sonobe/folding-schemes/src/folding/nova/zk.rs
folding-schemes/src/folding/nova/zk.rsRaw
1/// Implements Nova's zero-knowledge layer, as described in https://eprint.iacr.org/2023/573.pdf.
2///
3/// Remark: this zk layer implementation only covers a subset of the use cases:
4///
5/// We identify 3 interesting places to use the nova zk-layer: one before all the folding pipeline
6/// (Use-case-1), one at the end of the folding pipeline right before the final Decider SNARK
7/// proof (Use-case-2), and a third one for cases where compressed SNARK proofs are not needed, and
8/// just IVC proofs (bigger than SNARK proofs) suffice (Use-case-3):
9///
10/// * Use-case-1: at the beginning of the folding pipeline, right when the user has their original
11/// instance prior to be folded into the running instance, the user can fold it with the
12/// random-satisfying-instance to then have a blinded instance that can be sent to a server that
13/// will fold it with the running instance.
14/// --> In this one, the user could externalize all the IVC folding and also the Decider
15/// final proof generation to a server.
16/// * Use-case-2: at the end of all the IVC folding steps (after n iterations of nova.prove_step),
17/// to 'blind' the IVC proof so then it can be sent to a server that will generate the final
18/// decider SNARK proof.
19/// --> In this one, the user could externalize the Decider final proof generation to a
20/// server.
21/// * Use-case-3: the user does not care about the Decider (final compressed SNARK proof), and
22/// wants to generate a zk-proof of the IVC state to an IVC verifier (without any SNARK proof
23/// involved). In this use-case, the zk is only added at the last IVCProof. Note that this proof
24/// will be much bigger and expensive to verify than a Decider SNARK proof.
25///
26/// The current implementation covers the Use-case-3.
27/// Use-case-1 can be achieved directly by a simpler version of the zk IVC scheme skipping steps
28/// and implemented directly at the app level by folding the original instance with a randomized
29/// instance (steps 2,3,4 from section D.4 of the [HyperNova](https://eprint.iacr.org/2023/573.pdf)
30/// paper).
31/// And the Use-case-2 would require a modified version of the Decider circuits.
32///
33use ark_ff::PrimeField;
34use ark_std::{One, Zero};
35
36use crate::{
37 arith::{r1cs::R1CS, Arith, ArithSampler},
38 folding::traits::CommittedInstanceOps,
39 RngCore,
40};
41use ark_crypto_primitives::sponge::{
42 poseidon::{PoseidonConfig, PoseidonSponge},
43 Absorb, CryptographicSponge,
44};
45use ark_ec::{CurveGroup, Group};
46use ark_r1cs_std::{groups::CurveVar, ToConstraintFieldGadget};
47
48use crate::{commitment::CommitmentScheme, folding::circuits::CF2, frontend::FCircuit, Error};
49
50use super::{
51 nifs::{nova::NIFS, NIFSTrait},
52 CommittedInstance, Nova, Witness,
53};
54
55pub struct RandomizedIVCProof<C1: CurveGroup, C2: CurveGroup> {
56 pub U_i: CommittedInstance<C1>,
57 pub u_i: CommittedInstance<C1>,
58 pub U_r: CommittedInstance<C1>,
59 pub pi: C1, // proof = cmT
60 pub pi_prime: C1, // proof' = cmT'
61 pub W_i_prime: Witness<C1>,
62 pub cf_U_i: CommittedInstance<C2>,
63 pub cf_W_i: Witness<C2>,
64}
65
