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/// 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
89 #[allow(clippy::type_complexity)]
90 pub fn prove(
91 pedersen_params: &PedersenParams<C>,
92 // r comes from the transcript, and is a n-bit (N_BITS_CHALLENGE) element
93 r: C::ScalarField,
94 r1cs: &R1CS<C::ScalarField>,
95 w1: &Witness<C>,
96 ci1: &CommittedInstance<C>,
97 w2: &Witness<C>,
98 ci2: &CommittedInstance<C>,
99 ) -> Result<(Witness<C>, CommittedInstance<C>, Vec<C::ScalarField>, C), Error> {
100 let z1: Vec<C::ScalarField> = [vec![ci1.u], ci1.x.to_vec(), w1.W.to_vec()].concat();
101 let z2: Vec<C::ScalarField> = [vec![ci2.u], ci2.x.to_vec(), w2.W.to_vec()].concat();
102
103 // compute cross terms
104 let T = Self::compute_T(r1cs, ci1.u, ci2.u, &z1, &z2)?;
105 let rT = C::ScalarField::one(); // use 1 as rT since we don't need hiding property for cm(T)
106 let cmT = Pedersen::commit(pedersen_params, &T, &rT);
107
108 // fold witness
109 let w3 = NIFS::<C>::fold_witness(r, w1, w2, &T, rT)?;
110
111 // fold committed instancs
112 let ci3 = NIFS::<C>::fold_committed_instance(r, ci1, ci2, &cmT);
113
114 Ok((w3, ci3, T, cmT))
115 }
116
117 // NIFS.V
118 pub fn verify(
119 // r comes from the transcript, and is a n-bit (N_BITS_CHALLENGE) element
120 r: C::ScalarField,
121 ci1: &CommittedInstance<C>,
122 ci2: &CommittedInstance<C>,
123 cmT: &C,
124 ) -> CommittedInstance<C> {
125 NIFS::<C>::fold_committed_instance(r, ci1, ci2, cmT)
126 }
127
128 /// Verify commited folded instance (ci) relations. Notice that this method does not open the
129 /// commitments, but just checks that the given committed instances (ci1, ci2) when folded
130 /// result in the folded committed instance (ci3) values.
131 pub fn verify_folded_instance(
132 r: C::ScalarField,
133 ci1: &CommittedInstance<C>,
134 ci2: &CommittedInstance<C>,
135 ci3: &CommittedInstance<C>,
136 cmT: &C,
137 ) -> Result<(), Error> {
138 let r2 = r * r;
139 if ci3.cmE != (ci1.cmE + cmT.mul(r) + ci2.cmE.mul(r2))
140 || ci3.u != ci1.u + r * ci2.u
141 || ci3.cmW != (ci1.cmW + ci2.cmW.mul(r))
142 || ci3.x != vec_add(&ci1.x, &vec_scalar_mul(&ci2.x, &r))?
143 {
144 return Err(Error::NotSatisfied);
145 }
146 Ok(())
147 }
148
149 pub fn open_commitments(
150 tr: &mut impl Transcript<C>,
151 pedersen_params: &PedersenParams<C>,
152 w: &Witness<C>,
153 ci: &CommittedInstance<C>,
154 T: Vec<C::ScalarField>,
155 cmT: &C,
156 ) -> Result<[PedersenProof<C>; 3], Error> {
157 let cmE_proof = Pedersen::prove(pedersen_params, tr, &ci.cmE, &w.E, &w.rE)?;
158 let cmW_proof = Pedersen::prove(pedersen_params, tr, &ci.cmW, &w.W, &w.rW)?;
159 let cmT_proof = Pedersen::prove(pedersen_params, tr, cmT, &T, &C::ScalarField::one())?; // cm(T) is committed with rT=1
160 Ok([cmE_proof, cmW_proof, cmT_proof])
161 }
162 pub fn verify_commitments(
163 tr: &mut impl Transcript<C>,
164 pedersen_params: &PedersenParams<C>,
165 ci: CommittedInstance<C>,
166 cmT: C,
167 cm_proofs: [PedersenProof<C>; 3],
168 ) -> Result<(), Error> {
169 if cm_proofs.len() != 3 {
170 // cm_proofs should have length 3: [cmE_proof, cmW_proof, cmT_proof]
171 return Err(Error::NotExpectedLength);
172 }
173 if !Pedersen::verify(pedersen_params, tr, ci.cmE, cm_proofs[0].clone())
174 || !Pedersen::verify(pedersen_params, tr, ci.cmW, cm_proofs[1].clone())
175 || !Pedersen::verify(pedersen_params, tr, cmT, cm_proofs[2].clone())
176 {
177 return Err(Error::CommitmentVerificationFail);
