sonobe/folding-schemes/src/folding/nova/nifs.rs
folding-schemes/src/folding/nova/nifs.rsRaw
1use ark_crypto_primitives::sponge::Absorb;
2use ark_ec::{CurveGroup, Group};
3use ark_std::Zero;
4use std::marker::PhantomData;
5
6use super::{CommittedInstance, Witness};
7use crate::arith::r1cs::R1CS;
8use crate::commitment::CommitmentScheme;
9use crate::folding::circuits::cyclefold::{CycleFoldCommittedInstance, CycleFoldWitness};
10use crate::transcript::Transcript;
11use crate::utils::vec::{hadamard, mat_vec_mul, vec_add, vec_scalar_mul, vec_sub};
12use crate::Error;
13
14/// Implements the Non-Interactive Folding Scheme described in section 4 of
15/// [Nova](https://eprint.iacr.org/2021/370.pdf)
16/// `H` specifies whether the NIFS will use a blinding factor
17pub struct NIFS<C: CurveGroup, CS: CommitmentScheme<C, H>, const H: bool = false> {
18 _c: PhantomData<C>,
19 _cp: PhantomData<CS>,
20}
21
22impl<C: CurveGroup, CS: CommitmentScheme<C, H>, const H: bool> NIFS<C, CS, H>
23where
24 <C as Group>::ScalarField: Absorb,
25{
26 // compute_T: compute cross-terms T
27 pub fn compute_T(
28 r1cs: &R1CS<C::ScalarField>,
29 u1: C::ScalarField,
30 u2: C::ScalarField,
31 z1: &[C::ScalarField],
32 z2: &[C::ScalarField],
33 ) -> Result<Vec<C::ScalarField>, Error> {
34 let (A, B, C) = (r1cs.A.clone(), r1cs.B.clone(), r1cs.C.clone());
35
36 // this is parallelizable (for the future)
37 let Az1 = mat_vec_mul(&A, z1)?;
38 let Bz1 = mat_vec_mul(&B, z1)?;
39 let Cz1 = mat_vec_mul(&C, z1)?;
40 let Az2 = mat_vec_mul(&A, z2)?;
41 let Bz2 = mat_vec_mul(&B, z2)?;
42 let Cz2 = mat_vec_mul(&C, z2)?;
43
44 let Az1_Bz2 = hadamard(&Az1, &Bz2)?;
45 let Az2_Bz1 = hadamard(&Az2, &Bz1)?;
46 let u1Cz2 = vec_scalar_mul(&Cz2, &u1);
47 let u2Cz1 = vec_scalar_mul(&Cz1, &u2);
48
49 vec_sub(&vec_sub(&vec_add(&Az1_Bz2, &Az2_Bz1)?, &u1Cz2)?, &u2Cz1)
50 }
51
52 pub fn fold_witness(
53 r: C::ScalarField,
54 w1: &Witness<C>,
55 w2: &Witness<C>,
56 T: &[C::ScalarField],
57 rT: C::ScalarField,
58 ) -> Result<Witness<C>, Error> {
59 let r2 = r * r;
60 let E: Vec<C::ScalarField> = vec_add(
61 &vec_add(&w1.E, &vec_scalar_mul(T, &r))?,
62 &vec_scalar_mul(&w2.E, &r2),
63 )?;
64 let rE = w1.rE + r * rT + r2 * w2.rE;
65 let W: Vec<C::ScalarField> = w1.W.iter().zip(&w2.W).map(|(a, b)| *a + (r * b)).collect();
66
67 let rW = w1.rW + r * w2.rW;
68 Ok(Witness::<C> { E, rE, W, rW })
69 }
70
71 pub fn fold_committed_instance(
72 r: C::ScalarField,
73 ci1: &CommittedInstance<C>, // U_i
74 ci2: &CommittedInstance<C>, // u_i
75 cmT: &C,
76 ) -> CommittedInstance<C> {
77 let r2 = r * r;
78 let cmE = ci1.cmE + cmT.mul(r) + ci2.cmE.mul(r2);
79 let u = ci1.u + r * ci2.u;
80 let cmW = ci1.cmW + ci2.cmW.mul(r);
81 let x = ci1
82 .x
83 .iter()
84 .zip(&ci2.x)
85 .map(|(a, b)| *a + (r * b))
86 .collect::<Vec<C::ScalarField>>();
87
88 CommittedInstance::<C> { cmE, u, cmW, x }
89 }
90
91 /// NIFS.P is the consecutive combination of compute_cmT with fold_instances
92
93 /// compute_cmT is part of the NIFS.P logic