66impl<C1: CurveGroup, C2: CurveGroup> RandomizedIVCProof<C1, C2>
67where
68 <C1 as Group>::ScalarField: Absorb,
69 <C1 as CurveGroup>::BaseField: PrimeField,
70{
71 /// Compute a zero-knowledge proof of a Nova IVC proof
72 /// It implements the prover of appendix D.4.in https://eprint.iacr.org/2023/573.pdf
73 /// For further details on why folding is hiding, see lemma 9
74 pub fn new<
75 GC1: CurveVar<C1, CF2<C1>> + ToConstraintFieldGadget<CF2<C1>>,
76 GC2: CurveVar<C2, CF2<C2>>,
77 FC: FCircuit<C1::ScalarField>,
78 CS1: CommitmentScheme<C1, true>,
79 CS2: CommitmentScheme<C2, true>,
80 >(
81 nova: &Nova<C1, GC1, C2, GC2, FC, CS1, CS2, true>,
82 mut rng: impl RngCore,
83 ) -> Result<RandomizedIVCProof<C1, C2>, Error>
84 where
85 <C1 as Group>::ScalarField: Absorb,
86 <C2 as Group>::ScalarField: Absorb,
87 <C2 as Group>::ScalarField: PrimeField,
88 <C2 as CurveGroup>::BaseField: PrimeField,
89 <C2 as CurveGroup>::BaseField: Absorb,
90 GC2: ToConstraintFieldGadget<<C2 as CurveGroup>::BaseField>,
91 C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
92 {
93 let mut transcript = PoseidonSponge::<C1::ScalarField>::new(&nova.poseidon_config);
94
95 // I. Compute proof for 'regular' instances
96 // 1. Fold the instance-witness pairs (U_i, W_i) with (u_i, w_i)
97 let (W_f, U_f, cmT, _) = NIFS::<C1, CS1, PoseidonSponge<C1::ScalarField>, true>::prove(
98 &nova.cs_pp,
99 &nova.r1cs,
100 &mut transcript,
101 nova.pp_hash,
102 &nova.w_i,
103 &nova.u_i,
104 &nova.W_i,
105 &nova.U_i,
106 )?;
107
108 // 2. Sample a satisfying relaxed R1CS instance-witness pair (W_r, U_r)
109 let (W_r, U_r) = nova
110 .r1cs
111 .sample_witness_instance::<CS1>(&nova.cs_pp, &mut rng)?;
112
113 // 3. Fold the instance-witness pair (U_f, W_f) with (U_r, W_r)
114 let (W_i_prime, _, cmT_i_prime, _) =
115 NIFS::<C1, CS1, PoseidonSponge<C1::ScalarField>, true>::prove(
116 &nova.cs_pp,
117 &nova.r1cs,
118 &mut transcript,
119 nova.pp_hash,
120 &W_f,
121 &U_f,
122 &W_r,
123 &U_r,
124 )?;
125
126 Ok(RandomizedIVCProof {
127 U_i: nova.U_i.clone(),
128 u_i: nova.u_i.clone(),
129 U_r,
130 pi: cmT,
131 pi_prime: cmT_i_prime,
132 W_i_prime,
133 cf_U_i: nova.cf_U_i.clone(),
134 cf_W_i: nova.cf_W_i.clone(),
135 })
136 }
137
138 /// Verify a zero-knowledge proof of a Nova IVC proof
139 /// It implements the verifier of appendix D.4. in https://eprint.iacr.org/2023/573.pdf
140 #[allow(clippy::too_many_arguments)]
141 pub fn verify<
142 CS1: CommitmentScheme<C1, true>,
143 GC2: CurveVar<C2, CF2<C2>>,
144 CS2: CommitmentScheme<C2, true>,
145 >(
146 r1cs: &R1CS<C1::ScalarField>,
147 cf_r1cs: &R1CS<C2::ScalarField>,
148 pp_hash: C1::ScalarField,
149 poseidon_config: &PoseidonConfig<C1::ScalarField>,
150 i: C1::ScalarField,
151 z_0: Vec<C1::ScalarField>,
152 z_i: Vec<C1::ScalarField>,
153 proof: &RandomizedIVCProof<C1, C2>,
154 ) -> Result<(), Error>
155 where
156 <C1 as Group>::ScalarField: Absorb,
157 <C2 as Group>::ScalarField: Absorb,
158 <C2 as CurveGroup>::BaseField: PrimeField,
159 <C2 as CurveGroup>::BaseField: Absorb,
160 GC2: ToConstraintFieldGadget<<C2 as CurveGroup>::BaseField>,
161 C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
162 {
163 // Handles case where i=0
164 if i == C1::ScalarField::zero() {
165 if z_0 == z_i {
166 return Ok(());
