Nova/src/lib.rs
src/lib.rsRaw
1//! This library implements Nova, a high-speed recursive SNARK.
2#![deny(
3 warnings,
4 unused,
5 future_incompatible,
6 nonstandard_style,
7 rust_2018_idioms,
8 missing_docs
9)]
10#![allow(non_snake_case)]
11#![allow(clippy::type_complexity)]
12#![forbid(unsafe_code)]
13
14// private modules
15mod bellperson;
16mod circuit;
17mod constants;
18mod nifs;
19mod r1cs;
20
21// public modules
22pub mod errors;
23pub mod gadgets;
24pub mod provider;
25pub mod spartan;
26pub mod traits;
27
28use crate::bellperson::{
29 r1cs::{NovaShape, NovaWitness},
30 shape_cs::ShapeCS,
31 solver::SatisfyingAssignment,
32};
33use ::bellperson::{Circuit, ConstraintSystem};
34use circuit::{NovaAugmentedCircuit, NovaAugmentedCircuitInputs, NovaAugmentedCircuitParams};
35use constants::{BN_LIMB_WIDTH, BN_N_LIMBS, NUM_FE_WITHOUT_IO_FOR_CRHF, NUM_HASH_BITS};
36use core::marker::PhantomData;
37use errors::NovaError;
38use ff::Field;
39use gadgets::utils::scalar_as_base;
40use nifs::NIFS;
41use r1cs::{R1CSInstance, R1CSShape, R1CSWitness, RelaxedR1CSInstance, RelaxedR1CSWitness};
42use serde::{Deserialize, Serialize};
43use traits::{
44 circuit::StepCircuit,
45 commitment::{CommitmentEngineTrait, CommitmentTrait},
46 snark::RelaxedR1CSSNARKTrait,
47 AbsorbInROTrait, Group, ROConstants, ROConstantsCircuit, ROConstantsTrait, ROTrait,
48};
49
50/// A type that holds public parameters of Nova
51#[derive(Serialize, Deserialize)]
52#[serde(bound = "")]
53pub struct PublicParams<G1, G2, C1, C2>
54where
55 G1: Group<Base = <G2 as Group>::Scalar>,
56 G2: Group<Base = <G1 as Group>::Scalar>,
57 C1: StepCircuit<G1::Scalar>,
58 C2: StepCircuit<G2::Scalar>,
59{
60 F_arity_primary: usize,
61 F_arity_secondary: usize,
62 ro_consts_primary: ROConstants<G1>,
63 ro_consts_circuit_primary: ROConstantsCircuit<G2>,
64 ck_primary: CommitmentKey<G1>,
65 r1cs_shape_primary: R1CSShape<G1>,
66 ro_consts_secondary: ROConstants<G2>,
67 ro_consts_circuit_secondary: ROConstantsCircuit<G1>,
68 ck_secondary: CommitmentKey<G2>,
69 r1cs_shape_secondary: R1CSShape<G2>,
70 augmented_circuit_params_primary: NovaAugmentedCircuitParams,
71 augmented_circuit_params_secondary: NovaAugmentedCircuitParams,
72 _p_c1: PhantomData<C1>,
73 _p_c2: PhantomData<C2>,
74}
75
76impl<G1, G2, C1, C2> PublicParams<G1, G2, C1, C2>
77where
78 G1: Group<Base = <G2 as Group>::Scalar>,
79 G2: Group<Base = <G1 as Group>::Scalar>,
80 C1: StepCircuit<G1::Scalar>,
81 C2: StepCircuit<G2::Scalar>,
82{
83 /// Create a new `PublicParams`
84 pub fn setup(c_primary: C1, c_secondary: C2) -> Self {
85 let augmented_circuit_params_primary =
86 NovaAugmentedCircuitParams::new(BN_LIMB_WIDTH, BN_N_LIMBS, true);
87 let augmented_circuit_params_secondary =
88 NovaAugmentedCircuitParams::new(BN_LIMB_WIDTH, BN_N_LIMBS, false);
89
90 let ro_consts_primary: ROConstants<G1> = ROConstants::<G1>::new();
91 let ro_consts_secondary: ROConstants<G2> = ROConstants::<G2>::new();
92
93 let F_arity_primary = c_primary.arity();
94 let F_arity_secondary = c_secondary.arity();
95
96 // ro_consts_circuit_primary are parameterized by G2 because the type alias uses G2::Base = G1::Scalar
97 let ro_consts_circuit_primary: ROConstantsCircuit<G2> = ROConstantsCircuit::<G2>::new();
98 let ro_consts_circuit_secondary: ROConstantsCircuit<G1> = ROConstantsCircuit::<G1>::new();
99
100 // Initialize ck for the primary
101 let circuit_primary: NovaAugmentedCircuit<G2, C1> = NovaAugmentedCircuit::new(
102 augmented_circuit_params_primary.clone(),
103 None,
104 c_primary,
105 ro_consts_circuit_primary.clone(),
106 );
107 let mut cs: ShapeCS<G1> = ShapeCS::new();
108 let _ = circuit_primary.synthesize(&mut cs);
109 let (r1cs_shape_primary, ck_primary) = cs.r1cs_shape();
110
111 // Initialize ck for the secondary
112 let circuit_secondary: NovaAugmentedCircuit<G1, C2> = NovaAugmentedCircuit::new(
113 augmented_circuit_params_secondary.clone(),
114 None,
115 c_secondary,
116 ro_consts_circuit_secondary.clone(),
117 );
118 let mut cs: ShapeCS<G2> = ShapeCS::new();
119 let _ = circuit_secondary.synthesize(&mut cs);
120 let (r1cs_shape_secondary, ck_secondary) = cs.r1cs_shape();
121
122 Self {
123 F_arity_primary,
124 F_arity_secondary,
125 ro_consts_primary,
126 ro_consts_circuit_primary,
127 ck_primary,
128 r1cs_shape_primary,
129 ro_consts_secondary,
130 ro_consts_circuit_secondary,
131 ck_secondary,
132 r1cs_shape_secondary,
133 augmented_circuit_params_primary,
134 augmented_circuit_params_secondary,
135 _p_c1: Default::default(),
136 _p_c2: Default::default(),
137 }
138 }
139
140 /// Returns the number of constraints in the primary and secondary circuits
141 pub fn num_constraints(&self) -> (usize, usize) {
142 (
143 self.r1cs_shape_primary.num_cons,
144 self.r1cs_shape_secondary.num_cons,
145 )
146 }
147
148 /// Returns the number of variables in the primary and secondary circuits
149 pub fn num_variables(&self) -> (usize, usize) {
150 (
151 self.r1cs_shape_primary.num_vars,
152 self.r1cs_shape_secondary.num_vars,
153 )
154 }
155}
156
157/// A SNARK that proves the correct execution of an incremental computation
