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::*;
11
12pub struct NIFS<C: CurveGroup> {
13 _phantom: PhantomData<C>,
14}
15
16impl<C: CurveGroup> NIFS<C>
17where
18 <C as Group>::ScalarField: Absorb,
19{
20 // compute_T: compute cross-terms T
21 pub fn compute_T(
22 r1cs: &R1CS<C::ScalarField>,
23 u1: C::ScalarField,
24 u2: C::ScalarField,
25 z1: &[C::ScalarField],
26 z2: &[C::ScalarField],
27 ) -> Vec<C::ScalarField> {
28 let (A, B, C) = (r1cs.A.clone(), r1cs.B.clone(), r1cs.C.clone());
29
30 // this is parallelizable (for the future)
31 let Az1 = mat_vec_mul_sparse(&A, z1);
32 let Bz1 = mat_vec_mul_sparse(&B, z1);
33 let Cz1 = mat_vec_mul_sparse(&C, z1);
34 let Az2 = mat_vec_mul_sparse(&A, z2);
35 let Bz2 = mat_vec_mul_sparse(&B, z2);
36 let Cz2 = mat_vec_mul_sparse(&C, z2);
37
38 let Az1_Bz2 = hadamard(&Az1, &Bz2);
39 let Az2_Bz1 = hadamard(&Az2, &Bz1);
40 let u1Cz2 = vec_scalar_mul(&Cz2, &u1);
41 let u2Cz1 = vec_scalar_mul(&Cz1, &u2);
42
43 vec_sub(&vec_sub(&vec_add(&Az1_Bz2, &Az2_Bz1), &u1Cz2), &u2Cz1)
44 }
45
46 pub fn fold_witness(
47 r: C::ScalarField,
48 w1: &Witness<C>,
49 w2: &Witness<C>,
50 T: &[C::ScalarField],
51 rT: C::ScalarField,
52 ) -> Witness<C> {
53 let r2 = r * r;
54 let E: Vec<C::ScalarField> = vec_add(
55 &vec_add(&w1.E, &vec_scalar_mul(T, &r)),
56 &vec_scalar_mul(&w2.E, &r2),
57 );
58 let rE = w1.rE + r * rT + r2 * w2.rE;
59 let W: Vec<C::ScalarField> = w1.W.iter().zip(&w2.W).map(|(a, b)| *a + (r * b)).collect();
60
61 let rW = w1.rW + r * w2.rW;
62 Witness::<C> { E, rE, W, rW }
63 }
64
65 pub fn fold_committed_instance(
66 r: C::ScalarField,
67 ci1: &CommittedInstance<C>,
68 ci2: &CommittedInstance<C>,
69 cmT: &C,
70 ) -> CommittedInstance<C> {
71 let r2 = r * r;
72 let cmE = ci1.cmE + cmT.mul(r) + ci2.cmE.mul(r2);
73 let u = ci1.u + r * ci2.u;
74 let cmW = ci1.cmW + ci2.cmW.mul(r);
75 let x = ci1
76 .x
77 .iter()
78 .zip(&ci2.x)
79 .map(|(a, b)| *a + (r * b))
80 .collect::<Vec<C::ScalarField>>();
81
82 CommittedInstance::<C> { cmE, u, cmW, x }
83 }
84
85 // NIFS.P
86 #[allow(clippy::type_complexity)]
87 pub fn prove(
88 pedersen_params: &PedersenParams<C>,
89 // r comes from the transcript, and is a n-bit (N_BITS_CHALLENGE) element
90 r: C::ScalarField,
91 r1cs: &R1CS<C::ScalarField>,
92 w1: &Witness<C>,
93 ci1: &CommittedInstance<C>,
94 w2: &Witness<C>,
95 ci2: &CommittedInstance<C>,
96 ) -> (Witness<C>, CommittedInstance<C>, Vec<C::ScalarField>, C) {
97 let z1: Vec<C::ScalarField> = [vec![ci1.u], ci1.x.to_vec(), w1.W.to_vec()].concat();
98 let z2: Vec<C::ScalarField> = [vec![ci2.u], ci2.x.to_vec(), w2.W.to_vec()].concat();
99
100 // compute cross terms
101 let T = Self::compute_T(r1cs, ci1.u, ci2.u, &z1, &z2);
102 let rT = C::ScalarField::one(); // use 1 as rT since we don't need hiding property for cm(T)
103 let cmT = Pedersen::commit(pedersen_params, &T, &rT);
104
105 // fold witness
106 let w3 = NIFS::<C>::fold_witness(r, w1, w2, &T, rT);
107
108 // fold committed instancs
109 let ci3 = NIFS::<C>::fold_committed_instance(r, ci1, ci2, &cmT);
110
111 (w3, ci3, T, cmT)
112 }
113
114 // NIFS.V
115 pub fn verify(
116 // r comes from the transcript, and is a n-bit (N_BITS_CHALLENGE) element
117 r: C::ScalarField,
118 ci1: &CommittedInstance<C>,