94 pub fn compute_cmT(
95 cs_prover_params: &CS::ProverParams,
96 r1cs: &R1CS<C::ScalarField>,
97 w1: &Witness<C>,
98 ci1: &CommittedInstance<C>,
99 w2: &Witness<C>,
100 ci2: &CommittedInstance<C>,
101 ) -> Result<(Vec<C::ScalarField>, C), Error> {
102 let z1: Vec<C::ScalarField> = [vec![ci1.u], ci1.x.to_vec(), w1.W.to_vec()].concat();
103 let z2: Vec<C::ScalarField> = [vec![ci2.u], ci2.x.to_vec(), w2.W.to_vec()].concat();
104
105 // compute cross terms
106 let T = Self::compute_T(r1cs, ci1.u, ci2.u, &z1, &z2)?;
107 // use r_T=0 since we don't need hiding property for cm(T)
108 let cmT = CS::commit(cs_prover_params, &T, &C::ScalarField::zero())?;
109 Ok((T, cmT))
110 }
111 pub fn compute_cyclefold_cmT(
112 cs_prover_params: &CS::ProverParams,
113 r1cs: &R1CS<C::ScalarField>, // R1CS over C2.Fr=C1.Fq (here C=C2)
114 w1: &CycleFoldWitness<C>,
115 ci1: &CycleFoldCommittedInstance<C>,
116 w2: &CycleFoldWitness<C>,
117 ci2: &CycleFoldCommittedInstance<C>,
118 ) -> Result<(Vec<C::ScalarField>, C), Error>
119 where
120 <C as ark_ec::CurveGroup>::BaseField: ark_ff::PrimeField,
121 {
122 let z1: Vec<C::ScalarField> = [vec![ci1.u], ci1.x.to_vec(), w1.W.to_vec()].concat();
123 let z2: Vec<C::ScalarField> = [vec![ci2.u], ci2.x.to_vec(), w2.W.to_vec()].concat();
124
125 // compute cross terms
126 let T = Self::compute_T(r1cs, ci1.u, ci2.u, &z1, &z2)?;
127 // use r_T=0 since we don't need hiding property for cm(T)
128 let cmT = CS::commit(cs_prover_params, &T, &C::ScalarField::zero())?;
129 Ok((T, cmT))
130 }
131
132 /// fold_instances is part of the NIFS.P logic described in
133 /// [Nova](https://eprint.iacr.org/2021/370.pdf)'s section 4. It returns the folded Committed
134 /// Instances and the Witness.
135 pub fn fold_instances(
136 r: C::ScalarField,
137 w1: &Witness<C>,
138 ci1: &CommittedInstance<C>,
139 w2: &Witness<C>,
140 ci2: &CommittedInstance<C>,
141 T: &[C::ScalarField],
142 cmT: C,
143 ) -> Result<(Witness<C>, CommittedInstance<C>), Error> {
144 // fold witness
145 // use r_T=0 since we don't need hiding property for cm(T)
146 let w3 = NIFS::<C, CS, H>::fold_witness(r, w1, w2, T, C::ScalarField::zero())?;
147
148 // fold committed instances
149 let ci3 = NIFS::<C, CS, H>::fold_committed_instance(r, ci1, ci2, &cmT);
150
151 Ok((w3, ci3))
152 }
153
154 /// verify implements NIFS.V logic described in [Nova](https://eprint.iacr.org/2021/370.pdf)'s
155 /// section 4. It returns the folded Committed Instance
156 pub fn verify(
157 // r comes from the transcript, and is a n-bit (N_BITS_CHALLENGE) element
158 r: C::ScalarField,
159 ci1: &CommittedInstance<C>,
160 ci2: &CommittedInstance<C>,
161 cmT: &C,
162 ) -> CommittedInstance<C> {
163 NIFS::<C, CS, H>::fold_committed_instance(r, ci1, ci2, cmT)
164 }
165
166 /// Verify committed folded instance (ci) relations. Notice that this method does not open the
167 /// commitments, but just checks that the given committed instances (ci1, ci2) when folded
168 /// result in the folded committed instance (ci3) values.
