sonobe/src/folding/nova/nifs.rs
src/folding/nova/nifs.rsRaw
1use ark_crypto_primitives::sponge::Absorb;
2use ark_ec::{CurveGroup, Group};
3use ark_std::One;
4use std::marker::PhantomData;
5
6use crate::ccs::r1cs::R1CS;
7use crate::folding::nova::{CommittedInstance, Witness};
8use crate::pedersen::{Params as PedersenParams, Pedersen, Proof as PedersenProof};
9use crate::transcript::Transcript;
10use crate::utils::vec::*;
11use crate::Error;
12
13/// Implements the Non-Interactive Folding Scheme described in section 4 of
14/// [Nova](https://eprint.iacr.org/2021/370.pdf)
15pub struct NIFS<C: CurveGroup> {
16 _phantom: PhantomData<C>,
17}
18
19impl<C: CurveGroup> NIFS<C>
20where
21 <C as Group>::ScalarField: Absorb,
22{
23 // compute_T: compute cross-terms T
24 pub fn compute_T(
25 r1cs: &R1CS<C::ScalarField>,
26 u1: C::ScalarField,
27 u2: C::ScalarField,
28 z1: &[C::ScalarField],
29 z2: &[C::ScalarField],
30 ) -> Result<Vec<C::ScalarField>, Error> {
31 let (A, B, C) = (r1cs.A.clone(), r1cs.B.clone(), r1cs.C.clone());
32
33 // this is parallelizable (for the future)
34 let Az1 = mat_vec_mul_sparse(&A, z1);
35 let Bz1 = mat_vec_mul_sparse(&B, z1);
36 let Cz1 = mat_vec_mul_sparse(&C, z1);
37 let Az2 = mat_vec_mul_sparse(&A, z2);
38 let Bz2 = mat_vec_mul_sparse(&B, z2);
39 let Cz2 = mat_vec_mul_sparse(&C, z2);
40
41 let Az1_Bz2 = hadamard(&Az1, &Bz2)?;
42 let Az2_Bz1 = hadamard(&Az2, &Bz1)?;
43 let u1Cz2 = vec_scalar_mul(&Cz2, &u1);
44 let u2Cz1 = vec_scalar_mul(&Cz1, &u2);
45
46 vec_sub(&vec_sub(&vec_add(&Az1_Bz2, &Az2_Bz1)?, &u1Cz2)?, &u2Cz1)
47 }
48
49 pub fn fold_witness(
50 r: C::ScalarField,
51 w1: &Witness<C>,
52 w2: &Witness<C>,
53 T: &[C::ScalarField],
54 rT: C::ScalarField,
55 ) -> Result<Witness<C>, Error> {
56 let r2 = r * r;
57 let E: Vec<C::ScalarField> = vec_add(
58 &vec_add(&w1.E, &vec_scalar_mul(T, &r))?,
59 &vec_scalar_mul(&w2.E, &r2),
60 )?;
61 let rE = w1.rE + r * rT + r2 * w2.rE;
62 let W: Vec<C::ScalarField> = w1.W.iter().zip(&w2.W).map(|(a, b)| *a + (r * b)).collect();
63
64 let rW = w1.rW + r * w2.rW;
65 Ok(Witness::<C> { E, rE, W, rW })
66 }
67
68 pub fn fold_committed_instance(
69 r: C::ScalarField,
70 ci1: &CommittedInstance<C>,
71 ci2: &CommittedInstance<C>,
72 cmT: &C,
73 ) -> CommittedInstance<C> {
74 let r2 = r * r;
75 let cmE = ci1.cmE + cmT.mul(r) + ci2.cmE.mul(r2);
76 let u = ci1.u + r * ci2.u;
77 let cmW = ci1.cmW + ci2.cmW.mul(r);
78 let x = ci1
79 .x
80 .iter()
81 .zip(&ci2.x)
82 .map(|(a, b)| *a + (r * b))
83 .collect::<Vec<C::ScalarField>>();
84
85 CommittedInstance::<C> { cmE, u, cmW, x }
86 }
87
88 /// NIFS.P is the consecutive combination of compute_cmT with fold_instances
89
90 /// compute_cmT is part of the NIFS.P logic
91 pub fn compute_cmT(
92 pedersen_params: &PedersenParams<C>,
93 r1cs: &R1CS<C::ScalarField>,
94 w1: &Witness<C>,
95 ci1: &CommittedInstance<C>,
96 w2: &Witness<C>,
97 ci2: &CommittedInstance<C>,
98 ) -> Result<(Vec<C::ScalarField>, C), Error> {
99 let z1: Vec<C::ScalarField> = [vec![ci1.u], ci1.x.to_vec(), w1.W.to_vec()].concat();
100 let z2: Vec<C::ScalarField> = [vec![ci2.u], ci2.x.to_vec(), w2.W.to_vec()].concat();
101
102 // compute cross terms
103 let T = Self::compute_T(r1cs, ci1.u, ci2.u, &z1, &z2)?;
104 // use r_T=1 since we don't need hiding property for cm(T)
105 let cmT = Pedersen::commit(pedersen_params, &T, &C::ScalarField::one())?;
106 Ok((T, cmT))
107 }
108
109 /// fold_instances is part of the NIFS.P logic described in
110 /// [Nova](https://eprint.iacr.org/2021/370.pdf)'s section 4. It returns the folded Committed
111 /// Instances and the Witness.