178 }
179 Ok(())
180 }
181}
182
183#[cfg(test)]
184pub mod tests {
185 use super::*;
186 use ark_ff::PrimeField;
187 use ark_pallas::{Fr, Projective};
188 use ark_std::{ops::Mul, UniformRand, Zero};
189
190 use crate::ccs::r1cs::tests::{get_test_r1cs, get_test_z};
191 use crate::transcript::poseidon::{tests::poseidon_test_config, PoseidonTranscript};
192 use crate::utils::vec::vec_scalar_mul;
193
194 pub fn check_relaxed_r1cs<F: PrimeField>(r1cs: &R1CS<F>, z: &[F], u: &F, E: &[F]) -> bool {
195 let Az = mat_vec_mul_sparse(&r1cs.A, z);
196 let Bz = mat_vec_mul_sparse(&r1cs.B, z);
197 let Cz = mat_vec_mul_sparse(&r1cs.C, z);
198 hadamard(&Az, &Bz).unwrap() == vec_add(&vec_scalar_mul(&Cz, u), E).unwrap()
199 }
200
201 // fold 2 dummy instances and check that the folded instance holds the relaxed R1CS relation
202 #[test]
203 fn test_nifs_fold_dummy() {
204 let r1cs = get_test_r1cs::<Fr>();
205 let z1 = get_test_z(3);
206 let (w1, x1) = r1cs.split_z(&z1);
207
208 let mut rng = ark_std::test_rng();
209 let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
210
211 // dummy instance, witness and public inputs zeroes
212 let w_dummy = Witness::<Projective>::new(vec![Fr::zero(); w1.len()], r1cs.A.n_rows);
213 let mut u_dummy = w_dummy.commit(&pedersen_params, vec![Fr::zero(); x1.len()]);
214 u_dummy.u = Fr::zero();
215
216 let w_i = w_dummy.clone();
217 let u_i = u_dummy.clone();
218 let W_i = w_dummy.clone();
219 let U_i = u_dummy.clone();
220 let z_dummy = vec![Fr::zero(); z1.len()];
221 assert!(check_relaxed_r1cs(&r1cs, &z_dummy, &u_i.u, &w_i.E));
222 assert!(check_relaxed_r1cs(&r1cs, &z_dummy, &U_i.u, &W_i.E));
223
224 let r_Fr = Fr::from(3_u32);
225
226 let (W_i1, U_i1, _, _) =
227 NIFS::<Projective>::prove(&pedersen_params, r_Fr, &r1cs, &w_i, &u_i, &W_i, &U_i)
228 .unwrap();
229
230 let z: Vec<Fr> = [vec![U_i1.u], U_i1.x.to_vec(), W_i1.W.to_vec()].concat();
231 assert_eq!(z.len(), z1.len());
232 assert!(check_relaxed_r1cs(&r1cs, &z, &U_i1.u, &W_i1.E));
233 }
234
235 // fold 2 instances into one
236 #[test]
237 fn test_nifs_one_fold() {
238 let r1cs = get_test_r1cs();
239 let z1 = get_test_z(3);
240 let z2 = get_test_z(4);
241 let (w1, x1) = r1cs.split_z(&z1);
242 let (w2, x2) = r1cs.split_z(&z2);
243
244 let w1 = Witness::<Projective>::new(w1.clone(), r1cs.A.n_rows);
245 let w2 = Witness::<Projective>::new(w2.clone(), r1cs.A.n_rows);
246
247 let mut rng = ark_std::test_rng();
248 let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
249
250 let r = Fr::rand(&mut rng); // folding challenge would come from the transcript
251
252 // compute committed instances
253 let ci1 = w1.commit(&pedersen_params, x1.clone());
254 let ci2 = w2.commit(&pedersen_params, x2.clone());
255
256 // NIFS.P
257 let (w3, ci3_aux, T, cmT) =
258 NIFS::<Projective>::prove(&pedersen_params, r, &r1cs, &w1, &ci1, &w2, &ci2).unwrap();
259
260 // NIFS.V
261 let ci3 = NIFS::<Projective>::verify(r, &ci1, &ci2, &cmT);
262 assert_eq!(ci3, ci3_aux);
263
264 // naive check that the folded witness satisfies the relaxed r1cs
265 let z3: Vec<Fr> = [vec![ci3.u], ci3.x.to_vec(), w3.W.to_vec()].concat();
266 // check that z3 is as expected
267 let z3_aux = vec_add(&z1, &vec_scalar_mul(&z2, &r)).unwrap();
268 assert_eq!(z3, z3_aux);
269 // check that relations hold for the 2 inputted instances and the folded one
270 assert!(check_relaxed_r1cs(&r1cs, &z1, &ci1.u, &w1.E));