167 } else {
168 return Err(Error::zkIVCVerificationFail);
169 }
170 }
171
172 // 1. Check that u_i.x is correct - including the cyclefold running instance
173 // a. Check length
174 if proof.u_i.x.len() != 2 {
175 return Err(Error::IVCVerificationFail);
176 }
177
178 // b. Check computed hashes are correct
179 let sponge = PoseidonSponge::<C1::ScalarField>::new(poseidon_config);
180 let expected_u_i_x = proof.U_i.hash(&sponge, pp_hash, i, &z_0, &z_i);
181 if expected_u_i_x != proof.u_i.x[0] {
182 return Err(Error::zkIVCVerificationFail);
183 }
184
185 let expected_cf_u_i_x = proof.cf_U_i.hash_cyclefold(&sponge, pp_hash);
186 if expected_cf_u_i_x != proof.u_i.x[1] {
187 return Err(Error::IVCVerificationFail);
188 }
189
190 // 2. Check that u_i values are correct
191 if !proof.u_i.cmE.is_zero() || proof.u_i.u != C1::ScalarField::one() {
192 return Err(Error::zkIVCVerificationFail);
193 }
194
195 let mut transcript = PoseidonSponge::<C1::ScalarField>::new(poseidon_config);
196 // 3. Obtain the U_f folded instance
197 let (U_f, _) = NIFS::<C1, CS1, PoseidonSponge<C1::ScalarField>, true>::verify(
198 &mut transcript,
199 pp_hash,
200 &proof.u_i,
201 &proof.U_i,
202 &proof.pi,
203 )?;
204
205 // 4. Obtain the U^{\prime}_i folded instance
206 let (U_i_prime, _) = NIFS::<C1, CS1, PoseidonSponge<C1::ScalarField>, true>::verify(
207 &mut transcript,
208 pp_hash,
209 &U_f,
210 &proof.U_r,
211 &proof.pi_prime,
212 )?;
213
214 // 5. Check that W^{\prime}_i is a satisfying witness
215 r1cs.check_relation(&proof.W_i_prime, &U_i_prime)?;
216
217 // 6. Check that the cyclefold instance-witness pair satisfies the cyclefold relaxed r1cs
218 cf_r1cs.check_relation(&proof.cf_W_i, &proof.cf_U_i)?;
219
220 Ok(())
221 }
222}
223
224#[cfg(test)]
225pub mod tests {
226 use super::*;
227 use crate::commitment::pedersen::Pedersen;
228 use crate::folding::nova::tests::test_ivc_opt;
229 use crate::frontend::utils::CubicFCircuit;
230 use crate::transcript::poseidon::poseidon_canonical_config;
231 use ark_bn254::{Fr, G1Projective as Projective};
232 use ark_grumpkin::{constraints::GVar as GVar2, Projective as Projective2};
233 use rand::rngs::OsRng;
234
235 // Tests zk proof generation and verification for a valid nova IVC proof
236 #[test]
237 fn test_zk_nova_ivc() {
238 let mut rng = OsRng;
239 let poseidon_config = poseidon_canonical_config::<Fr>();
240 let F_circuit = CubicFCircuit::<Fr>::new(()).unwrap();
241 let (_, nova) = test_ivc_opt::<Pedersen<Projective, true>, Pedersen<Projective2, true>, true>(
242 poseidon_config.clone(),
243 F_circuit,
244 3,
245 );
246
247 let proof = RandomizedIVCProof::new(&nova, &mut rng).unwrap();
248 let verify = RandomizedIVCProof::verify::<
249 Pedersen<Projective, true>,
250 GVar2,
251 Pedersen<Projective2, true>,
252 >(
253 &nova.r1cs,
254 &nova.cf_r1cs,
255 nova.pp_hash,
256 &nova.poseidon_config,
257 nova.i,
258 nova.z_0,
259 nova.z_i,
260 &proof,
261 );
262 assert!(verify.is_ok());
263 }
264
265 #[test]
266 fn test_zk_nova_when_i_is_zero() {
267 let mut rng = OsRng;
268 let poseidon_config = poseidon_canonical_config::<Fr>();
269 let F_circuit = CubicFCircuit::<Fr>::new(()).unwrap();
270 let (_, nova) = test_ivc_opt::<Pedersen<Projective, true>, Pedersen<Projective2, true>, true>(