112 pub fn fold_instances(
113 // r comes from the transcript, and is a n-bit (N_BITS_CHALLENGE) element
114 r: C::ScalarField,
115 w1: &Witness<C>,
116 ci1: &CommittedInstance<C>,
117 w2: &Witness<C>,
118 ci2: &CommittedInstance<C>,
119 T: &[C::ScalarField],
120 cmT: C,
121 ) -> Result<(Witness<C>, CommittedInstance<C>), Error> {
122 // fold witness
123 // use r_T=1 since we don't need hiding property for cm(T)
124 let w3 = NIFS::<C>::fold_witness(r, w1, w2, T, C::ScalarField::one())?;
125
126 // fold committed instancs
127 let ci3 = NIFS::<C>::fold_committed_instance(r, ci1, ci2, &cmT);
128
129 Ok((w3, ci3))
130 }
131
132 /// verify implements NIFS.V logic described in [Nova](https://eprint.iacr.org/2021/370.pdf)'s
133 /// section 4. It returns the folded Committed Instance
134 pub fn verify(
135 // r comes from the transcript, and is a n-bit (N_BITS_CHALLENGE) element
136 r: C::ScalarField,
137 ci1: &CommittedInstance<C>,
138 ci2: &CommittedInstance<C>,
139 cmT: &C,
140 ) -> CommittedInstance<C> {
141 NIFS::<C>::fold_committed_instance(r, ci1, ci2, cmT)
142 }
143
144 /// Verify commited folded instance (ci) relations. Notice that this method does not open the
145 /// commitments, but just checks that the given committed instances (ci1, ci2) when folded
146 /// result in the folded committed instance (ci3) values.
147 pub fn verify_folded_instance(
148 r: C::ScalarField,
149 ci1: &CommittedInstance<C>,
150 ci2: &CommittedInstance<C>,
151 ci3: &CommittedInstance<C>,
152 cmT: &C,
153 ) -> Result<(), Error> {
154 let expected = Self::fold_committed_instance(r, ci1, ci2, cmT);
155 if ci3.cmE != expected.cmE
156 || ci3.u != expected.u
157 || ci3.cmW != expected.cmW
158 || ci3.x != expected.x
159 {
160 return Err(Error::NotSatisfied);
161 }
162 Ok(())
163 }
164
165 pub fn open_commitments(
166 tr: &mut impl Transcript<C>,
167 pedersen_params: &PedersenParams<C>,
168 w: &Witness<C>,
169 ci: &CommittedInstance<C>,
170 T: Vec<C::ScalarField>,
171 cmT: &C,
172 ) -> Result<[PedersenProof<C>; 3], Error> {
173 let cmE_proof = Pedersen::prove(pedersen_params, tr, &ci.cmE, &w.E, &w.rE)?;
174 let cmW_proof = Pedersen::prove(pedersen_params, tr, &ci.cmW, &w.W, &w.rW)?;
175 let cmT_proof = Pedersen::prove(pedersen_params, tr, cmT, &T, &C::ScalarField::one())?; // cm(T) is committed with rT=1
176 Ok([cmE_proof, cmW_proof, cmT_proof])
177 }
178 pub fn verify_commitments(
179 tr: &mut impl Transcript<C>,
180 pedersen_params: &PedersenParams<C>,
181 ci: CommittedInstance<C>,
182 cmT: C,
183 cm_proofs: [PedersenProof<C>; 3],
184 ) -> Result<(), Error> {
185 if cm_proofs.len() != 3 {
186 // cm_proofs should have length 3: [cmE_proof, cmW_proof, cmT_proof]
187 return Err(Error::NotExpectedLength(cm_proofs.len(), 3));
188 }
189 Pedersen::verify(pedersen_params, tr, ci.cmE, cm_proofs[0].clone())?;
190 Pedersen::verify(pedersen_params, tr, ci.cmW, cm_proofs[1].clone())?;
191 Pedersen::verify(pedersen_params, tr, cmT, cm_proofs[2].clone())?;
192 Ok(())
193 }
194}
195
196#[cfg(test)]
197pub mod tests {
198 use super::*;
199 use ark_ff::PrimeField;
200 use ark_pallas::{Fr, Projective};
201 use ark_std::{ops::Mul, UniformRand, Zero};
202
203 use crate::ccs::r1cs::tests::{get_test_r1cs, get_test_z};
204 use crate::transcript::poseidon::{tests::poseidon_test_config, PoseidonTranscript};
205 use crate::utils::vec::vec_scalar_mul;
206
207 pub fn check_relaxed_r1cs<F: PrimeField>(r1cs: &R1CS<F>, z: &[F], u: &F, E: &[F]) -> bool {
