifyError(err.to_string()))?;
355
356 // Step 2: Dig into the sumcheck claim and extract the randomness used
357 let r_x_prime = sumcheck_subclaim.point.clone();
358
359 // Step 5: Finish verifying sumcheck (verify the claim c)
360 let c = compute_c(
361 ccs,
362 &proof.sigmas_thetas,
363 gamma,
364 &beta,
365 &running_instances
366 .iter()
367 .map(|lcccs| lcccs.r_x.clone())
368 .collect(),
369 &r_x_prime,
370 )?;
371
372 // check that the g(r_x') from the sumcheck proof is equal to the computed c from sigmas&thetas
373 if c != sumcheck_subclaim.expected_evaluation {
374 return Err(Error::NotEqual);
375 }
376
377 // Sanity check: we can also compute g(r_x') from the proof last evaluation value, and
378 // should be equal to the previously obtained values.
379 let g_on_rxprime_from_sumcheck_last_eval = DensePolynomial::from_coefficients_slice(
380 &proof.sc_proof.proofs.last().ok_or(Error::Empty)?.coeffs,
381 )
382 .evaluate(r_x_prime.last().ok_or(Error::Empty)?);
383 if g_on_rxprime_from_sumcheck_last_eval != c {
384 return Err(Error::NotEqual);
385 }
386 if g_on_rxprime_from_sumcheck_last_eval != sumcheck_subclaim.expected_evaluation {
387 return Err(Error::NotEqual);
388 }
389
390 // Step 6: Get the folding challenge
391 let rho_scalar = C::ScalarField::from_le_bytes_mod_order(b"rho");
392 transcript.absorb(&rho_scalar);
393 let rho_bits: Vec<bool> = transcript.get_challenge_nbits(N_BITS_RO);
394 let rho: C::ScalarField =
395 C::ScalarField::from_bigint(BigInteger::from_bits_le(&rho_bits)).unwrap();
396
397 // Step 7: Compute the folded instance
398 Ok(Self::fold(
399 running_instances,
400 new_instances,
401 &proof.sigmas_thetas,
402 r_x_prime,
403 rho,
404 ))
405 }
406}
407
408#[cfg(test)]
409pub mod tests {
410 use super::*;
411 use crate::ccs::tests::{get_test_ccs, get_test_z};
412 use crate::transcript::poseidon::poseidon_canonical_config;
413 use crate::transcript::poseidon::PoseidonTranscript;
414 use ark_std::test_rng;
415 use ark_std::UniformRand;
416
417 use crate::commitment::{pedersen::Pedersen, CommitmentScheme};
418 use ark_pallas::{Fr, Projective};
419
420 #[test]
421 fn test_fold() {
422 let ccs = get_test_ccs();
423 let z1 = get_test_z::<Fr>(3);
424 let z2 = get_test_z::<Fr>(4);
425 ccs.check_relation(&z1).unwrap();
426 ccs.check_relation(&z2).unwrap();
427
428 let mut rng = test_rng();
429 let r_x_prime: Vec<Fr> = (0..ccs.s).map(|_| Fr::rand(&mut rng)).collect();
430
431 let sigmas_thetas =
432 compute_sigmas_thetas(&ccs, &[z1.clone()], &[z2.clone()], &r_x_prime).unwrap();
433
434 let (pedersen_params, _) =
435 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
436
437 let (lcccs, w1) = ccs
438 .to_lcccs::<_, Projective, Pedersen<Projective>>(&mut rng, &pedersen_params, &z1)
439 .unwrap();
440 let (cccs, w2) = ccs
441 .to_cccs::<_, Projective, Pedersen<Projective>>(&mut rng, &pedersen_params, &z2)
442 .unwrap();
443
444 lcccs.check_relation(&ccs, &w1).unwrap();
445 cccs.check_relation(&ccs, &w2).unwrap();
446
447 let mut rng = test_rng();
448 let rho = Fr::rand(&mut rng);
449
450 let folded = NIMFS::<Projective, PoseidonTranscript<Projective>>::fold(
451 &[lcccs],
452 &[cccs],
453 &sigmas_thetas,
454 r_x_prime,
455 rho,
456 );
457
458 let w_folded =
459 NIMFS::<Projective, PoseidonTranscript<Projective>>::fold_witness(&[w1], &[w2], rho);
460
461 // check lcccs relation
462 folded.check_relation(&ccs, &w_folded).unwrap();