271 assert!(check_relaxed_r1cs(&r1cs, &z2, &ci2.u, &w2.E));
272 assert!(check_relaxed_r1cs(&r1cs, &z3, &ci3.u, &w3.E));
273
274 // check that folded commitments from folded instance (ci) are equal to folding the
275 // use folded rE, rW to commit w3
276 let ci3_expected = w3.commit(&pedersen_params, ci3.x.clone());
277 assert_eq!(ci3_expected.cmE, ci3.cmE);
278 assert_eq!(ci3_expected.cmW, ci3.cmW);
279
280 // next equalities should hold since we started from two cmE of zero-vector E's
281 assert_eq!(ci3.cmE, cmT.mul(r));
282 assert_eq!(w3.E, vec_scalar_mul(&T, &r));
283
284 // NIFS.Verify_Folded_Instance:
285 NIFS::<Projective>::verify_folded_instance(r, &ci1, &ci2, &ci3, &cmT).unwrap();
286
287 let poseidon_config = poseidon_test_config::<Fr>();
288 // init Prover's transcript
289 let mut transcript_p = PoseidonTranscript::<Projective>::new(&poseidon_config);
290 // init Verifier's transcript
291 let mut transcript_v = PoseidonTranscript::<Projective>::new(&poseidon_config);
292
293 // check openings of ci3.cmE, ci3.cmW and cmT
294 let cm_proofs = NIFS::<Projective>::open_commitments(
295 &mut transcript_p,
296 &pedersen_params,
297 &w3,
298 &ci3,
299 T,
300 &cmT,
301 )
302 .unwrap();
303
304 NIFS::<Projective>::verify_commitments(
305 &mut transcript_v,
306 &pedersen_params,
307 ci3,
308 cmT,
309 cm_proofs,
310 )
311 .unwrap();
312 }
313
314 #[test]
315 fn test_nifs_fold_loop() {
316 let r1cs = get_test_r1cs();
317 let z = get_test_z(3);
318 let (w, x) = r1cs.split_z(&z);
319
320 let mut rng = ark_std::test_rng();
321 let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
322
323 // prepare the running instance
324 let mut running_instance_w = Witness::<Projective>::new(w.clone(), r1cs.A.n_rows);
325 let mut running_committed_instance = running_instance_w.commit(&pedersen_params, x);
326 assert!(check_relaxed_r1cs(
327 &r1cs,
328 &z,
329 &running_committed_instance.u,
330 &running_instance_w.E,
331 ));
332
333 let num_iters = 10;
334 for i in 0..num_iters {
335 // prepare the incomming instance
336 let incomming_instance_z = get_test_z(i + 4);
337 let (w, x) = r1cs.split_z(&incomming_instance_z);
338 let incomming_instance_w = Witness::<Projective>::new(w.clone(), r1cs.A.n_rows);
339 let incomming_committed_instance = incomming_instance_w.commit(&pedersen_params, x);
340 assert!(check_relaxed_r1cs(
341 &r1cs,
342 &incomming_instance_z.clone(),
343 &incomming_committed_instance.u,
344 &incomming_instance_w.E,
345 ));
346
347 let r = Fr::rand(&mut rng); // folding challenge would come from the transcript
348
349 // NIFS.P
350 let (folded_w, _, _, cmT) = NIFS::<Projective>::prove(
351 &pedersen_params,
352 r,
353 &r1cs,
354 &running_instance_w,
355 &running_committed_instance,
356 &incomming_instance_w,
357 &incomming_committed_instance,
358 )
359 .unwrap();
360
361 // NIFS.V
362 let folded_committed_instance = NIFS::<Projective>::verify(
363 r,
364 &running_committed_instance,
365 &incomming_committed_instance,
366 &cmT,
367 );
368
369 let folded_z: Vec<Fr> = [
370 vec![folded_committed_instance.u],
371 folded_committed_instance.x.to_vec(),
372 folded_w.W.to_vec(),
373 ]
374 .concat();
375
376 assert!(check_relaxed_r1cs(
377 &r1cs,
378 &folded_z,
379 &folded_committed_instance.u,
380 &folded_w.E
381 ));
382
383 // set running_instance for next loop iteration
384 running_instance_w = folded_w;
385 running_committed_instance = folded_committed_instance;
386 }
387 }
388}