Some Type simplifications (#297)

* refactor: Reorder generic parameters across all SNARK methods and structs

TL;DR: This is deinterleaving, i.e. E1, E2, C1, C2 .. becomes E1, C1, .. E2, C2, ...

- Reorganized order of generic parameters across various rust function calls and implementations, affecting structures such as `PublicParams`, `RecursiveSNARK`, and `CompressedSNARK`, among others.
- Updated all relevant unit tests to align with the new ordering of parameters.

* feat: Implement CurveCycleEquipped for various engines

- Introduced a new convenience trait to pair engines with fields in a curve cycle relationship, extending mod.rs traits.
- Added CurveCycleEquipped to the provider mod.rs traits list.
- Implemented CurveCycleEquipped to Bn256Engine, Bn256EngineKZG, Bn256EngineZM, Secp256k1Engine, and PallasEngine, setting respective secondary types accordingly.
- Expanded functionality for multiple engine systems with the addition of a secondary engine of 'Self'.

* refactor: Refactor SNARK parameters and update related functions

- Refactored the bench, examples, and source files to simplify `PublicParams`, `CompressedSNARK`, and `RecursiveSNARK` setup by removing the redundant secondary engine type and circuit parameters.
- Modified all functions, methods, and type definitions that depend on the `PublicParams`, `CompressedSNARK`, and `RecursiveSNARK` setup to reflect these changes.
- Removed all (default) instances of `TrivialCircuit` parameters from the codebase, simplifying the setup process.
- Renamed `SecEngine` to `SecEng`,
- Adjustments were made to functions to reflect the updated parameters without changing the functionality or behavior of the code.

* chore: remove type boilerplate

* refactor: Refactor supernova for single engine parameters and simplified testing

TL;DR : use CurveCycle and remove Phantom parameters

- Altered and simplified generic parameter restrictions for `NonUniformBench` and `NonUniformCircuit`.
- Refactored import statements in `benches/common/supernova/mod.rs` for a cleaner and simplified codebase.
- Refactored the use of `TrivialTestCircuit` from the `benches/common/supernova/bench.rs` file.
- Revised the `RecursiveSNARK` type in `bench.rs`,
- Refactored and simplified function signatures in `test.rs`,
- Made significant changes to the `TestROM` structure and adjusted related function implementations within `src/supernova/test.rs`.
- Overall, improved the use of generics.

* refactor: Refactor engine parameterization in circuit tests

- Simplified engine parameterization by replacing dual `E1` and `E2` variables with a single `E1` in relevant function definitions.
- Enhanced code readability by changing type constraints to `CurveCycleEquipped` and implementing the `SecEng` projection across multiple function modules.
- Updated calls and variable assignments to align with the new engine parameterization.
- Retained original functionalities of the affected functions even with the considerable code modifications and simplifications.

* chore: rename SecEng -> Dual

* docs: Improve code readability and testing robustness

- Improved readability of CurveCycleEquipped function comment in traits module by adding backticks around function name.

benches/common/supernova/bench.rs

@@ -8,7 +8,6 @@ use crate::common::{noise_threshold_env, BenchParams};
 use arecibo::{
   provider::{PallasEngine, VestaEngine},
   supernova::NonUniformCircuit,
-  supernova::TrivialTestCircuit,
   supernova::{snark::CompressedSNARK, PublicParams, RecursiveSNARK},
   traits::{
     snark::RelaxedR1CSSNARKTrait,
@@ -33,10 +32,9 @@ pub fn bench_snark_internal_with_arity<
   num_cons: usize,
   snark_type: SnarkType,
 ) {
-  let bench: NonUniformBench<E1, E2, TrivialTestCircuit<<E2 as Engine>::Scalar>> = match snark_type
-  {
-    SnarkType::Recursive => NonUniformBench::new(2, num_cons),
-    SnarkType::Compressed => NonUniformBench::new(num_augmented_circuits, num_cons),
+  let bench: NonUniformBench<E1> = match snark_type {
+    SnarkType::Recursive => NonUniformBench::<E1>::new(2, num_cons),
+    SnarkType::Compressed => NonUniformBench::<E1>::new(num_augmented_circuits, num_cons),
   };
   let pp = match snark_type {
     SnarkType::Recursive => PublicParams::setup(&bench, &*default_ck_hint(), &*default_ck_hint()),
@@ -50,7 +48,7 @@ pub fn bench_snark_internal_with_arity<
   };
   let z0_primary = vec![<E1 as Engine>::Scalar::from(2u64)];
   let z0_secondary = vec![<E2 as Engine>::Scalar::from(2u64)];
-  let mut recursive_snark_option: Option<RecursiveSNARK<E1, E2>> = None;
+  let mut recursive_snark_option: Option<RecursiveSNARK<E1>> = None;
   let mut selected_augmented_circuit = 0;
 