463 }
464
465 /// Perform multifolding of an LCCCS instance with a CCCS instance (as described in the paper)
466 #[test]
467 pub fn test_basic_multifolding() {
468 let mut rng = test_rng();
469
470 // Create a basic CCS circuit
471 let ccs = get_test_ccs::<Fr>();
472 let (pedersen_params, _) =
473 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
474
475 // Generate a satisfying witness
476 let z_1 = get_test_z(3);
477 // Generate another satisfying witness
478 let z_2 = get_test_z(4);
479
480 // Create the LCCCS instance out of z_1
481 let (running_instance, w1) = ccs
482 .to_lcccs::<_, _, Pedersen<Projective>>(&mut rng, &pedersen_params, &z_1)
483 .unwrap();
484 // Create the CCCS instance out of z_2
485 let (new_instance, w2) = ccs
486 .to_cccs::<_, _, Pedersen<Projective>>(&mut rng, &pedersen_params, &z_2)
487 .unwrap();
488
489 // Prover's transcript
490 let poseidon_config = poseidon_canonical_config::<Fr>();
491 let mut transcript_p: PoseidonTranscript<Projective> =
492 PoseidonTranscript::<Projective>::new(&poseidon_config);
493 transcript_p.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
494
495 // Run the prover side of the multifolding
496 let (proof, folded_lcccs, folded_witness, _) =
497 NIMFS::<Projective, PoseidonTranscript<Projective>>::prove(
498 &mut transcript_p,
499 &ccs,
500 &[running_instance.clone()],
501 &[new_instance.clone()],
502 &[w1],
503 &[w2],
504 )
505 .unwrap();
506
507 // Verifier's transcript
508 let mut transcript_v: PoseidonTranscript<Projective> =
509 PoseidonTranscript::<Projective>::new(&poseidon_config);
510 transcript_v.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
511
512 // Run the verifier side of the multifolding
513 let folded_lcccs_v = NIMFS::<Projective, PoseidonTranscript<Projective>>::verify(
514 &mut transcript_v,
515 &ccs,
516 &[running_instance.clone()],
517 &[new_instance.clone()],
518 proof,
519 )
520 .unwrap();
521 assert_eq!(folded_lcccs, folded_lcccs_v);
522
523 // Check that the folded LCCCS instance is a valid instance with respect to the folded witness
524 folded_lcccs.check_relation(&ccs, &folded_witness).unwrap();
525 }
526
527 /// Perform multiple steps of multifolding of an LCCCS instance with a CCCS instance
528 #[test]
529 pub fn test_multifolding_two_instances_multiple_steps() {
530 let mut rng = test_rng();
531
532 let ccs = get_test_ccs::<Fr>();
533
534 let (pedersen_params, _) =
535 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
536
537 // LCCCS witness
538 let z_1 = get_test_z(2);
539 let (mut running_instance, mut w1) = ccs
540 .to_lcccs::<_, _, Pedersen<Projective>>(&mut rng, &pedersen_params, &z_1)
541 .unwrap();
542
543 let poseidon_config = poseidon_canonical_config::<Fr>();
544
545 let mut transcript_p: PoseidonTranscript<Projective> =
546 PoseidonTranscript::<Projective>::new(&poseidon_config);
547 transcript_p.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
548
549 let mut transcript_v: PoseidonTranscript<Projective> =
550 PoseidonTranscript::<Projective>::new(&poseidon_config);
551 transcript_v.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
552
553 let n: usize = 10;
554 for i in 3..n {
555 // CCS witness
556 let z_2 = get_test_z(i);
557
558 let (new_instance, w2) = ccs
559 .to_cccs::<_, _, Pedersen<Projective>>(&mut rng, &pedersen_params, &z_2)
560 .unwrap();
561
562 // run the prover side of the multifolding