208 let Az = mat_vec_mul_sparse(&r1cs.A, z);
209 let Bz = mat_vec_mul_sparse(&r1cs.B, z);
210 let Cz = mat_vec_mul_sparse(&r1cs.C, z);
211 hadamard(&Az, &Bz).unwrap() == vec_add(&vec_scalar_mul(&Cz, u), E).unwrap()
212 }
213
214 // fold 2 dummy instances and check that the folded instance holds the relaxed R1CS relation
215 #[test]
216 fn test_nifs_fold_dummy() {
217 let r1cs = get_test_r1cs::<Fr>();
218 let z1 = get_test_z(3);
219 let (w1, x1) = r1cs.split_z(&z1);
220
221 let mut rng = ark_std::test_rng();
222 let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
223
224 // dummy instance, witness and public inputs zeroes
225 let w_dummy = Witness::<Projective>::new(vec![Fr::zero(); w1.len()], r1cs.A.n_rows);
226 let mut u_dummy = w_dummy
227 .commit(&pedersen_params, vec![Fr::zero(); x1.len()])
228 .unwrap();
229 u_dummy.u = Fr::zero();
230
231 let w_i = w_dummy.clone();
232 let u_i = u_dummy.clone();
233 let W_i = w_dummy.clone();
234 let U_i = u_dummy.clone();
235 let z_dummy = vec![Fr::zero(); z1.len()];
236 assert!(check_relaxed_r1cs(&r1cs, &z_dummy, &u_i.u, &w_i.E));
237 assert!(check_relaxed_r1cs(&r1cs, &z_dummy, &U_i.u, &W_i.E));
238
239 let r_Fr = Fr::from(3_u32);
240
241 let (T, cmT) =
242 NIFS::<Projective>::compute_cmT(&pedersen_params, &r1cs, &w_i, &u_i, &W_i, &U_i)
243 .unwrap();
244 let (W_i1, U_i1) =
245 NIFS::<Projective>::fold_instances(r_Fr, &w_i, &u_i, &W_i, &U_i, &T, cmT).unwrap();
246
247 let z: Vec<Fr> = [vec![U_i1.u], U_i1.x.to_vec(), W_i1.W.to_vec()].concat();
248 assert_eq!(z.len(), z1.len());
249 assert!(check_relaxed_r1cs(&r1cs, &z, &U_i1.u, &W_i1.E));
250 }
251
252 // fold 2 instances into one
253 #[test]
254 fn test_nifs_one_fold() {
255 let r1cs = get_test_r1cs();
256 let z1 = get_test_z(3);
257 let z2 = get_test_z(4);
258 let (w1, x1) = r1cs.split_z(&z1);
259 let (w2, x2) = r1cs.split_z(&z2);
260
261 let w1 = Witness::<Projective>::new(w1.clone(), r1cs.A.n_rows);
262 let w2 = Witness::<Projective>::new(w2.clone(), r1cs.A.n_rows);
263
264 let mut rng = ark_std::test_rng();
265 let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
266
267 let r = Fr::rand(&mut rng); // folding challenge would come from the transcript
268
269 // compute committed instances
270 let ci1 = w1.commit(&pedersen_params, x1.clone()).unwrap();
271 let ci2 = w2.commit(&pedersen_params, x2.clone()).unwrap();
272
273 // NIFS.P
274 let (T, cmT) =
275 NIFS::<Projective>::compute_cmT(&pedersen_params, &r1cs, &w1, &ci1, &w2, &ci2).unwrap();
276 let (w3, ci3_aux) =
277 NIFS::<Projective>::fold_instances(r, &w1, &ci1, &w2, &ci2, &T, cmT).unwrap();
278
279 // NIFS.V
280 let ci3 = NIFS::<Projective>::verify(r, &ci1, &ci2, &cmT);
281 assert_eq!(ci3, ci3_aux);
282
283 // naive check that the folded witness satisfies the relaxed r1cs
284 let z3: Vec<Fr> = [vec![ci3.u], ci3.x.to_vec(), w3.W.to_vec()].concat();
285 // check that z3 is as expected
286 let z3_aux = vec_add(&z1, &vec_scalar_mul(&z2, &r)).unwrap();
287 assert_eq!(z3, z3_aux);
288 // check that relations hold for the 2 inputted instances and the folded one
289 assert!(check_relaxed_r1cs(&r1cs, &z1, &ci1.u, &w1.E));
290 assert!(check_relaxed_r1cs(&r1cs, &z2, &ci2.u, &w2.E));
291 assert!(check_relaxed_r1cs(&r1cs, &z3, &ci3.u, &w3.E));
292
293 // check that folded commitments from folded instance (ci) are equal to folding the
294 // use folded rE, rW to commit w3