   for _ in 0..num_warmup_steps {
@@ -97,11 +95,11 @@ pub fn bench_snark_internal_with_arity<
 
   match snark_type {
     SnarkType::Compressed => {
-      let (prover_key, verifier_key) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
+      let (prover_key, verifier_key) = CompressedSNARK::<_, S1, S2>::setup(&pp).unwrap();
       // Benchmark the prove time
       group.bench_function(bench_params.bench_id("Prove"), |b| {
         b.iter(|| {
-          assert!(CompressedSNARK::<_, _, _, _, S1, S2>::prove(
+          assert!(CompressedSNARK::<_, S1, S2>::prove(
             black_box(&pp),
             black_box(&prover_key),
             black_box(&recursive_snark)
@@ -110,7 +108,7 @@ pub fn bench_snark_internal_with_arity<
         })
       });
 
-      let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &prover_key, &recursive_snark);
+      let res = CompressedSNARK::<_, S1, S2>::prove(&pp, &prover_key, &recursive_snark);
       assert!(res.is_ok());
       let compressed_snark = res.unwrap();
       // Benchmark the verification time

benches/common/supernova/mod.rs

@@ -6,9 +6,8 @@ pub mod targets;
 
 use anyhow::anyhow;
 use arecibo::{
-  supernova::NonUniformCircuit,
-  supernova::{StepCircuit, TrivialTestCircuit},
-  traits::Engine,
+  supernova::{NonUniformCircuit, StepCircuit, TrivialTestCircuit},
+  traits::{CurveCycleEquipped, Dual, Engine},
 };
 use bellpepper_core::{num::AllocatedNum, ConstraintSystem, SynthesisError};
 use core::marker::PhantomData;
@@ -68,45 +67,40 @@ fn num_cons_env() -> anyhow::Result<Vec<usize>> {
     })
 }
 
-pub struct NonUniformBench<E1, E2, S>
+pub struct NonUniformBench<E1>
 where
-  E1: Engine<Base = <E2 as Engine>::Scalar>,
-  E2: Engine<Base = <E1 as Engine>::Scalar>,
-  S: StepCircuit<E2::Scalar> + Default,
+  E1: CurveCycleEquipped,
 {
   num_circuits: usize,
   num_cons: usize,
-  _p: PhantomData<(E1, E2, S)>,
+  _p: PhantomData<E1>,
 }
 
-impl<E1, E2, S> NonUniformBench<E1, E2, S>
+impl<E1> NonUniformBench<E1>
 where
-  E1: Engine<Base = <E2 as Engine>::Scalar>,
-  E2: Engine<Base = <E1 as Engine>::Scalar>,
-  S: StepCircuit<E2::Scalar> + Default,
+  E1: CurveCycleEquipped,
 {
   fn new(num_circuits: usize, num_cons: usize) -> Self {
     Self {
       num_circuits,
       num_cons,
-      _p: Default::default(),
+      _p: PhantomData,
     }
   }
 }
 
-impl<E1, E2, S>
-  NonUniformCircuit<E1, E2, NonTrivialTestCircuit<E1::Scalar>, TrivialTestCircuit<E2::Scalar>>
-  for NonUniformBench<E1, E2, S>
+impl<E1> NonUniformCircuit<E1> for NonUniformBench<E1>
 where
-  E1: Engine<Base = <E2 as Engine>::Scalar>,
-  E2: Engine<Base = <E1 as Engine>::Scalar>,
-  S: StepCircuit<E2::Scalar> + Default,
+  E1: CurveCycleEquipped,
 {
+  type C1 = NonTrivialTestCircuit<E1::Scalar>;
+  type C2 = TrivialTestCircuit<<Dual<E1> as Engine>::Scalar>;
+
   fn num_circuits(&self) -> usize {
     self.num_circuits
   }
 
-  fn primary_circuit(&self, circuit_index: usize) -> NonTrivialTestCircuit<E1::Scalar> {
+  fn primary_circuit(&self, circuit_index: usize) -> Self::C1 {
     assert!(
       circuit_index < self.num_circuits,
       "Circuit index out of bounds: asked for {circuit_index}, but there are only {} circuits.",
@@ -116,7 +110,7 @@ where
     NonTrivialTestCircuit::new(self.num_cons)
   }
 