158#[derive(Clone, Debug, Serialize, Deserialize)]
159#[serde(bound = "")]
160pub struct RecursiveSNARK<G1, G2, C1, C2>
161where
162 G1: Group<Base = <G2 as Group>::Scalar>,
163 G2: Group<Base = <G1 as Group>::Scalar>,
164 C1: StepCircuit<G1::Scalar>,
165 C2: StepCircuit<G2::Scalar>,
166{
167 r_W_primary: RelaxedR1CSWitness<G1>,
168 r_U_primary: RelaxedR1CSInstance<G1>,
169 l_w_primary: R1CSWitness<G1>,
170 l_u_primary: R1CSInstance<G1>,
171 r_W_secondary: RelaxedR1CSWitness<G2>,
172 r_U_secondary: RelaxedR1CSInstance<G2>,
173 l_w_secondary: R1CSWitness<G2>,
174 l_u_secondary: R1CSInstance<G2>,
175 i: usize,
176 zi_primary: Vec<G1::Scalar>,
177 zi_secondary: Vec<G2::Scalar>,
178 _p_c1: PhantomData<C1>,
179 _p_c2: PhantomData<C2>,
180}
181
182impl<G1, G2, C1, C2> RecursiveSNARK<G1, G2, C1, C2>
183where
184 G1: Group<Base = <G2 as Group>::Scalar>,
185 G2: Group<Base = <G1 as Group>::Scalar>,
186 C1: StepCircuit<G1::Scalar>,
187 C2: StepCircuit<G2::Scalar>,
188{
189 /// Create a new `RecursiveSNARK` (or updates the provided `RecursiveSNARK`)
190 /// by executing a step of the incremental computation
191 pub fn prove_step(
192 pp: &PublicParams<G1, G2, C1, C2>,
193 recursive_snark: Option<Self>,
194 c_primary: C1,
195 c_secondary: C2,
196 z0_primary: Vec<G1::Scalar>,
197 z0_secondary: Vec<G2::Scalar>,
198 ) -> Result<Self, NovaError> {
199 if z0_primary.len() != pp.F_arity_primary || z0_secondary.len() != pp.F_arity_secondary {
200 return Err(NovaError::InvalidInitialInputLength);
201 }
202
203 match recursive_snark {
204 None => {
205 // base case for the primary
206 let mut cs_primary: SatisfyingAssignment<G1> = SatisfyingAssignment::new();
207 let inputs_primary: NovaAugmentedCircuitInputs<G2> = NovaAugmentedCircuitInputs::new(
208 pp.r1cs_shape_secondary.get_digest(),
209 G1::Scalar::zero(),
210 z0_primary.clone(),
211 None,
212 None,
213 None,
214 None,
215 );
216
217 let circuit_primary: NovaAugmentedCircuit<G2, C1> = NovaAugmentedCircuit::new(
218 pp.augmented_circuit_params_primary.clone(),
219 Some(inputs_primary),
220 c_primary.clone(),
221 pp.ro_consts_circuit_primary.clone(),
222 );
223 let _ = circuit_primary.synthesize(&mut cs_primary);
224 let (u_primary, w_primary) = cs_primary
225 .r1cs_instance_and_witness(&pp.r1cs_shape_primary, &pp.ck_primary)
226 .map_err(|_e| NovaError::UnSat)?;
227
228 // base case for the secondary
229 let mut cs_secondary: SatisfyingAssignment<G2> = SatisfyingAssignment::new();
230 let inputs_secondary: NovaAugmentedCircuitInputs<G1> = NovaAugmentedCircuitInputs::new(
231 pp.r1cs_shape_primary.get_digest(),
232 G2::Scalar::zero(),
233 z0_secondary.clone(),
234 None,
235 None,
236 Some(u_primary.clone()),
237 None,
238 );
239 let circuit_secondary: NovaAugmentedCircuit<G1, C2> = NovaAugmentedCircuit::new(
240 pp.augmented_circuit_params_secondary.clone(),
241 Some(inputs_secondary),
242 c_secondary.clone(),
243 pp.ro_consts_circuit_secondary.clone(),
244 );
245 let _ = circuit_secondary.synthesize(&mut cs_secondary);
246 let (u_secondary, w_secondary) = cs_secondary
247 .r1cs_instance_and_witness(&pp.r1cs_shape_secondary, &pp.ck_secondary)
248 .map_err(|_e| NovaError::UnSat)?;
249
250 // IVC proof for the primary circuit
251 let l_w_primary = w_primary;
252 let l_u_primary = u_primary;
253 let r_W_primary =
254 RelaxedR1CSWitness::from_r1cs_witness(&pp.r1cs_shape_primary, &l_w_primary);
255 let r_U_primary = RelaxedR1CSInstance::from_r1cs_instance(
256 &pp.ck_primary,
257 &pp.r1cs_shape_primary,
258 &l_u_primary,
259 );
260
261 // IVC proof of the secondary circuit
262 let l_w_secondary = w_secondary;
263 let l_u_secondary = u_secondary;
264 let r_W_secondary = RelaxedR1CSWitness::<G2>::default(&pp.r1cs_shape_secondary);
265 let r_U_secondary =
266 RelaxedR1CSInstance::<G2>::default(&pp.ck_secondary, &pp.r1cs_shape_secondary);
267
268 // Outputs of the two circuits thus far
269 let zi_primary = c_primary.output(&z0_primary);
270 let zi_secondary = c_secondary.output(&z0_secondary);
271
272 if zi_primary.len() != pp.F_arity_primary || zi_secondary.len() != pp.F_arity_secondary {
273 return Err(NovaError::InvalidStepOutputLength);
274 }
275
276 Ok(Self {
277 r_W_primary,
278 r_U_primary,
279 l_w_primary,
280 l_u_primary,
281 r_W_secondary,
282 r_U_secondary,
283 l_w_secondary,
284 l_u_secondary,
285 i: 1_usize,
286 zi_primary,
287 zi_secondary,
288 _p_c1: Default::default(),
289 _p_c2: Default::default(),
290 })
291 }
292 Some(r_snark) => {
293 // fold the secondary circuit's instance
294 let (nifs_secondary, (r_U_secondary, r_W_secondary)) = NIFS::prove(
295 &pp.ck_secondary,
296 &pp.ro_consts_secondary,
297 &pp.r1cs_shape_secondary,
298 &r_snark.r_U_secondary,
299 &r_snark.r_W_secondary,
300 &r_snark.l_u_secondary,
301 &r_snark.l_w_secondary,
302 )?;
303
304 let mut cs_primary: SatisfyingAssignment<G1> = SatisfyingAssignment::new();
305 let inputs_primary: NovaAugmentedCircuitInputs<G2> = NovaAugmentedCircuitInputs::new(
306 pp.r1cs_shape_secondary.get_digest(),
307 G1::Scalar::from(r_snark.i as u64),
308 z0_primary,