295 let ci3_expected = w3.commit(&pedersen_params, ci3.x.clone()).unwrap();
296 assert_eq!(ci3_expected.cmE, ci3.cmE);
297 assert_eq!(ci3_expected.cmW, ci3.cmW);
298
299 // next equalities should hold since we started from two cmE of zero-vector E's
300 assert_eq!(ci3.cmE, cmT.mul(r));
301 assert_eq!(w3.E, vec_scalar_mul(&T, &r));
302
303 // NIFS.Verify_Folded_Instance:
304 NIFS::<Projective>::verify_folded_instance(r, &ci1, &ci2, &ci3, &cmT).unwrap();
305
306 let poseidon_config = poseidon_test_config::<Fr>();
307 // init Prover's transcript
308 let mut transcript_p = PoseidonTranscript::<Projective>::new(&poseidon_config);
309 // init Verifier's transcript
310 let mut transcript_v = PoseidonTranscript::<Projective>::new(&poseidon_config);
311
312 // check openings of ci3.cmE, ci3.cmW and cmT
313 let cm_proofs = NIFS::<Projective>::open_commitments(
314 &mut transcript_p,
315 &pedersen_params,
316 &w3,
317 &ci3,
318 T,
319 &cmT,
320 )
321 .unwrap();
322
323 NIFS::<Projective>::verify_commitments(
324 &mut transcript_v,
325 &pedersen_params,
326 ci3,
327 cmT,
328 cm_proofs,
329 )
330 .unwrap();
331 }
332
333 #[test]
334 fn test_nifs_fold_loop() {
335 let r1cs = get_test_r1cs();
336 let z = get_test_z(3);
337 let (w, x) = r1cs.split_z(&z);
338
339 let mut rng = ark_std::test_rng();
340 let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
341
342 // prepare the running instance
343 let mut running_instance_w = Witness::<Projective>::new(w.clone(), r1cs.A.n_rows);
344 let mut running_committed_instance =
345 running_instance_w.commit(&pedersen_params, x).unwrap();
346 assert!(check_relaxed_r1cs(
347 &r1cs,
348 &z,
349 &running_committed_instance.u,
350 &running_instance_w.E,
351 ));
352
353 let num_iters = 10;
354 for i in 0..num_iters {
355 // prepare the incomming instance
356 let incomming_instance_z = get_test_z(i + 4);
357 let (w, x) = r1cs.split_z(&incomming_instance_z);
358 let incomming_instance_w = Witness::<Projective>::new(w.clone(), r1cs.A.n_rows);
359 let incomming_committed_instance =
360 incomming_instance_w.commit(&pedersen_params, x).unwrap();
361 assert!(check_relaxed_r1cs(
362 &r1cs,
363 &incomming_instance_z.clone(),
364 &incomming_committed_instance.u,
365 &incomming_instance_w.E,
366 ));
367
368 let r = Fr::rand(&mut rng); // folding challenge would come from the transcript
369
370 // NIFS.P
371 let (T, cmT) = NIFS::<Projective>::compute_cmT(
372 &pedersen_params,
373 &r1cs,
374 &running_instance_w,
375 &running_committed_instance,
376 &incomming_instance_w,
377 &incomming_committed_instance,
378 )
379 .unwrap();
380 let (folded_w, _) = NIFS::<Projective>::fold_instances(
381 r,
382 &running_instance_w,
383 &running_committed_instance,
384 &incomming_instance_w,
385 &incomming_committed_instance,
386 &T,
387 cmT,
388 )
389 .unwrap();
390
391 // NIFS.V
392 let folded_committed_instance = NIFS::<Projective>::verify(
393 r,
394 &running_committed_instance,
395 &incomming_committed_instance,
396 &cmT,
397 );
398
399 let folded_z: Vec<Fr> = [
400 vec![folded_committed_instance.u],
401 folded_committed_instance.x.to_vec(),
402 folded_w.W.to_vec(),
403 ]
404 .concat();
405
406 assert!(check_relaxed_r1cs(
407 &r1cs,
408 &folded_z,
409 &folded_committed_instance.u,
410 &folded_w.E
411 ));
412
413 // set running_instance for next loop iteration
414 running_instance_w = folded_w;
415 running_committed_instance = folded_committed_instance;
416 }
417 }
418}