-  fn secondary_circuit(&self) -> TrivialTestCircuit<E2::Scalar> {
+  fn secondary_circuit(&self) -> Self::C2 {
     Default::default()
   }
 }

benches/compressed-snark.rs

@@ -27,8 +27,6 @@ type S2 = arecibo::spartan::snark::RelaxedR1CSSNARK<E2, EE2>;
 // SNARKs with computation commitmnets
 type SS1 = arecibo::spartan::ppsnark::RelaxedR1CSSNARK<E1, EE1>;
 type SS2 = arecibo::spartan::ppsnark::RelaxedR1CSSNARK<E2, EE2>;
-type C1 = NonTrivialCircuit<<E1 as Engine>::Scalar>;
-type C2 = TrivialCircuit<<E2 as Engine>::Scalar>;
 
 // To run these benchmarks, first download `criterion` with `cargo install cargo-criterion`.
 // Then `cargo criterion --bench compressed-snark`. The results are located in `target/criterion/data/<name-of-benchmark>`.
@@ -69,19 +67,14 @@ fn bench_compressed_snark_internal<S1: RelaxedR1CSSNARKTrait<E1>, S2: RelaxedR1C
   let c_secondary = TrivialCircuit::default();
 
   // Produce public parameters
-  let pp = PublicParams::<E1, E2, C1, C2>::setup(
-    &c_primary,
-    &c_secondary,
-    &*S1::ck_floor(),
-    &*S2::ck_floor(),
-  );
+  let pp = PublicParams::<E1>::setup(&c_primary, &c_secondary, &*S1::ck_floor(), &*S2::ck_floor());
 
   // Produce prover and verifier keys for CompressedSNARK
-  let (pk, vk) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
+  let (pk, vk) = CompressedSNARK::<_, S1, S2>::setup(&pp).unwrap();
 
   // produce a recursive SNARK
   let num_steps = 3;
-  let mut recursive_snark: RecursiveSNARK<E1, E2, C1, C2> = RecursiveSNARK::new(
+  let mut recursive_snark: RecursiveSNARK<E1> = RecursiveSNARK::new(
     &pp,
     &c_primary,
     &c_secondary,
@@ -113,15 +106,15 @@ fn bench_compressed_snark_internal<S1: RelaxedR1CSSNARKTrait<E1>, S2: RelaxedR1C
   // Bench time to produce a compressed SNARK
   group.bench_function(bench_params.bench_id("Prove"), |b| {
     b.iter(|| {
-      assert!(CompressedSNARK::<_, _, _, _, S1, S2>::prove(
+      assert!(CompressedSNARK::<_, S1, S2>::prove(
         black_box(&pp),
         black_box(&pk),
         black_box(&recursive_snark)
       )
       .is_ok());
     })
   });
-  let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &pk, &recursive_snark);
+  let res = CompressedSNARK::<_, S1, S2>::prove(&pp, &pk, &recursive_snark);
   assert!(res.is_ok());
   let compressed_snark = res.unwrap();
 

benches/compute-digest.rs

@@ -29,7 +29,7 @@ criterion_main!(compute_digest);
 fn bench_compute_digest(c: &mut Criterion) {
   c.bench_function("compute_digest", |b| {
     b.iter(|| {
-      PublicParams::<E1, E2, C1, C2>::setup(
+      PublicParams::<E1>::setup(
         black_box(&C1::new(10)),
         black_box(&C2::default()),
         black_box(&*default_ck_hint()),

benches/recursive-snark.rs

@@ -19,8 +19,6 @@ use common::{noise_threshold_env, BenchParams};
 
 type E1 = PallasEngine;
 type E2 = VestaEngine;
-type C1 = NonTrivialCircuit<<E1 as Engine>::Scalar>;
-type C2 = TrivialCircuit<<E2 as Engine>::Scalar>;
 
 // To run these benchmarks, first download `criterion` with `cargo install cargo-criterion`.
 // Then `cargo criterion --bench recursive-snark`. The results are located in `target/criterion/data/<name-of-benchmark>`.
@@ -73,7 +71,7 @@ fn bench_recursive_snark(c: &mut Criterion) {
     let c_secondary = TrivialCircuit::default();
 
