Feature/nova ivc (#36)

* Implement Nova IVC's new & prove_step methods

Implement Nova IVC's new & prove_step methods (without CycleFold part yet)

* transcript.absorb_point err handling, and update C.xy() usage

* add transcript usage to IVC prove, add NovaTranscript trait extending Transcript trait, refactor NIFS.P to allow absorbing in transcript inbetween

* Implement Nova's IVC.V method (without CycleFold part yet)

* clippy lints

* move challenge r computation in-circuit

* reuse computed points with coordinates over CF (non-native) to save constraints in AugmentedFCircuit

(constraint count went down ~6k)

* rm 128 bit constant

* add params to Errors

* Updates from review suggestions. Additionally refactored nova/nifs fold, and rm transcript from nova/IVC.

- Updates from PR suggestions
- Additionally updated:
  - in nova/nifs.rs: reuse folded_committed_instance for verify_folded_instance, computationally is the same, but reusing the same code so avoiding duplication and having an error on one of the two versions.
  - in nova/ivc.rs: remove transcript from IVC (not needed, it uses the RO)

src/lib.rs

@@ -20,21 +20,29 @@ pub mod utils;
 pub enum Error {
     #[error("ark_relations::r1cs::SynthesisError")]
     SynthesisError(#[from] ark_relations::r1cs::SynthesisError),
+    #[error("{0}")]
+    Other(String),
 
     #[error("Relation not satisfied")]
     NotSatisfied,
     #[error("Not equal")]
     NotEqual,
-    #[error("Vectors should have the same length")]
-    NotSameLength,
-    #[error("Vector's length is not the expected")]
-    NotExpectedLength,
+    #[error("Vectors should have the same length ({0}, {1})")]
+    NotSameLength(usize, usize),
+    #[error("Vector's length ({0}) is not the expected ({1})")]
+    NotExpectedLength(usize, usize),
     #[error("Can not be empty")]
     Empty,
-    #[error("Pedersen parameters length is not suficient")]
-    PedersenParamsLen,
+    #[error("Pedersen parameters length is not suficient (generators.len={0} < vector.len={1} unsatisfied)")]
+    PedersenParamsLen(usize, usize),
     #[error("Pedersen verification failed")]
     PedersenVerificationFail,
+    #[error("IVC verification failed")]
+    IVCVerificationFail,
+    #[error("R1CS instance is expected to not be relaxed")]
+    R1CSUnrelaxedFail,
+    #[error("Could not find the inner ConstraintSystem")]
+    NoInnerConstraintSystem,
 }
 
 /// FoldingScheme defines trait that is implemented by the diverse folding schemes. It is defined