HyperNova: add multi-instances folding to AugmentedFCircuit & IVC (#119)

- Adds the logic to support multi-instances folding in HyperNova's
AugmentedFCircuit & IVC.
- Adds also methods to generate new LCCCS & CCCS instances that don't
depend on the main folding chain, to be folded in in the next step
- Updates CycleFold circuit & methods to work other folding schemes than
  Nova, adapting it to fold multiple points per circuit (instead of
2-to-1 as till now)
- Handle multi-instances folding in the FoldingScheme trait
  interface, which expects 'None' in Nova, and 'Some' in HyperNova &
other multi-folding schemes.

examples/circom_full_flow.rs

@@ -85,7 +85,7 @@ fn main() {
     let nova_params = N::preprocess(&mut rng, &nova_preprocess_params).unwrap();
 
     // initialize the folding scheme engine, in our case we use Nova
-    let mut nova = N::init(nova_params.clone(), f_circuit.clone(), z_0).unwrap();
+    let mut nova = N::init(&nova_params, f_circuit.clone(), z_0).unwrap();
 
     // prepare the Decider prover & verifier params
     let (decider_pp, decider_vp) = D::preprocess(&mut rng, &nova_params, nova.clone()).unwrap();
@@ -93,7 +93,7 @@ fn main() {
     // run n steps of the folding iteration
     for (i, external_inputs_at_step) in external_inputs.iter().enumerate() {
         let start = Instant::now();
-        nova.prove_step(rng, external_inputs_at_step.clone())
+        nova.prove_step(rng, external_inputs_at_step.clone(), None)
             .unwrap();
         println!("Nova::prove_step {}: {:?}", i, start.elapsed());
     }

examples/external_inputs.rs

@@ -190,14 +190,13 @@ fn main() {
     let nova_params = N::preprocess(&mut rng, &nova_preprocess_params).unwrap();
 
     println!("Initialize FoldingScheme");
-    let mut folding_scheme =
-        N::init(nova_params.clone(), F_circuit, initial_state.clone()).unwrap();
+    let mut folding_scheme = N::init(&nova_params, F_circuit, initial_state.clone()).unwrap();
 
     // compute a step of the IVC
     for (i, external_inputs_at_step) in external_inputs.iter().enumerate() {
         let start = Instant::now();
         folding_scheme
-            .prove_step(rng, external_inputs_at_step.clone())
+            .prove_step(rng, external_inputs_at_step.clone(), None)
             .unwrap();
         println!("Nova::prove_step {}: {:?}", i, start.elapsed());
     }

examples/full_flow.rs

@@ -102,7 +102,7 @@ fn main() {
     let nova_params = N::preprocess(&mut rng, &nova_preprocess_params).unwrap();
 
     // initialize the folding scheme engine, in our case we use Nova
-    let mut nova = N::init(nova_params.clone(), f_circuit, z_0).unwrap();
+    let mut nova = N::init(&nova_params, f_circuit, z_0).unwrap();
 
     // prepare the Decider prover & verifier params
     let (decider_pp, decider_vp) = D::preprocess(&mut rng, &nova_params, nova.clone()).unwrap();
@@ -110,7 +110,7 @@ fn main() {
     // run n steps of the folding iteration
     for i in 0..n_steps {
         let start = Instant::now();
-        nova.prove_step(rng, vec![]).unwrap();
+        nova.prove_step(rng, vec![], None).unwrap();
         println!("Nova::prove_step {}: {:?}", i, start.elapsed());
     }
 

examples/multi_inputs.rs

@@ -144,13 +144,12 @@ fn main() {
     let nova_params = N::preprocess(&mut rng, &nova_preprocess_params).unwrap();
 
     println!("Initialize FoldingScheme");
-    let mut folding_scheme =
-        N::init(nova_params.clone(), F_circuit, initial_state.clone()).unwrap();
+    let mut folding_scheme = N::init(&nova_params, F_circuit, initial_state.clone()).unwrap();
 
     // compute a step of the IVC
     for i in 0..num_steps {
         let start = Instant::now();
-        folding_scheme.prove_step(rng, vec![]).unwrap();
+        folding_scheme.prove_step(rng, vec![], None).unwrap();
         println!("Nova::prove_step {}: {:?}", i, start.elapsed());
     }
 

examples/noname_full_flow.rs

@@ -86,7 +86,7 @@ fn main() {
     let nova_params = N::preprocess(&mut rng, &nova_preprocess_params).unwrap();
 
     // initialize the folding scheme engine, in our case we use Nova
-    let mut nova = N::init(nova_params.clone(), f_circuit.clone(), z_0).unwrap();
+    let mut nova = N::init(&nova_params, f_circuit.clone(), z_0).unwrap();
 
     // prepare the Decider prover & verifier params
     let (decider_pp, decider_vp) = D::preprocess(&mut rng, &nova_params, nova.clone()).unwrap();
@@ -94,7 +94,7 @@ fn main() {
     // run n steps of the folding iteration
     for (i, external_inputs_at_step) in external_inputs.iter().enumerate() {
         let start = Instant::now();
-        nova.prove_step(rng, external_inputs_at_step.clone())
+        nova.prove_step(rng, external_inputs_at_step.clone(), None)
             .unwrap();
         println!("Nova::prove_step {}: {:?}", i, start.elapsed());
     }

examples/sha256.rs

@@ -129,12 +129,11 @@ fn main() {
     let nova_params = N::preprocess(&mut rng, &nova_preprocess_params).unwrap();
 
     println!("Initialize FoldingScheme");
-    let mut folding_scheme =
-        N::init(nova_params.clone(), F_circuit, initial_state.clone()).unwrap();
+    let mut folding_scheme = N::init(&nova_params, F_circuit, initial_state.clone()).unwrap();
     // compute a step of the IVC
     for i in 0..num_steps {
         let start = Instant::now();
-        folding_scheme.prove_step(rng, vec![]).unwrap();
+        folding_scheme.prove_step(rng, vec![], None).unwrap();
         println!("Nova::prove_step {}: {:?}", i, start.elapsed());
     }