     // Produce public parameters
-    let pp = PublicParams::<E1, E2, C1, C2>::setup(
+    let pp = PublicParams::<E1>::setup(
       &c_primary,
       &c_secondary,
       &*default_ck_hint(),
@@ -85,7 +83,7 @@ fn bench_recursive_snark(c: &mut Criterion) {
     // the first step is cheaper than other steps owing to the presence of
     // a lot of zeros in the satisfying assignment
     let num_warmup_steps = 10;
-    let mut recursive_snark: RecursiveSNARK<E1, E2, C1, C2> = RecursiveSNARK::new(
+    let mut recursive_snark: RecursiveSNARK<E1> = RecursiveSNARK::new(
       &pp,
       &c_primary,
       &c_secondary,

benches/sha256.rs

@@ -122,9 +122,6 @@ impl<Scalar: PrimeField + PrimeFieldBits> StepCircuit<Scalar> for Sha256Circuit<
   }
 }
 
-type C1 = Sha256Circuit<<E1 as Engine>::Scalar>;
-type C2 = TrivialCircuit<<E2 as Engine>::Scalar>;
-
 criterion_group! {
 name = recursive_snark;
 config = Criterion::default().warm_up_time(Duration::from_millis(3000));
@@ -158,7 +155,7 @@ fn bench_recursive_snark(c: &mut Criterion) {
 
     // Produce public parameters
     let ttc = TrivialCircuit::default();
-    let pp = PublicParams::<E1, E2, C1, C2>::setup(
+    let pp = PublicParams::<E1>::setup(
       &circuit_primary,
       &ttc,
       &*default_ck_hint(),

examples/and.rs

@@ -208,11 +208,14 @@ fn main() {
   println!("Nova-based 64-bit bitwise AND example");
   println!("=========================================================");
 
+  type C1 = AndCircuit<<E1 as Engine>::GE>;
+  type C2 = TrivialCircuit<<E2 as Engine>::Scalar>;
+
   let num_steps = 32;
   for num_ops_per_step in [1024, 2048, 4096, 8192, 16384, 32768, 65536] {
     // number of instances of AND per Nova's recursive step
-    let circuit_primary = AndCircuit::new(num_ops_per_step);
-    let circuit_secondary = TrivialCircuit::default();
+    let circuit_primary = C1::new(num_ops_per_step);
+    let circuit_secondary = C2::default();
 
     println!(
       "Proving {} AND ops ({num_ops_per_step} instances per step and {num_steps} steps)",
@@ -222,12 +225,7 @@ fn main() {
     // produce public parameters
     let start = Instant::now();
     println!("Producing public parameters...");
-    let pp = PublicParams::<
-      E1,
-      E2,
-      AndCircuit<<E1 as Engine>::GE>,
-      TrivialCircuit<<E2 as Engine>::Scalar>,
-    >::setup(
+    let pp = PublicParams::<E1>::setup(
       &circuit_primary,
       &circuit_secondary,
       &*S1::ck_floor(),
@@ -255,23 +253,19 @@ fn main() {
 
     // produce non-deterministic advice
     let circuits = (0..num_steps)
-      .map(|_| AndCircuit::new(num_ops_per_step))
+      .map(|_| C1::new(num_ops_per_step))
       .collect::<Vec<_>>();
 
-    type C1 = AndCircuit<<E1 as Engine>::GE>;
-    type C2 = TrivialCircuit<<E2 as Engine>::Scalar>;
-
     // produce a recursive SNARK
     println!("Generating a RecursiveSNARK...");
-    let mut recursive_snark: RecursiveSNARK<E1, E2, C1, C2> =
-      RecursiveSNARK::<E1, E2, C1, C2>::new(
-        &pp,
-        &circuits[0],
-        &circuit_secondary,
-        &[<E1 as Engine>::Scalar::zero()],
-        &[<E2 as Engine>::Scalar::zero()],
-      )
-      .unwrap();
+    let mut recursive_snark: RecursiveSNARK<E1> = RecursiveSNARK::<E1>::new(
+      &pp,
+      &circuits[0],
+      &circuit_secondary,
+      &[<E1 as Engine>::Scalar::zero()],
+      &[<E2 as Engine>::Scalar::zero()],
+    )
+    .unwrap();
 
     let start = Instant::now();
     for circuit_primary in circuits.iter() {
@@ -297,11 +291,11 @@ fn main() {
 
     // produce a compressed SNARK
     println!("Generating a CompressedSNARK using Spartan with multilinear KZG...");
-    let (pk, vk) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
+    let (pk, vk) = CompressedSNARK::<_, S1, S2>::setup(&pp).unwrap();
 
     let start = Instant::now();
 
-    let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &pk, &recursive_snark);
+    let res = CompressedSNARK::<_, S1, S2>::prove(&pp, &pk, &recursive_snark);
     println!(
       "CompressedSNARK::prove: {:?}, took {:?}",
       res.is_ok(),