309 Some(r_snark.zi_primary.clone()),
310 Some(r_snark.r_U_secondary.clone()),
311 Some(r_snark.l_u_secondary.clone()),
312 Some(Commitment::<G2>::decompress(&nifs_secondary.comm_T)?),
313 );
314
315 let circuit_primary: NovaAugmentedCircuit<G2, C1> = NovaAugmentedCircuit::new(
316 pp.augmented_circuit_params_primary.clone(),
317 Some(inputs_primary),
318 c_primary.clone(),
319 pp.ro_consts_circuit_primary.clone(),
320 );
321 let _ = circuit_primary.synthesize(&mut cs_primary);
322
323 let (l_u_primary, l_w_primary) = cs_primary
324 .r1cs_instance_and_witness(&pp.r1cs_shape_primary, &pp.ck_primary)
325 .map_err(|_e| NovaError::UnSat)?;
326
327 // fold the primary circuit's instance
328 let (nifs_primary, (r_U_primary, r_W_primary)) = NIFS::prove(
329 &pp.ck_primary,
330 &pp.ro_consts_primary,
331 &pp.r1cs_shape_primary,
332 &r_snark.r_U_primary,
333 &r_snark.r_W_primary,
334 &l_u_primary,
335 &l_w_primary,
336 )?;
337
338 let mut cs_secondary: SatisfyingAssignment<G2> = SatisfyingAssignment::new();
339 let inputs_secondary: NovaAugmentedCircuitInputs<G1> = NovaAugmentedCircuitInputs::new(
340 pp.r1cs_shape_primary.get_digest(),
341 G2::Scalar::from(r_snark.i as u64),
342 z0_secondary,
343 Some(r_snark.zi_secondary.clone()),
344 Some(r_snark.r_U_primary.clone()),
345 Some(l_u_primary.clone()),
346 Some(Commitment::<G1>::decompress(&nifs_primary.comm_T)?),
347 );
348
349 let circuit_secondary: NovaAugmentedCircuit<G1, C2> = NovaAugmentedCircuit::new(
350 pp.augmented_circuit_params_secondary.clone(),
351 Some(inputs_secondary),
352 c_secondary.clone(),
353 pp.ro_consts_circuit_secondary.clone(),
354 );
355 let _ = circuit_secondary.synthesize(&mut cs_secondary);
356
357 let (l_u_secondary, l_w_secondary) = cs_secondary
358 .r1cs_instance_and_witness(&pp.r1cs_shape_secondary, &pp.ck_secondary)
359 .map_err(|_e| NovaError::UnSat)?;
360
361 // update the running instances and witnesses
362 let zi_primary = c_primary.output(&r_snark.zi_primary);
363 let zi_secondary = c_secondary.output(&r_snark.zi_secondary);
364
365 Ok(Self {
366 r_W_primary,
367 r_U_primary,
368 l_w_primary,
369 l_u_primary,
370 r_W_secondary,
371 r_U_secondary,
372 l_w_secondary,
373 l_u_secondary,
374 i: r_snark.i + 1,
375 zi_primary,
376 zi_secondary,
377 _p_c1: Default::default(),
378 _p_c2: Default::default(),
379 })
380 }
381 }
382 }
383
384 /// Verify the correctness of the `RecursiveSNARK`
385 pub fn verify(
386 &self,
387 pp: &PublicParams<G1, G2, C1, C2>,
388 num_steps: usize,
389 z0_primary: Vec<G1::Scalar>,
390 z0_secondary: Vec<G2::Scalar>,
391 ) -> Result<(Vec<G1::Scalar>, Vec<G2::Scalar>), NovaError> {
392 // number of steps cannot be zero
393 if num_steps == 0 {
394 return Err(NovaError::ProofVerifyError);
395 }
396
397 // check if the provided proof has executed num_steps
398 if self.i != num_steps {
399 return Err(NovaError::ProofVerifyError);
400 }
401
402 // check if the (relaxed) R1CS instances have two public outputs
403 if self.l_u_primary.X.len() != 2
404 || self.l_u_secondary.X.len() != 2
405 || self.r_U_primary.X.len() != 2
406 || self.r_U_secondary.X.len() != 2
407 {
408 return Err(NovaError::ProofVerifyError);
409 }
410
411 // check if the output hashes in R1CS instances point to the right running instances
412 let (hash_primary, hash_secondary) = {
413 let mut hasher = <G2 as Group>::RO::new(
414 pp.ro_consts_secondary.clone(),
415 NUM_FE_WITHOUT_IO_FOR_CRHF + 2 * pp.F_arity_primary,
416 );
417 hasher.absorb(scalar_as_base::<G2>(pp.r1cs_shape_secondary.get_digest()));
418 hasher.absorb(G1::Scalar::from(num_steps as u64));
419 for e in &z0_primary {
420 hasher.absorb(*e);
421 }
422 for e in &self.zi_primary {
423 hasher.absorb(*e);
424 }
425 self.r_U_secondary.absorb_in_ro(&mut hasher);
426
427 let mut hasher2 = <G1 as Group>::RO::new(
428 pp.ro_consts_primary.clone(),
429 NUM_FE_WITHOUT_IO_FOR_CRHF + 2 * pp.F_arity_secondary,
430 );
431 hasher2.absorb(scalar_as_base::<G1>(pp.r1cs_shape_primary.get_digest()));
432 hasher2.absorb(G2::Scalar::from(num_steps as u64));
433 for e in &z0_secondary {
434 hasher2.absorb(*e);
435 }
436 for e in &self.zi_secondary {
437 hasher2.absorb(*e);
438 }
439 self.r_U_primary.absorb_in_ro(&mut hasher2);
440
441 (
442 hasher.squeeze(NUM_HASH_BITS),
443 hasher2.squeeze(NUM_HASH_BITS),
444 )
445 };
446
447 if hash_primary != scalar_as_base::<G1>(self.l_u_primary.X[1])
448 || hash_secondary != scalar_as_base::<G2>(self.l_u_secondary.X[1])
449 {
450 return Err(NovaError::ProofVerifyError);
451 }
452
453 // check the satisfiability of the provided instances
454 let ((res_r_primary, res_l_primary), (res_r_secondary, res_l_secondary)) = rayon::join(
455 || {
456 rayon::join(
457 || {
458 pp.r1cs_shape_primary.is_sat_relaxed(
459 &pp.ck_primary,
460 &self.r_U_primary,
461 &self.r_W_primary,
462 )
463 },
464 || {
465 pp.r1cs_shape_primary
466 .is_sat(&pp.ck_primary, &self.l_u_primary, &self.l_w_primary)
467 },
468 )
469 },
470 || {
471 rayon::join(
472 || {
473 pp.r1cs_shape_secondary.is_sat_relaxed(
474 &pp.ck_secondary,
475 &self.r_U_secondary,
476 &self.r_W_secondary,
477 )
478 },