169 pub fn verify_folded_instance(
170 r: C::ScalarField,
171 ci1: &CommittedInstance<C>,
172 ci2: &CommittedInstance<C>,
173 ci3: &CommittedInstance<C>,
174 cmT: &C,
175 ) -> Result<(), Error> {
176 let expected = Self::fold_committed_instance(r, ci1, ci2, cmT);
177 if ci3.cmE != expected.cmE
178 || ci3.u != expected.u
179 || ci3.cmW != expected.cmW
180 || ci3.x != expected.x
181 {
182 return Err(Error::NotSatisfied);
183 }
184 Ok(())
185 }
186
187 pub fn prove_commitments(
188 tr: &mut impl Transcript<C::ScalarField>,
189 cs_prover_params: &CS::ProverParams,
190 w: &Witness<C>,
191 ci: &CommittedInstance<C>,
192 T: Vec<C::ScalarField>,
193 cmT: &C,
194 ) -> Result<[CS::Proof; 3], Error> {
195 let cmE_proof = CS::prove(cs_prover_params, tr, &ci.cmE, &w.E, &w.rE, None)?;
196 let cmW_proof = CS::prove(cs_prover_params, tr, &ci.cmW, &w.W, &w.rW, None)?;
197 let cmT_proof = CS::prove(cs_prover_params, tr, cmT, &T, &C::ScalarField::zero(), None)?; // cm(T) is committed with rT=0
198 Ok([cmE_proof, cmW_proof, cmT_proof])
199 }
200}
201
202#[cfg(test)]
203pub mod tests {
204 use super::*;
205 use ark_crypto_primitives::sponge::{
206 poseidon::{PoseidonConfig, PoseidonSponge},
207 CryptographicSponge,
208 };
209 use ark_ff::{BigInteger, PrimeField};
210 use ark_pallas::{Fr, Projective};
211 use ark_std::{ops::Mul, test_rng, UniformRand};
212
213 use crate::commitment::pedersen::{Params as PedersenParams, Pedersen};
214 use crate::folding::nova::circuits::ChallengeGadget;
215 use crate::transcript::poseidon::poseidon_canonical_config;
216 use crate::{
217 arith::{
218 r1cs::tests::{get_test_r1cs, get_test_z},
219 Arith,
220 },
221 folding::traits::Dummy,
222 };
223
224 #[allow(clippy::type_complexity)]
225 pub(crate) fn prepare_simple_fold_inputs<C>() -> (
226 PedersenParams<C>,
227 PoseidonConfig<C::ScalarField>,
228 R1CS<C::ScalarField>,
229 Witness<C>, // w1
230 CommittedInstance<C>, // ci1
231 Witness<C>, // w2
232 CommittedInstance<C>, // ci2
233 Witness<C>, // w3
234 CommittedInstance<C>, // ci3
235 Vec<C::ScalarField>, // T
236 C, // cmT
237 Vec<bool>, // r_bits
238 C::ScalarField, // r_Fr
239 )
240 where
241 C: CurveGroup,
242 <C as CurveGroup>::BaseField: PrimeField,
243 C::ScalarField: Absorb,
244 {
245 let r1cs = get_test_r1cs();
246 let z1 = get_test_z(3);
247 let z2 = get_test_z(4);
248 let (w1, x1) = r1cs.split_z(&z1);
249 let (w2, x2) = r1cs.split_z(&z2);
250
251 let w1 = Witness::<C>::new::<false>(w1.clone(), r1cs.A.n_rows, test_rng());
252 let w2 = Witness::<C>::new::<false>(w2.clone(), r1cs.A.n_rows, test_rng());
253
254 let mut rng = ark_std::test_rng();
255 let (pedersen_params, _) = Pedersen::<C>::setup(&mut rng, r1cs.A.n_cols).unwrap();
256
257 // compute committed instances
258 let ci1 = w1
259 .commit::<Pedersen<C>, false>(&pedersen_params, x1.clone())
260 .unwrap();
261 let ci2 = w2
262 .commit::<Pedersen<C>, false>(&pedersen_params, x2.clone())
263 .unwrap();
264
265 // NIFS.P
266 let (T, cmT) =
267 NIFS::<C, Pedersen<C>>::compute_cmT(&pedersen_params, &r1cs, &w1, &ci1, &w2, &ci2)
268 .unwrap();
269
270 let poseidon_config = poseidon_canonical_config::<C::ScalarField>();