271 poseidon_config.clone(),
272 F_circuit,
273 0,
274 );
275
276 let proof = RandomizedIVCProof::new(&nova, &mut rng).unwrap();
277 let verify = RandomizedIVCProof::verify::<
278 Pedersen<Projective, true>,
279 GVar2,
280 Pedersen<Projective2, true>,
281 >(
282 &nova.r1cs,
283 &nova.cf_r1cs,
284 nova.pp_hash,
285 &nova.poseidon_config,
286 nova.i,
287 nova.z_0,
288 nova.z_i,
289 &proof,
290 );
291 assert!(verify.is_ok());
292 }
293
294 #[test]
295 fn test_zk_nova_verification_fails_with_wrong_running_instance() {
296 let mut rng = OsRng;
297 let poseidon_config = poseidon_canonical_config::<Fr>();
298 let F_circuit = CubicFCircuit::<Fr>::new(()).unwrap();
299 let (_, nova) = test_ivc_opt::<Pedersen<Projective, true>, Pedersen<Projective2, true>, true>(
300 poseidon_config.clone(),
301 F_circuit,
302 3,
303 );
304 let (_, sampled_committed_instance) = nova
305 .r1cs
306 .sample_witness_instance::<Pedersen<Projective, true>>(&nova.cs_pp, rng)
307 .unwrap();
308
309 // proof verification fails with incorrect running instance
310 let mut nova_with_incorrect_running_instance = nova.clone();
311 nova_with_incorrect_running_instance.U_i = sampled_committed_instance;
312 let incorrect_proof =
313 RandomizedIVCProof::new(&nova_with_incorrect_running_instance, &mut rng).unwrap();
314 let verify = RandomizedIVCProof::verify::<
315 Pedersen<Projective, true>,
316 GVar2,
317 Pedersen<Projective2, true>,
318 >(
319 &nova_with_incorrect_running_instance.r1cs,
320 &nova_with_incorrect_running_instance.cf_r1cs,
321 nova_with_incorrect_running_instance.pp_hash,
322 &nova_with_incorrect_running_instance.poseidon_config,
323 nova_with_incorrect_running_instance.i,
324 nova_with_incorrect_running_instance.z_0,
325 nova_with_incorrect_running_instance.z_i,
326 &incorrect_proof,
327 );
328 assert!(verify.is_err());
329 }
330
331 #[test]
332 fn test_zk_nova_verification_fails_with_wrong_running_witness() {
333 let mut rng = OsRng;
334 let poseidon_config = poseidon_canonical_config::<Fr>();
335 let F_circuit = CubicFCircuit::<Fr>::new(()).unwrap();
336 let (_, nova) = test_ivc_opt::<Pedersen<Projective, true>, Pedersen<Projective2, true>, true>(
337 poseidon_config.clone(),
338 F_circuit,
339 3,
340 );
341 let (sampled_committed_witness, _) = nova
342 .r1cs
343 .sample_witness_instance::<Pedersen<Projective, true>>(&nova.cs_pp, rng)
344 .unwrap();
345
346 // proof generation fails with incorrect running witness
347 let mut nova_with_incorrect_running_witness = nova.clone();
348 nova_with_incorrect_running_witness.W_i = sampled_committed_witness;
349 let incorrect_proof =
350 RandomizedIVCProof::new(&nova_with_incorrect_running_witness, &mut rng).unwrap();
351 let verify = RandomizedIVCProof::verify::<
352 Pedersen<Projective, true>,
353 GVar2,
354 Pedersen<Projective2, true>,
355 >(
356 &nova_with_incorrect_running_witness.r1cs,
357 &nova_with_incorrect_running_witness.cf_r1cs,
358 nova_with_incorrect_running_witness.pp_hash,
359 &nova_with_incorrect_running_witness.poseidon_config,
360 nova_with_incorrect_running_witness.i,
361 nova_with_incorrect_running_witness.z_0,
362 nova_with_incorrect_running_witness.z_i,
363 &incorrect_proof,
364 );
365 assert!(verify.is_err());
366 }
367}