563 let (proof, folded_lcccs, folded_witness, _) =
564 NIMFS::<Projective, PoseidonTranscript<Projective>>::prove(
565 &mut transcript_p,
566 &ccs,
567 &[running_instance.clone()],
568 &[new_instance.clone()],
569 &[w1],
570 &[w2],
571 )
572 .unwrap();
573
574 // run the verifier side of the multifolding
575 let folded_lcccs_v = NIMFS::<Projective, PoseidonTranscript<Projective>>::verify(
576 &mut transcript_v,
577 &ccs,
578 &[running_instance.clone()],
579 &[new_instance.clone()],
580 proof,
581 )
582 .unwrap();
583 assert_eq!(folded_lcccs, folded_lcccs_v);
584
585 // check that the folded instance with the folded witness holds the LCCCS relation
586 folded_lcccs.check_relation(&ccs, &folded_witness).unwrap();
587
588 running_instance = folded_lcccs;
589 w1 = folded_witness;
590 }
591 }
592
593 /// Test that generates mu>1 and nu>1 instances, and folds them in a single multifolding step.
594 #[test]
595 pub fn test_multifolding_mu_nu_instances() {
596 let mut rng = test_rng();
597
598 // Create a basic CCS circuit
599 let ccs = get_test_ccs::<Fr>();
600 let (pedersen_params, _) =
601 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
602
603 let mu = 10;
604 let nu = 15;
605
606 // Generate a mu LCCCS & nu CCCS satisfying witness
607 let mut z_lcccs = Vec::new();
608 for i in 0..mu {
609 let z = get_test_z(i + 3);
610 z_lcccs.push(z);
611 }
612 let mut z_cccs = Vec::new();
613 for i in 0..nu {
614 let z = get_test_z(nu + i + 3);
615 z_cccs.push(z);
616 }
617
618 // Create the LCCCS instances out of z_lcccs
619 let mut lcccs_instances = Vec::new();
620 let mut w_lcccs = Vec::new();
621 for z_i in z_lcccs.iter() {
622 let (running_instance, w) = ccs
623 .to_lcccs::<_, _, Pedersen<Projective>>(&mut rng, &pedersen_params, z_i)
624 .unwrap();
625 lcccs_instances.push(running_instance);
626 w_lcccs.push(w);
627 }
628 // Create the CCCS instance out of z_cccs
629 let mut cccs_instances = Vec::new();
630 let mut w_cccs = Vec::new();
631 for z_i in z_cccs.iter() {
632 let (new_instance, w) = ccs
633 .to_cccs::<_, _, Pedersen<Projective>>(&mut rng, &pedersen_params, z_i)
634 .unwrap();
635 cccs_instances.push(new_instance);
636 w_cccs.push(w);
637 }
638
639 // Prover's transcript
640 let poseidon_config = poseidon_canonical_config::<Fr>();
641 let mut transcript_p: PoseidonTranscript<Projective> =
642 PoseidonTranscript::<Projective>::new(&poseidon_config);
643 transcript_p.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
644
645 // Run the prover side of the multifolding
646 let (proof, folded_lcccs, folded_witness, _) =
647 NIMFS::<Projective, PoseidonTranscript<Projective>>::prove(
648 &mut transcript_p,
649 &ccs,
650 &lcccs_instances,
651 &cccs_instances,
652 &w_lcccs,
653 &w_cccs,
654 )
655 .unwrap();
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 // Run the verifier side of the multifolding
663 let folded_lcccs_v = NIMFS::<Projective, PoseidonTranscript<Projective>>::verify(
664 &mut transcript_v,
665 &ccs,
666 &lcccs_instances,
667 &cccs_instances,
668 proof,
669 )
670 .unwrap();
671 assert_eq!(folded_lcccs, folded_lcccs_v);
672
673 // Check that the folded LCCCS instance is a valid instance with respect to the folded witness
674 folded_lcccs.check_relation(&ccs, &folded_witness).unwrap();
675 }
676
677 /// Test that generates mu>1 and nu>1 instances, and folds them in a single multifolding step
678 /// and repeats the process doing multiple steps.