479 || {
480 pp.r1cs_shape_secondary.is_sat(
481 &pp.ck_secondary,
482 &self.l_u_secondary,
483 &self.l_w_secondary,
484 )
485 },
486 )
487 },
488 );
489
490 // check the returned res objects
491 res_r_primary?;
492 res_l_primary?;
493 res_r_secondary?;
494 res_l_secondary?;
495
496 Ok((self.zi_primary.clone(), self.zi_secondary.clone()))
497 }
498}
499
500/// A type that holds the prover key for `CompressedSNARK`
501#[derive(Clone, Debug, Serialize, Deserialize)]
502#[serde(bound = "")]
503pub struct ProverKey<G1, G2, C1, C2, S1, S2>
504where
505 G1: Group<Base = <G2 as Group>::Scalar>,
506 G2: Group<Base = <G1 as Group>::Scalar>,
507 C1: StepCircuit<G1::Scalar>,
508 C2: StepCircuit<G2::Scalar>,
509 S1: RelaxedR1CSSNARKTrait<G1>,
510 S2: RelaxedR1CSSNARKTrait<G2>,
511{
512 pk_primary: S1::ProverKey,
513 pk_secondary: S2::ProverKey,
514 _p_c1: PhantomData<C1>,
515 _p_c2: PhantomData<C2>,
516}
517
518/// A type that holds the verifier key for `CompressedSNARK`
519#[derive(Clone, Serialize, Deserialize)]
520#[serde(bound = "")]
521pub struct VerifierKey<G1, G2, C1, C2, S1, S2>
522where
523 G1: Group<Base = <G2 as Group>::Scalar>,
524 G2: Group<Base = <G1 as Group>::Scalar>,
525 C1: StepCircuit<G1::Scalar>,
526 C2: StepCircuit<G2::Scalar>,
527 S1: RelaxedR1CSSNARKTrait<G1>,
528 S2: RelaxedR1CSSNARKTrait<G2>,
529{
530 F_arity_primary: usize,
531 F_arity_secondary: usize,
532 ro_consts_primary: ROConstants<G1>,
533 ro_consts_secondary: ROConstants<G2>,
534 r1cs_shape_primary_digest: G1::Scalar,
535 r1cs_shape_secondary_digest: G2::Scalar,
536 vk_primary: S1::VerifierKey,
537 vk_secondary: S2::VerifierKey,
538 _p_c1: PhantomData<C1>,
539 _p_c2: PhantomData<C2>,
540}
541
542/// A SNARK that proves the knowledge of a valid `RecursiveSNARK`
543#[derive(Clone, Serialize, Deserialize)]
544#[serde(bound = "")]
545pub struct CompressedSNARK<G1, G2, C1, C2, S1, S2>
546where
547 G1: Group<Base = <G2 as Group>::Scalar>,
548 G2: Group<Base = <G1 as Group>::Scalar>,
549 C1: StepCircuit<G1::Scalar>,
550 C2: StepCircuit<G2::Scalar>,
551 S1: RelaxedR1CSSNARKTrait<G1>,
552 S2: RelaxedR1CSSNARKTrait<G2>,
553{
554 r_U_primary: RelaxedR1CSInstance<G1>,
555 l_u_primary: R1CSInstance<G1>,
556 nifs_primary: NIFS<G1>,
557 f_W_snark_primary: S1,
558
559 r_U_secondary: RelaxedR1CSInstance<G2>,
560 l_u_secondary: R1CSInstance<G2>,
561 nifs_secondary: NIFS<G2>,
562 f_W_snark_secondary: S2,
563
564 zn_primary: Vec<G1::Scalar>,
565 zn_secondary: Vec<G2::Scalar>,
566
567 _p_c1: PhantomData<C1>,
568 _p_c2: PhantomData<C2>,
569}
570
571impl<G1, G2, C1, C2, S1, S2> CompressedSNARK<G1, G2, C1, C2, S1, S2>
572where
573 G1: Group<Base = <G2 as Group>::Scalar>,
574 G2: Group<Base = <G1 as Group>::Scalar>,
575 C1: StepCircuit<G1::Scalar>,
576 C2: StepCircuit<G2::Scalar>,
577 S1: RelaxedR1CSSNARKTrait<G1>,
578 S2: RelaxedR1CSSNARKTrait<G2>,
579{
580 /// Creates prover and verifier keys for `CompressedSNARK`
581 pub fn setup(
582 pp: &PublicParams<G1, G2, C1, C2>,
583 ) -> Result<
584 (
585 ProverKey<G1, G2, C1, C2, S1, S2>,
586 VerifierKey<G1, G2, C1, C2, S1, S2>,
587 ),
588 NovaError,
589 > {
590 let (pk_primary, vk_primary) = S1::setup(&pp.ck_primary, &pp.r1cs_shape_primary)?;
591 let (pk_secondary, vk_secondary) = S2::setup(&pp.ck_secondary, &pp.r1cs_shape_secondary)?;
592
593 let pk = ProverKey {
594 pk_primary,
595 pk_secondary,
596 _p_c1: Default::default(),
597 _p_c2: Default::default(),
598 };
599
600 let vk = VerifierKey {
601 F_arity_primary: pp.F_arity_primary,
602 F_arity_secondary: pp.F_arity_secondary,
603 ro_consts_primary: pp.ro_consts_primary.clone(),
604 ro_consts_secondary: pp.ro_consts_secondary.clone(),
605 r1cs_shape_primary_digest: pp.r1cs_shape_primary.get_digest(),
606 r1cs_shape_secondary_digest: pp.r1cs_shape_secondary.get_digest(),
607 vk_primary,
608 vk_secondary,
609 _p_c1: Default::default(),
610 _p_c2: Default::default(),
611 };
612
613 Ok((pk, vk))
614 }
615
616 /// Create a new `CompressedSNARK`
617 pub fn prove(
618 pp: &PublicParams<G1, G2, C1, C2>,
619 pk: &ProverKey<G1, G2, C1, C2, S1, S2>,
620 recursive_snark: &RecursiveSNARK<G1, G2, C1, C2>,
621 ) -> Result<Self, NovaError> {
622 let (res_primary, res_secondary) = rayon::join(
623 // fold the primary circuit's instance
624 || {
625 NIFS::prove(
626 &pp.ck_primary,
627 &pp.ro_consts_primary,
628 &pp.r1cs_shape_primary,
629 &recursive_snark.r_U_primary,
630 &recursive_snark.r_W_primary,
631 &recursive_snark.l_u_primary,
632 &recursive_snark.l_w_primary,
633 )
634 },
635 || {
636 // fold the secondary circuit's instance
637 NIFS::prove(
638 &pp.ck_secondary,
639 &pp.ro_consts_secondary,
640 &pp.r1cs_shape_secondary,
641 &recursive_snark.r_U_secondary,
642 &recursive_snark.r_W_secondary,
643 &recursive_snark.l_u_secondary,
644 &recursive_snark.l_w_secondary,
645 )
646 },
647 );
648
649 let (nifs_primary, (f_U_primary, f_W_primary)) = res_primary?;
650 let (nifs_secondary, (f_U_secondary, f_W_secondary)) = res_secondary?;
651
652 // create SNARKs proving the knowledge of f_W_primary and f_W_secondary
653 let (f_W_snark_primary, f_W_snark_secondary) = rayon::join(