119 ci2: &CommittedInstance<C>,
120 cmT: &C,
121 ) -> CommittedInstance<C> {
122 NIFS::<C>::fold_committed_instance(r, ci1, ci2, cmT)
123 }
124
125 // verify commited folded instance (ci) relations
126 pub fn verify_folded_instance(
127 r: C::ScalarField,
128 ci1: &CommittedInstance<C>,
129 ci2: &CommittedInstance<C>,
130 ci3: &CommittedInstance<C>,
131 cmT: &C,
132 ) -> bool {
133 let r2 = r * r;
134 if ci3.cmE != (ci1.cmE + cmT.mul(r) + ci2.cmE.mul(r2)) {
135 return false;
136 }
137 if ci3.u != ci1.u + r * ci2.u {
138 return false;
139 }
140 if ci3.cmW != (ci1.cmW + ci2.cmW.mul(r)) {
141 return false;
142 }
143 if ci3.x != vec_add(&ci1.x, &vec_scalar_mul(&ci2.x, &r)) {
144 return false;
145 }
146 true
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 ) -> (PedersenProof<C>, PedersenProof<C>, PedersenProof<C>) {
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 (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 cmE_proof: PedersenProof<C>,
168 cmW_proof: PedersenProof<C>,
169 cmT_proof: PedersenProof<C>,
170 ) -> bool {
171 if !Pedersen::verify(pedersen_params, tr, ci.cmE, cmE_proof) {
172 return false;
173 }
174 if !Pedersen::verify(pedersen_params, tr, ci.cmW, cmW_proof) {
175 return false;
176 }
177 if !Pedersen::verify(pedersen_params, tr, cmT, cmT_proof) {
178 return false;
179 }
180 true
181 }
182}
183
184#[cfg(test)]
185mod tests {
186 use super::*;
187 use crate::ccs::r1cs::tests::{get_test_r1cs, get_test_z};
188 use crate::transcript::poseidon::{tests::poseidon_test_config, PoseidonTranscript};
189 use ark_ff::PrimeField;
190 use ark_pallas::{Fr, Projective};
191 use ark_std::UniformRand;
192
193 pub fn check_relaxed_r1cs<F: PrimeField>(r1cs: &R1CS<F>, z: Vec<F>, u: F, E: &[F]) {
194 let Az = mat_vec_mul_sparse(&r1cs.A, &z);
195 let Bz = mat_vec_mul_sparse(&r1cs.B, &z);
196 let Cz = mat_vec_mul_sparse(&r1cs.C, &z);
197 assert_eq!(hadamard(&Az, &Bz), vec_add(&vec_scalar_mul(&Cz, &u), E));
198 }
199
200 // fold 2 instances into one
201 #[test]
202 fn test_nifs_one_fold() {
203 let r1cs = get_test_r1cs();
204 let z1 = get_test_z(3);
205 let z2 = get_test_z(4);
206 let (w1, x1) = r1cs.split_z(&z1);
207 let (w2, x2) = r1cs.split_z(&z2);
208
209 let w1 = Witness::<Projective>::new(w1.clone(), r1cs.A.n_rows);
210 let w2 = Witness::<Projective>::new(w2.clone(), r1cs.A.n_rows);
211
212 let mut rng = ark_std::test_rng();
213 let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
214
215 let r = Fr::rand(&mut rng); // folding challenge would come from the transcript
216
217 // compute committed instances
218 let ci1 = w1.commit(&pedersen_params, x1.clone());
219 let ci2 = w2.commit(&pedersen_params, x2.clone());
220
221 // NIFS.P
222 let (w3, _, T, cmT) =
223 NIFS::<Projective>::prove(&pedersen_params, r, &r1cs, &w1, &ci1, &w2, &ci2);
224
225 // NIFS.V
226 let ci3 = NIFS::<Projective>::verify(r, &ci1, &ci2, &cmT);
227
228 // naive check that the folded witness satisfies the relaxed r1cs
229 let z3: Vec<Fr> = [vec![ci3.u], ci3.x.to_vec(), w3.W.to_vec()].concat();
230 // check that z3 is as expected
231 let z3_aux = vec_add(&z1, &vec_scalar_mul(&z2, &r));
232 assert_eq!(z3, z3_aux);
233 // check that relations hold for the 2 inputted instances and the folded one
234 check_relaxed_r1cs(&r1cs, z1, ci1.u, &w1.E);