679 #[test]
680 pub fn test_multifolding_mu_nu_instances_multiple_steps() {
681 let mut rng = test_rng();
682
683 // Create a basic CCS circuit
684 let ccs = get_test_ccs::<Fr>();
685 let (pedersen_params, _) =
686 Pedersen::<Projective>::setup(&mut rng, ccs.n - ccs.l - 1).unwrap();
687
688 let poseidon_config = poseidon_canonical_config::<Fr>();
689 // Prover's transcript
690 let mut transcript_p: PoseidonTranscript<Projective> =
691 PoseidonTranscript::<Projective>::new(&poseidon_config);
692 transcript_p.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
693
694 // Verifier's transcript
695 let mut transcript_v: PoseidonTranscript<Projective> =
696 PoseidonTranscript::<Projective>::new(&poseidon_config);
697 transcript_v.absorb(&Fr::from_le_bytes_mod_order(b"init init"));
698
699 let n_steps = 3;
700
701 // number of LCCCS & CCCS instances in each multifolding step
702 let mu = 10;
703 let nu = 15;
704
705 // Generate a mu LCCCS & nu CCCS satisfying witness, for each step
706 for step in 0..n_steps {
707 let mut z_lcccs = Vec::new();
708 for i in 0..mu {
709 let z = get_test_z(step + i + 3);
710 z_lcccs.push(z);
711 }
712 let mut z_cccs = Vec::new();
713 for i in 0..nu {
714 let z = get_test_z(nu + i + 3);
715 z_cccs.push(z);
716 }
717
718 // Create the LCCCS instances out of z_lcccs
719 let mut lcccs_instances = Vec::new();
720 let mut w_lcccs = Vec::new();
721 for z_i in z_lcccs.iter() {
722 let (running_instance, w) = ccs
723 .to_lcccs::<_, _, Pedersen<Projective>>(&mut rng, &pedersen_params, z_i)
724 .unwrap();
725 lcccs_instances.push(running_instance);
726 w_lcccs.push(w);
727 }
728 // Create the CCCS instance out of z_cccs
729 let mut cccs_instances = Vec::new();
730 let mut w_cccs = Vec::new();
731 for z_i in z_cccs.iter() {
732 let (new_instance, w) = ccs
733 .to_cccs::<_, _, Pedersen<Projective>>(&mut rng, &pedersen_params, z_i)
734 .unwrap();
735 cccs_instances.push(new_instance);
736 w_cccs.push(w);
737 }
738
739 // Run the prover side of the multifolding
740 let (proof, folded_lcccs, folded_witness, _) =
741 NIMFS::<Projective, PoseidonTranscript<Projective>>::prove(
742 &mut transcript_p,
743 &ccs,
744 &lcccs_instances,
745 &cccs_instances,
746 &w_lcccs,
747 &w_cccs,
748 )
749 .unwrap();
750
751 // Run the verifier side of the multifolding
752 let folded_lcccs_v = NIMFS::<Projective, PoseidonTranscript<Projective>>::verify(
753 &mut transcript_v,
754 &ccs,
755 &lcccs_instances,
756 &cccs_instances,
757 proof,
758 )
759 .unwrap();
760
761 assert_eq!(folded_lcccs, folded_lcccs_v);
762
763 // Check that the folded LCCCS instance is a valid instance with respect to the folded witness
764 folded_lcccs.check_relation(&ccs, &folded_witness).unwrap();
765 }
766 }
767}