654 || S1::prove(&pp.ck_primary, &pk.pk_primary, &f_U_primary, &f_W_primary),
655 || {
656 S2::prove(
657 &pp.ck_secondary,
658 &pk.pk_secondary,
659 &f_U_secondary,
660 &f_W_secondary,
661 )
662 },
663 );
664
665 Ok(Self {
666 r_U_primary: recursive_snark.r_U_primary.clone(),
667 l_u_primary: recursive_snark.l_u_primary.clone(),
668 nifs_primary,
669 f_W_snark_primary: f_W_snark_primary?,
670
671 r_U_secondary: recursive_snark.r_U_secondary.clone(),
672 l_u_secondary: recursive_snark.l_u_secondary.clone(),
673 nifs_secondary,
674 f_W_snark_secondary: f_W_snark_secondary?,
675
676 zn_primary: recursive_snark.zi_primary.clone(),
677 zn_secondary: recursive_snark.zi_secondary.clone(),
678
679 _p_c1: Default::default(),
680 _p_c2: Default::default(),
681 })
682 }
683
684 /// Verify the correctness of the `CompressedSNARK`
685 pub fn verify(
686 &self,
687 vk: &VerifierKey<G1, G2, C1, C2, S1, S2>,
688 num_steps: usize,
689 z0_primary: Vec<G1::Scalar>,
690 z0_secondary: Vec<G2::Scalar>,
691 ) -> Result<(Vec<G1::Scalar>, Vec<G2::Scalar>), NovaError> {
692 // number of steps cannot be zero
693 if num_steps == 0 {
694 return Err(NovaError::ProofVerifyError);
695 }
696
697 // check if the (relaxed) R1CS instances have two public outputs
698 if self.l_u_primary.X.len() != 2
699 || self.l_u_secondary.X.len() != 2
700 || self.r_U_primary.X.len() != 2
701 || self.r_U_secondary.X.len() != 2
702 {
703 return Err(NovaError::ProofVerifyError);
704 }
705
706 // check if the output hashes in R1CS instances point to the right running instances
707 let (hash_primary, hash_secondary) = {
708 let mut hasher = <G2 as Group>::RO::new(
709 vk.ro_consts_secondary.clone(),
710 NUM_FE_WITHOUT_IO_FOR_CRHF + 2 * vk.F_arity_primary,
711 );
712 hasher.absorb(scalar_as_base::<G2>(vk.r1cs_shape_secondary_digest));
713 hasher.absorb(G1::Scalar::from(num_steps as u64));
714 for e in z0_primary {
715 hasher.absorb(e);
716 }
717 for e in &self.zn_primary {
718 hasher.absorb(*e);
719 }
720 self.r_U_secondary.absorb_in_ro(&mut hasher);
721
722 let mut hasher2 = <G1 as Group>::RO::new(
723 vk.ro_consts_primary.clone(),
724 NUM_FE_WITHOUT_IO_FOR_CRHF + 2 * vk.F_arity_secondary,
725 );
726 hasher2.absorb(scalar_as_base::<G1>(vk.r1cs_shape_primary_digest));
727 hasher2.absorb(G2::Scalar::from(num_steps as u64));
728 for e in z0_secondary {
729 hasher2.absorb(e);
730 }
731 for e in &self.zn_secondary {
732 hasher2.absorb(*e);
733 }
734 self.r_U_primary.absorb_in_ro(&mut hasher2);
735
736 (
737 hasher.squeeze(NUM_HASH_BITS),
738 hasher2.squeeze(NUM_HASH_BITS),
739 )
740 };
741
742 if hash_primary != scalar_as_base::<G1>(self.l_u_primary.X[1])
743 || hash_secondary != scalar_as_base::<G2>(self.l_u_secondary.X[1])
744 {
745 return Err(NovaError::ProofVerifyError);
746 }
747
748 // fold the running instance and last instance to get a folded instance
749 let f_U_primary = self.nifs_primary.verify(
750 &vk.ro_consts_primary,
751 &vk.r1cs_shape_primary_digest,
752 &self.r_U_primary,
753 &self.l_u_primary,
754 )?;
755 let f_U_secondary = self.nifs_secondary.verify(
756 &vk.ro_consts_secondary,
757 &vk.r1cs_shape_secondary_digest,
758 &self.r_U_secondary,
759 &self.l_u_secondary,
760 )?;
761
762 // check the satisfiability of the folded instances using SNARKs proving the knowledge of their satisfying witnesses
763 let (res_primary, res_secondary) = rayon::join(
764 || self.f_W_snark_primary.verify(&vk.vk_primary, &f_U_primary),
765 || {
766 self
767 .f_W_snark_secondary
768 .verify(&vk.vk_secondary, &f_U_secondary)
769 },
770 );
771
772 res_primary?;
773 res_secondary?;
774
775 Ok((self.zn_primary.clone(), self.zn_secondary.clone()))
776 }
777}
778
779type CommitmentKey<G> = <<G as traits::Group>::CE as CommitmentEngineTrait<G>>::CommitmentKey;
780type Commitment<G> = <<G as Group>::CE as CommitmentEngineTrait<G>>::Commitment;
781type CompressedCommitment<G> = <<<G as Group>::CE as CommitmentEngineTrait<G>>::Commitment as CommitmentTrait<G>>::CompressedCommitment;
782type CE<G> = <G as Group>::CE;
783
784#[cfg(test)]
785mod tests {
786 use super::*;
787 type G1 = pasta_curves::pallas::Point;
788 type G2 = pasta_curves::vesta::Point;
789 type EE1 = provider::ipa_pc::EvaluationEngine<G1>;
790 type EE2 = provider::ipa_pc::EvaluationEngine<G2>;
791 type S1 = spartan::RelaxedR1CSSNARK<G1, EE1>;
792 type S2 = spartan::RelaxedR1CSSNARK<G2, EE2>;
793 use ::bellperson::{gadgets::num::AllocatedNum, ConstraintSystem, SynthesisError};
794 use core::marker::PhantomData;
795 use ff::PrimeField;
796 use traits::circuit::TrivialTestCircuit;
797
798 #[derive(Clone, Debug, Default)]
799 struct CubicCircuit<F: PrimeField> {
800 _p: PhantomData<F>,
801 }
802
803 impl<F> StepCircuit<F> for CubicCircuit<F>
804 where
805 F: PrimeField,
806 {
807 fn arity(&self) -> usize {
808 1
809 }
810
811 fn synthesize<CS: ConstraintSystem<F>>(
812 &self,
813 cs: &mut CS,
814 z: &[AllocatedNum<F>],
815 ) -> Result<Vec<AllocatedNum<F>>, SynthesisError> {
816 // Consider a cubic equation: `x^3 + x + 5 = y`, where `x` and `y` are respectively the input and output.