235 check_relaxed_r1cs(&r1cs, z2, ci2.u, &w2.E);
236 check_relaxed_r1cs(&r1cs, z3, ci3.u, &w3.E);
237
238 // check that folded commitments from folded instance (ci) are equal to folding the
239 // use folded rE, rW to commit w3
240 let ci3_expected = w3.commit(&pedersen_params, ci3.x.clone());
241 assert_eq!(ci3_expected.cmE, ci3.cmE);
242 assert_eq!(ci3_expected.cmW, ci3.cmW);
243
244 // NIFS.Verify_Folded_Instance:
245 assert!(NIFS::<Projective>::verify_folded_instance(
246 r, &ci1, &ci2, &ci3, &cmT
247 ));
248
249 let poseidon_config = poseidon_test_config::<Fr>();
250 // init Prover's transcript
251 let mut transcript_p = PoseidonTranscript::<Projective>::new(&poseidon_config);
252 // init Verifier's transcript
253 let mut transcript_v = PoseidonTranscript::<Projective>::new(&poseidon_config);
254
255 // check openings of ci3.cmE, ci3.cmW and cmT
256 let (cmE_proof, cmW_proof, cmT_proof) = NIFS::<Projective>::open_commitments(
257 &mut transcript_p,
258 &pedersen_params,
259 &w3,
260 &ci3,
261 T,
262 &cmT,
263 );
264 let v = NIFS::<Projective>::verify_commitments(
265 &mut transcript_v,
266 &pedersen_params,
267 ci3,
268 cmT,
269 cmE_proof,
270 cmW_proof,
271 cmT_proof,
272 );
273 assert!(v);
274 }
275
276 #[test]
277 fn test_nifs_fold_loop() {
278 let r1cs = get_test_r1cs();
279 let z = get_test_z(3);
280 let (w, x) = r1cs.split_z(&z);
281
282 let mut rng = ark_std::test_rng();
283 let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
284
285 // prepare the running instance
286 let mut running_instance_w = Witness::<Projective>::new(w.clone(), r1cs.A.n_rows);
287 let mut running_committed_instance = running_instance_w.commit(&pedersen_params, x);
288 check_relaxed_r1cs(
289 &r1cs,
290 z,
291 running_committed_instance.u,
292 &running_instance_w.E,
293 );
294
295 let num_iters = 10;
296 for i in 0..num_iters {
297 // prepare the incomming instance
298 let incomming_instance_z = get_test_z(i + 4);
299 let (w, x) = r1cs.split_z(&incomming_instance_z);
300 let incomming_instance_w = Witness::<Projective>::new(w.clone(), r1cs.A.n_rows);
301 let incomming_committed_instance = incomming_instance_w.commit(&pedersen_params, x);
302 check_relaxed_r1cs(
303 &r1cs,
304 incomming_instance_z.clone(),
305 incomming_committed_instance.u,
306 &incomming_instance_w.E,
307 );
308
309 let r = Fr::rand(&mut rng); // folding challenge would come from the transcript
310
311 // NIFS.P
312 let (folded_w, _, _, cmT) = NIFS::<Projective>::prove(
313 &pedersen_params,
314 r,
315 &r1cs,
316 &running_instance_w,
317 &running_committed_instance,
318 &incomming_instance_w,
319 &incomming_committed_instance,
320 );
321
322 // NIFS.V
323 let folded_committed_instance = NIFS::<Projective>::verify(
324 r,
325 &running_committed_instance,
326 &incomming_committed_instance,
327 &cmT,
328 );
329
330 let folded_z: Vec<Fr> = [
331 vec![folded_committed_instance.u],
332 folded_committed_instance.x.to_vec(),
333 folded_w.W.to_vec(),
334 ]
335 .concat();
336
337 check_relaxed_r1cs(&r1cs, folded_z, folded_committed_instance.u, &folded_w.E);
338
339 // set running_instance for next loop iteration
340 running_instance_w = folded_w;
341 running_committed_instance = folded_committed_instance;
342 }
343 }
344}