271 let mut transcript = PoseidonSponge::<C::ScalarField>::new(&poseidon_config);
272
273 let pp_hash = C::ScalarField::from(42u32); // only for test
274 let r_bits = ChallengeGadget::<C>::get_challenge_native(
275 &mut transcript,
276 pp_hash,
277 ci1.clone(),
278 ci2.clone(),
279 cmT,
280 );
281 let r_Fr = C::ScalarField::from_bigint(BigInteger::from_bits_le(&r_bits)).unwrap();
282
283 let (w3, ci3) =
284 NIFS::<C, Pedersen<C>>::fold_instances(r_Fr, &w1, &ci1, &w2, &ci2, &T, cmT).unwrap();
285
286 (
287 pedersen_params,
288 poseidon_config,
289 r1cs,
290 w1,
291 ci1,
292 w2,
293 ci2,
294 w3,
295 ci3,
296 T,
297 cmT,
298 r_bits,
299 r_Fr,
300 )
301 }
302
303 // fold 2 dummy instances and check that the folded instance holds the relaxed R1CS relation
304 #[test]
305 fn test_nifs_fold_dummy() {
306 let r1cs = get_test_r1cs::<Fr>();
307 let z1 = get_test_z(3);
308 let (_, x1) = r1cs.split_z(&z1);
309
310 let mut rng = ark_std::test_rng();
311 let (pedersen_params, _) = Pedersen::<Projective>::setup(&mut rng, r1cs.A.n_cols).unwrap();
312
313 // dummy instance, witness and public inputs zeroes
314 let w_dummy = Witness::<Projective>::dummy(&r1cs);
315 let mut u_dummy = w_dummy
316 .commit::<Pedersen<Projective>, false>(&pedersen_params, vec![Fr::zero(); x1.len()])
317 .unwrap();
318 u_dummy.u = Fr::zero();
319
320 let w_i = w_dummy.clone();
321 let u_i = u_dummy.clone();
322 let W_i = w_dummy.clone();
323 let U_i = u_dummy.clone();
324 r1cs.check_relation(&w_i, &u_i).unwrap();
325 r1cs.check_relation(&W_i, &U_i).unwrap();
326
327 let r_Fr = Fr::from(3_u32);
328
329 let (T, cmT) = NIFS::<Projective, Pedersen<Projective>>::compute_cmT(
330 &pedersen_params,
331 &r1cs,
332 &w_i,
333 &u_i,
334 &W_i,
335 &U_i,
336 )
337 .unwrap();
338 let (W_i1, U_i1) = NIFS::<Projective, Pedersen<Projective>>::fold_instances(
339 r_Fr, &w_i, &u_i, &W_i, &U_i, &T, cmT,
340 )
341 .unwrap();
342 r1cs.check_relation(&W_i1, &U_i1).unwrap();
343 }
344
345 // fold 2 instances into one
346 #[test]
347 fn test_nifs_one_fold() {
348 let (pedersen_params, poseidon_config, r1cs, w1, ci1, w2, ci2, w3, ci3, T, cmT, _, r) =
349 prepare_simple_fold_inputs();
350
351 // NIFS.V
352 let ci3_v = NIFS::<Projective, Pedersen<Projective>>::verify(r, &ci1, &ci2, &cmT);
353 assert_eq!(ci3_v, ci3);
354
355 // check that relations hold for the 2 inputted instances and the folded one
356 r1cs.check_relation(&w1, &ci1).unwrap();
357 r1cs.check_relation(&w2, &ci2).unwrap();
358 r1cs.check_relation(&w3, &ci3).unwrap();
359
360 // check that folded commitments from folded instance (ci) are equal to folding the
361 // use folded rE, rW to commit w3
362 let ci3_expected = w3
363 .commit::<Pedersen<Projective>, false>(&pedersen_params, ci3.x.clone())
364 .unwrap();
365 assert_eq!(ci3_expected.cmE, ci3.cmE);
366 assert_eq!(ci3_expected.cmW, ci3.cmW);
367
368 // next equalities should hold since we started from two cmE of zero-vector E's
369 assert_eq!(ci3.cmE, cmT.mul(r));
370 assert_eq!(w3.E, vec_scalar_mul(T.as_slice(), &r));
371
372 // NIFS.Verify_Folded_Instance:
373 NIFS::<Projective, Pedersen<Projective>>::verify_folded_instance(r, &ci1, &ci2, &ci3, &cmT)
374 .unwrap();
375
376 // init Prover's transcript