817 let x = &z[0];
818 let x_sq = x.square(cs.namespace(|| "x_sq"))?;
819 let x_cu = x_sq.mul(cs.namespace(|| "x_cu"), x)?;
820 let y = AllocatedNum::alloc(cs.namespace(|| "y"), || {
821 Ok(x_cu.get_value().unwrap() + x.get_value().unwrap() + F::from(5u64))
822 })?;
823
824 cs.enforce(
825 || "y = x^3 + x + 5",
826 |lc| {
827 lc + x_cu.get_variable()
828 + x.get_variable()
829 + CS::one()
830 + CS::one()
831 + CS::one()
832 + CS::one()
833 + CS::one()
834 },
835 |lc| lc + CS::one(),
836 |lc| lc + y.get_variable(),
837 );
838
839 Ok(vec![y])
840 }
841
842 fn output(&self, z: &[F]) -> Vec<F> {
843 vec![z[0] * z[0] * z[0] + z[0] + F::from(5u64)]
844 }
845 }
846
847 #[test]
848 fn test_ivc_trivial() {
849 // produce public parameters
850 let pp = PublicParams::<
851 G1,
852 G2,
853 TrivialTestCircuit<<G1 as Group>::Scalar>,
854 TrivialTestCircuit<<G2 as Group>::Scalar>,
855 >::setup(TrivialTestCircuit::default(), TrivialTestCircuit::default());
856
857 let num_steps = 1;
858
859 // produce a recursive SNARK
860 let res = RecursiveSNARK::prove_step(
861 &pp,
862 None,
863 TrivialTestCircuit::default(),
864 TrivialTestCircuit::default(),
865 vec![<G1 as Group>::Scalar::zero()],
866 vec![<G2 as Group>::Scalar::zero()],
867 );
868 assert!(res.is_ok());
869 let recursive_snark = res.unwrap();
870
871 // verify the recursive SNARK
872 let res = recursive_snark.verify(
873 &pp,
874 num_steps,
875 vec![<G1 as Group>::Scalar::zero()],
876 vec![<G2 as Group>::Scalar::zero()],
877 );
878 assert!(res.is_ok());
879 }
880
881 #[test]
882 fn test_ivc_nontrivial() {
883 let circuit_primary = TrivialTestCircuit::default();
884 let circuit_secondary = CubicCircuit::default();
885
886 // produce public parameters
887 let pp = PublicParams::<
888 G1,
889 G2,
890 TrivialTestCircuit<<G1 as Group>::Scalar>,
891 CubicCircuit<<G2 as Group>::Scalar>,
892 >::setup(circuit_primary.clone(), circuit_secondary.clone());
893
894 let num_steps = 3;
895
896 // produce a recursive SNARK
897 let mut recursive_snark: Option<
898 RecursiveSNARK<
899 G1,
900 G2,
901 TrivialTestCircuit<<G1 as Group>::Scalar>,
902 CubicCircuit<<G2 as Group>::Scalar>,
903 >,
904 > = None;
905
906 for i in 0..num_steps {
907 let res = RecursiveSNARK::prove_step(
908 &pp,
909 recursive_snark,
910 circuit_primary.clone(),
911 circuit_secondary.clone(),
912 vec![<G1 as Group>::Scalar::one()],
913 vec![<G2 as Group>::Scalar::zero()],
914 );
915 assert!(res.is_ok());
916 let recursive_snark_unwrapped = res.unwrap();
917
918 // verify the recursive snark at each step of recursion
919 let res = recursive_snark_unwrapped.verify(
920 &pp,
921 i + 1,
922 vec![<G1 as Group>::Scalar::one()],
923 vec![<G2 as Group>::Scalar::zero()],
924 );
925 assert!(res.is_ok());
926
927 // set the running variable for the next iteration
928 recursive_snark = Some(recursive_snark_unwrapped);
929 }
930
931 assert!(recursive_snark.is_some());
932 let recursive_snark = recursive_snark.unwrap();
933
934 // verify the recursive SNARK
935 let res = recursive_snark.verify(
936 &pp,
937 num_steps,
938 vec![<G1 as Group>::Scalar::one()],
939 vec![<G2 as Group>::Scalar::zero()],
940 );
941 assert!(res.is_ok());
942
943 let (zn_primary, zn_secondary) = res.unwrap();
944
945 // sanity: check the claimed output with a direct computation of the same
946 assert_eq!(zn_primary, vec![<G1 as Group>::Scalar::one()]);
947 let mut zn_secondary_direct = vec![<G2 as Group>::Scalar::zero()];
948 for _i in 0..num_steps {
949 zn_secondary_direct = CubicCircuit::default().output(&zn_secondary_direct);
950 }
951 assert_eq!(zn_secondary, zn_secondary_direct);
952 assert_eq!(zn_secondary, vec![<G2 as Group>::Scalar::from(2460515u64)]);
953 }
954
955 #[test]
956 fn test_ivc_nontrivial_with_compression() {
957 let circuit_primary = TrivialTestCircuit::default();
958 let circuit_secondary = CubicCircuit::default();
959
960 // produce public parameters
961 let pp = PublicParams::<
962 G1,
963 G2,
964 TrivialTestCircuit<<G1 as Group>::Scalar>,
965 CubicCircuit<<G2 as Group>::Scalar>,
966 >::setup(circuit_primary.clone(), circuit_secondary.clone());
967
968 let num_steps = 3;
969
970 // produce a recursive SNARK
971 let mut recursive_snark: Option<
972 RecursiveSNARK<
973 G1,
974 G2,
975 TrivialTestCircuit<<G1 as Group>::Scalar>,
976 CubicCircuit<<G2 as Group>::Scalar>,
977 >,
978 > = None;
979
980 for _i in 0..num_steps {
981 let res = RecursiveSNARK::prove_step(
982 &pp,
983 recursive_snark,
