Compute Decider's CM challenges in Groth16 circuit, link G16 & KZG proofs in Onchain Decider, refactor CommitmentScheme trait (#79)

* Compute Decider's CM challenges in Groth16 circuit, link G16 & KZG proofs in Onchain Decider, refactor CommitmentScheme trait

- Refactor commitment package
  - Refactor `Commitment` trait and the kzg, ipa, pedersen impls
  - Add methods to prove & verify given challenges (not computing them in-method)
- Add KZG challenges computation in decider_eth_circuit
- Add cmE & cmW KZG proving & verification in DeciderEth
- Link Decider's Groth16 proof & KZG proofs data
- Fix point to bytes arkworks inconsistency
- Patch ark_curves to use a cherry-picked version with bn254::constraints & grumpkin for v0.4.0 (once arkworks v0.5.0 is released this will no longer be needed)

* DeciderEthCircuit: Add check eval=p(c) for E & W

The check is temporary disabled due
https://github.com/privacy-scaling-explorations/folding-schemes/issues/80,
but the public inputs and logic are there, to be able to continue the
other parts development while issue #80 is solved.

folding-schemes/src/lib.rs

@@ -21,6 +21,7 @@ pub mod utils;
 
 #[derive(Debug, Error)]
 pub enum Error {
+    // Wrappers on top of other errors
     #[error("ark_relations::r1cs::SynthesisError")]
     SynthesisError(#[from] ark_relations::r1cs::SynthesisError),
     #[error("ark_serialize::SerializationError")]
@@ -29,27 +30,16 @@ pub enum Error {
     PolyCommitError(#[from] ark_poly_commit::Error),
     #[error("crate::utils::espresso::virtual_polynomial::ArithErrors")]
     ArithError(#[from] utils::espresso::virtual_polynomial::ArithErrors),
+    #[error(transparent)]
+    ProtoGalaxy(folding::protogalaxy::ProtoGalaxyError),
     #[error("{0}")]
     Other(String),
 
+    // Relation errors
     #[error("Relation not satisfied")]
     NotSatisfied,
-    #[error("Not equal")]
-    NotEqual,
-    #[error("Vectors should have the same length ({0}: {1}, {2}: {3})")]
-    NotSameLength(String, usize, String, usize),
-    #[error("Vector's length ({0}) is not the expected ({1})")]
-    NotExpectedLength(usize, usize),
-    #[error("Vector ({0}) length ({1}) is not a power of two")]
-    NotPowerOfTwo(String, usize),
-    #[error("Can not be empty")]
-    Empty,
-    #[error("Pedersen parameters length is not sufficient (generators.len={0} < vector.len={1} unsatisfied)")]
-    PedersenParamsLen(usize, usize),
-    #[error("Randomness for blinding not found")]
-    MissingRandomness,
-    #[error("Commitment verification failed")]
-    CommitmentVerificationFail,
+    #[error("SNARK verification failed")]
+    SNARKVerificationFail,
     #[error("IVC verification failed")]
     IVCVerificationFail,
     #[error("R1CS instance is expected to not be relaxed")]
@@ -60,17 +50,42 @@ pub enum Error {
     SumCheckProveError(String),
     #[error("Sum-check verify failed: {0}")]
     SumCheckVerifyError(String),
+
+    // Comparators errors
+    #[error("Not equal")]
+    NotEqual,
+    #[error("Vectors should have the same length ({0}: {1}, {2}: {3})")]
+    NotSameLength(String, usize, String, usize),
+    #[error("Vector's length ({0}) is not the expected ({1})")]
+    NotExpectedLength(usize, usize),
+    #[error("Vector ({0}) length ({1}) is not a power of two")]
+    NotPowerOfTwo(String, usize),
+    #[error("Can not be empty")]
+    Empty,
     #[error("Value out of bounds")]
     OutOfBounds,
     #[error("Could not construct the Evaluation Domain")]
     NewDomainFail,
+
+    // Commitment errors
+    #[error("Pedersen parameters length is not sufficient (generators.len={0} < vector.len={1} unsatisfied)")]
+    PedersenParamsLen(usize, usize),
+    #[error("Blinding factor not 0 for Commitment without hiding")]
+    BlindingNotZero,
+    #[error("Commitment verification failed")]
+    CommitmentVerificationFail,
+
+    // Other
+    #[error("Randomness for blinding not found")]
+    MissingRandomness,
+    #[error("Missing value: {0}")]
+    MissingValue(String),
     #[error("Feature '{0}' not supported yet")]
     NotSupportedYet(String),
+    #[error("Feature '{0}' is not supported and it will not be")]
+    NotSupported(String),
     #[error("max i-th step reached (usize limit reached)")]
     MaxStep,
-
-    #[error(transparent)]
-    ProtoGalaxy(folding::protogalaxy::ProtoGalaxyError),
 }
 
 /// FoldingScheme defines trait that is implemented by the diverse folding schemes. It is defined
@@ -138,24 +153,25 @@ pub trait Decider<
     C2::BaseField: PrimeField,
 {
     type ProverParam: Clone;
-    type Proof: Clone;
+    type Proof;
     type VerifierParam;
     type PublicInput: Debug;
     type CommittedInstanceWithWitness: Debug;
     type CommittedInstance: Clone + Debug;
 
     fn prove(
-        pp: &Self::ProverParam,
+        pp: Self::ProverParam,
         rng: impl RngCore + CryptoRng,
         folding_scheme: FS,
     ) -> Result<Self::Proof, Error>;
 
     fn verify(
-        vp: &Self::VerifierParam,
+        vp: Self::VerifierParam,
         i: C1::ScalarField,
         z_0: Vec<C1::ScalarField>,
         z_i: Vec<C1::ScalarField>,
         running_instance: &Self::CommittedInstance,
+        incoming_instance: &Self::CommittedInstance,
         proof: Self::Proof,
         // returns `Result<bool, Error>` to differentiate between an error occurred while performing
         // the verification steps, and the verification logic of the scheme not passing.