377 let mut transcript_p = PoseidonSponge::<Fr>::new(&poseidon_config);
378 // init Verifier's transcript
379 let mut transcript_v = PoseidonSponge::<Fr>::new(&poseidon_config);
380
381 // prove the ci3.cmE, ci3.cmW, cmT commitments
382 let cm_proofs = NIFS::<Projective, Pedersen<Projective>>::prove_commitments(
383 &mut transcript_p,
384 &pedersen_params,
385 &w3,
386 &ci3,
387 T,
388 &cmT,
389 )
390 .unwrap();
391
392 // verify the ci3.cmE, ci3.cmW, cmT commitments
393 assert_eq!(cm_proofs.len(), 3);
394 Pedersen::<Projective>::verify(
395 &pedersen_params,
396 &mut transcript_v,
397 &ci3.cmE,
398 &cm_proofs[0].clone(),
399 )
400 .unwrap();
401 Pedersen::<Projective>::verify(
402 &pedersen_params,
403 &mut transcript_v,
404 &ci3.cmW,
405 &cm_proofs[1].clone(),
406 )
407 .unwrap();
408 Pedersen::<Projective>::verify(
409 &pedersen_params,
410 &mut transcript_v,
411 &cmT,
412 &cm_proofs[2].clone(),
413 )
414 .unwrap();
415 }
416
417 #[test]
418 fn test_nifs_fold_loop() {
419 let r1cs = get_test_r1cs();
420 let z = get_test_z(3);
421 let (w, x) = r1cs.split_z(&z);
422
423 let mut rng = ark_std::test_rng();
424 let (pedersen_params, _) = Pedersen::<Projective>::setup(&mut rng, r1cs.A.n_cols).unwrap();
425
426 // prepare the running instance
427 let mut running_instance_w =
428 Witness::<Projective>::new::<false>(w.clone(), r1cs.A.n_rows, test_rng());
429 let mut running_committed_instance = running_instance_w
430 .commit::<Pedersen<Projective>, false>(&pedersen_params, x)
431 .unwrap();
432
433 r1cs.check_relation(&running_instance_w, &running_committed_instance)
434 .unwrap();
435
436 let num_iters = 10;
437 for i in 0..num_iters {
438 // prepare the incoming instance
439 let incoming_instance_z = get_test_z(i + 4);
440 let (w, x) = r1cs.split_z(&incoming_instance_z);
441 let incoming_instance_w =
442 Witness::<Projective>::new::<false>(w.clone(), r1cs.A.n_rows, test_rng());
443 let incoming_committed_instance = incoming_instance_w
444 .commit::<Pedersen<Projective>, false>(&pedersen_params, x)
445 .unwrap();
446 r1cs.check_relation(&incoming_instance_w, &incoming_committed_instance)
447 .unwrap();
448
449 let r = Fr::rand(&mut rng); // folding challenge would come from the RO
450
451 // NIFS.P
452 let (T, cmT) = NIFS::<Projective, Pedersen<Projective>>::compute_cmT(
453 &pedersen_params,
454 &r1cs,
455 &running_instance_w,
456 &running_committed_instance,
457 &incoming_instance_w,
458 &incoming_committed_instance,
459 )
460 .unwrap();
461 let (folded_w, _) = NIFS::<Projective, Pedersen<Projective>>::fold_instances(
462 r,
463 &running_instance_w,
464 &running_committed_instance,
465 &incoming_instance_w,
466 &incoming_committed_instance,
467 &T,
468 cmT,
469 )
470 .unwrap();
471
472 // NIFS.V
473 let folded_committed_instance = NIFS::<Projective, Pedersen<Projective>>::verify(
474 r,
475 &running_committed_instance,
476 &incoming_committed_instance,
477 &cmT,
478 );
479
480 r1cs.check_relation(&folded_w, &folded_committed_instance)
481 .unwrap();
482
483 // set running_instance for next loop iteration
484 running_instance_w = folded_w;
485 running_committed_instance = folded_committed_instance;
486 }
487 }
488}