984 circuit_primary.clone(),
985 circuit_secondary.clone(),
986 vec![<G1 as Group>::Scalar::one()],
987 vec![<G2 as Group>::Scalar::zero()],
988 );
989 assert!(res.is_ok());
990 recursive_snark = Some(res.unwrap());
991 }
992
993 assert!(recursive_snark.is_some());
994 let recursive_snark = recursive_snark.unwrap();
995
996 // verify the recursive SNARK
997 let res = recursive_snark.verify(
998 &pp,
999 num_steps,
1000 vec![<G1 as Group>::Scalar::one()],
1001 vec![<G2 as Group>::Scalar::zero()],
1002 );
1003 assert!(res.is_ok());
1004
1005 let (zn_primary, zn_secondary) = res.unwrap();
1006
1007 // sanity: check the claimed output with a direct computation of the same
1008 assert_eq!(zn_primary, vec![<G1 as Group>::Scalar::one()]);
1009 let mut zn_secondary_direct = vec![<G2 as Group>::Scalar::zero()];
1010 for _i in 0..num_steps {
1011 zn_secondary_direct = CubicCircuit::default().output(&zn_secondary_direct);
1012 }
1013 assert_eq!(zn_secondary, zn_secondary_direct);
1014 assert_eq!(zn_secondary, vec![<G2 as Group>::Scalar::from(2460515u64)]);
1015
1016 // produce the prover and verifier keys for compressed snark
1017 let (pk, vk) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
1018
1019 // produce a compressed SNARK
1020 let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &pk, &recursive_snark);
1021 assert!(res.is_ok());
1022 let compressed_snark = res.unwrap();
1023
1024 // verify the compressed SNARK
1025 let res = compressed_snark.verify(
1026 &vk,
1027 num_steps,
1028 vec![<G1 as Group>::Scalar::one()],
1029 vec![<G2 as Group>::Scalar::zero()],
1030 );
1031 assert!(res.is_ok());
1032 }
1033
1034 #[test]
1035 fn test_ivc_nontrivial_with_spark_compression() {
1036 let circuit_primary = TrivialTestCircuit::default();
1037 let circuit_secondary = CubicCircuit::default();
1038
1039 // produce public parameters
1040 let pp = PublicParams::<
1041 G1,
1042 G2,
1043 TrivialTestCircuit<<G1 as Group>::Scalar>,
1044 CubicCircuit<<G2 as Group>::Scalar>,
1045 >::setup(circuit_primary.clone(), circuit_secondary.clone());
1046
1047 let num_steps = 3;
1048
1049 // produce a recursive SNARK
1050 let mut recursive_snark: Option<
1051 RecursiveSNARK<
1052 G1,
1053 G2,
1054 TrivialTestCircuit<<G1 as Group>::Scalar>,
1055 CubicCircuit<<G2 as Group>::Scalar>,
1056 >,
1057 > = None;
1058
1059 for _i in 0..num_steps {
1060 let res = RecursiveSNARK::prove_step(
1061 &pp,
1062 recursive_snark,
1063 circuit_primary.clone(),
1064 circuit_secondary.clone(),
1065 vec![<G1 as Group>::Scalar::one()],
1066 vec![<G2 as Group>::Scalar::zero()],
1067 );
1068 assert!(res.is_ok());
1069 recursive_snark = Some(res.unwrap());
1070 }
1071
1072 assert!(recursive_snark.is_some());
1073 let recursive_snark = recursive_snark.unwrap();
1074
1075 // verify the recursive SNARK
1076 let res = recursive_snark.verify(
1077 &pp,
1078 num_steps,
1079 vec![<G1 as Group>::Scalar::one()],
1080 vec![<G2 as Group>::Scalar::zero()],
1081 );
1082 assert!(res.is_ok());
1083
1084 let (zn_primary, zn_secondary) = res.unwrap();
1085
1086 // sanity: check the claimed output with a direct computation of the same
1087 assert_eq!(zn_primary, vec![<G1 as Group>::Scalar::one()]);
1088 let mut zn_secondary_direct = vec![<G2 as Group>::Scalar::zero()];
1089 for _i in 0..num_steps {
1090 zn_secondary_direct = CubicCircuit::default().output(&zn_secondary_direct);
1091 }
1092 assert_eq!(zn_secondary, zn_secondary_direct);
1093 assert_eq!(zn_secondary, vec![<G2 as Group>::Scalar::from(2460515u64)]);
1094
1095 // run the compressed snark with Spark compiler
1096 type S1Prime = spartan::pp::RelaxedR1CSSNARK<G1, EE1>;
1097 type S2Prime = spartan::pp::RelaxedR1CSSNARK<G2, EE2>;
1098
1099 // produce the prover and verifier keys for compressed snark
1100 let (pk, vk) = CompressedSNARK::<_, _, _, _, S1Prime, S2Prime>::setup(&pp).unwrap();
1101
1102 // produce a compressed SNARK
1103 let res = CompressedSNARK::<_, _, _, _, S1Prime, S2Prime>::prove(&pp, &pk, &recursive_snark);
1104 assert!(res.is_ok());
1105 let compressed_snark = res.unwrap();
1106
1107 // verify the compressed SNARK
1108 let res = compressed_snark.verify(
1109 &vk,
1110 num_steps,
1111 vec![<G1 as Group>::Scalar::one()],
1112 vec![<G2 as Group>::Scalar::zero()],
1113 );
1114 assert!(res.is_ok());
1115 }
1116
1117 #[test]
1118 fn test_ivc_nondet_with_compression() {
1119 // y is a non-deterministic advice representing the fifth root of the input at a step.
1120 #[derive(Clone, Debug)]
1121 struct FifthRootCheckingCircuit<F: PrimeField> {
1122 y: F,
1123 }
1124
1125 impl<F> FifthRootCheckingCircuit<F>
1126 where
1127 F: PrimeField,
1128 {
1129 fn new(num_steps: usize) -> (Vec<F>, Vec<Self>) {
1130 let mut powers = Vec::new();
1131 let rng = &mut rand::rngs::OsRng;
1132 let mut seed = F::random(rng);
1133 for _i in 0..num_steps + 1 {
1134 let mut power = seed;
1135 power = power.square();
1136 power = power.square();
1137 power *= seed;
1138
1139 powers.push(Self { y: power });
1140
1141 seed = power;
1142 }
1143
1144 // reverse the powers to get roots
1145 let roots = powers.into_iter().rev().collect::<Vec<Self>>();
1146 (vec![roots[0].y], roots[1..].to_vec())
1147 }
1148 }
1149
1150 impl<F> StepCircuit<F> for FifthRootCheckingCircuit<F>
1151 where
1152 F: PrimeField,
1153 {
1154 fn arity(&self) -> usize {
1155 1
1156 }
1157
1158 fn synthesize<CS: ConstraintSystem<F>>(
1159 &self,
1160 cs: &mut CS,
1161 z: &[AllocatedNum<F>],
1162 ) -> Result<Vec<AllocatedNum<F>>, SynthesisError> {
1163 let x = &z[0];
1164
1165 // we allocate a variable and set it to the provided non-deterministic advice.
1166 let y = AllocatedNum::alloc(cs.namespace(|| "y"), || Ok(self.y))?;
1167
1168 // We now check if y = x^{1/5} by checking if y^5 = x
1169 let y_sq = y.square(cs.namespace(|| "y_sq"))?;
1170 let y_quad = y_sq.square(cs.namespace(|| "y_quad"))?;
1171 let y_pow_5 = y_quad.mul(cs.namespace(|| "y_fifth"), &y)?;
1172
1173 cs.enforce(
1174 || "y^5 = x",
1175 |lc| lc + y_pow_5.get_variable(),
1176 |lc| lc + CS::one(),
1177 |lc| lc + x.get_variable(),
1178 );
1179
1180 Ok(vec![y])
1181 }
1182
1183 fn output(&self, z: &[F]) -> Vec<F> {
1184 // sanity check
1185 let x = z[0];
1186 let y_pow_5 = {
1187 let y = self.y;
1188 let y_sq = y.square();
1189 let y_quad = y_sq.square();
1190 y_quad * self.y
1191 };
1192 assert_eq!(x, y_pow_5);
1193
1194 // return non-deterministic advice
1195 // as the output of the step
1196 vec![self.y]
1197 }
1198 }
1199
1200 let circuit_primary = FifthRootCheckingCircuit {
1201 y: <G1 as Group>::Scalar::zero(),
1202 };
1203
1204 let circuit_secondary = TrivialTestCircuit::default();
1205
1206 // produce public parameters
1207 let pp = PublicParams::<
1208 G1,
1209 G2,
1210 FifthRootCheckingCircuit<<G1 as Group>::Scalar>,
1211 TrivialTestCircuit<<G2 as Group>::Scalar>,
1212 >::setup(circuit_primary, circuit_secondary.clone());
1213
1214 let num_steps = 3;
1215
1216 // produce non-deterministic advice
1217 let (z0_primary, roots) = FifthRootCheckingCircuit::new(num_steps);
1218 let z0_secondary = vec![<G2 as Group>::Scalar::zero()];
1219
1220 // produce a recursive SNARK
1221 let mut recursive_snark: Option<
1222 RecursiveSNARK<
1223 G1,
1224 G2,
1225 FifthRootCheckingCircuit<<G1 as Group>::Scalar>,
1226 TrivialTestCircuit<<G2 as Group>::Scalar>,
1227 >,
1228 > = None;
1229
1230 for circuit_primary in roots.iter().take(num_steps) {
1231 let res = RecursiveSNARK::prove_step(
1232 &pp,
1233 recursive_snark,
1234 circuit_primary.clone(),
1235 circuit_secondary.clone(),
1236 z0_primary.clone(),
1237 z0_secondary.clone(),
1238 );
1239 assert!(res.is_ok());
1240 recursive_snark = Some(res.unwrap());
1241 }
1242
1243 assert!(recursive_snark.is_some());
1244 let recursive_snark = recursive_snark.unwrap();
1245
1246 // verify the recursive SNARK
1247 let res = recursive_snark.verify(&pp, num_steps, z0_primary.clone(), z0_secondary.clone());
1248 assert!(res.is_ok());
1249
1250 // produce the prover and verifier keys for compressed snark
1251 let (pk, vk) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
1252
1253 // produce a compressed SNARK
1254 let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &pk, &recursive_snark);
1255 assert!(res.is_ok());
1256 let compressed_snark = res.unwrap();
1257
1258 // verify the compressed SNARK
1259 let res = compressed_snark.verify(&vk, num_steps, z0_primary, z0_secondary);
1260 assert!(res.is_ok());
1261 }
1262
1263 #[test]
1264 fn test_ivc_base() {
1265 // produce public parameters
1266 let pp = PublicParams::<
1267 G1,
1268 G2,
1269 TrivialTestCircuit<<G1 as Group>::Scalar>,
1270 CubicCircuit<<G2 as Group>::Scalar>,
1271 >::setup(TrivialTestCircuit::default(), CubicCircuit::default());
1272
1273 let num_steps = 1;
1274
1275 // produce a recursive SNARK
1276 let res = RecursiveSNARK::prove_step(
1277 &pp,
1278 None,
1279 TrivialTestCircuit::default(),
1280 CubicCircuit::default(),
1281 vec![<G1 as Group>::Scalar::one()],
1282 vec![<G2 as Group>::Scalar::zero()],
1283 );
1284 assert!(res.is_ok());
1285 let recursive_snark = res.unwrap();
1286
1287 // verify the recursive SNARK
1288 let res = recursive_snark.verify(
1289 &pp,
1290 num_steps,
1291 vec![<G1 as Group>::Scalar::one()],
1292 vec![<G2 as Group>::Scalar::zero()],
1293 );
1294 assert!(res.is_ok());
1295
1296 let (zn_primary, zn_secondary) = res.unwrap();
1297
1298 assert_eq!(zn_primary, vec![<G1 as Group>::Scalar::one()]);
1299 assert_eq!(zn_secondary, vec![<G2 as Group>::Scalar::from(5u64)]);
1300 }
1301}