Adapt Nova usage of commitment to the generic trait (#63)

rust-toolchain

@@ -1 +1 @@
-1.73.0
+1.75.0

src/folding/hypernova/circuit.rs

@@ -237,7 +237,7 @@ mod tests {
         // Initialize cs
         let cs = ConstraintSystem::<Fr>::new_ref();
         let vec_thetas = sigmas_thetas.1;
-        for (_, thetas) in vec_thetas.iter().enumerate() {
+        for thetas in vec_thetas.iter() {
             // sum c_i * prod theta_j
             let expected = sum_ci_mul_prod_thetaj(&ccs, thetas); // from `compute_c_from_sigmas_and_thetas`
             let mut prepared_thetas = Vec::new();

src/folding/nova/circuits.rs

@@ -503,7 +503,7 @@ pub mod tests {
     fn test_nifs_gadget() {
         let (_, _, _, _, ci1, _, ci2, _, ci3, _, cmT, _, r_Fr) = prepare_simple_fold_inputs();
 
-        let ci3_verifier = NIFS::<Projective>::verify(r_Fr, &ci1, &ci2, &cmT);
+        let ci3_verifier = NIFS::<Projective, Pedersen<Projective>>::verify(r_Fr, &ci1, &ci2, &cmT);
         assert_eq!(ci3_verifier, ci3);
 
         let cs = ConstraintSystem::<Fr>::new_ref();
@@ -721,7 +721,7 @@ pub mod tests {
 
                 // U_{i+1}
                 let T: Vec<Fr>;
-                (T, cmT) = NIFS::<Projective>::compute_cmT(
+                (T, cmT) = NIFS::<Projective, Pedersen<Projective>>::compute_cmT(
                     &pedersen_params,
                     &r1cs,
                     &w_i,
@@ -741,9 +741,10 @@ pub mod tests {
                 .unwrap();
                 let r_Fr = Fr::from_bigint(BigInteger::from_bits_le(&r_bits)).unwrap();
 
-                (W_i1, U_i1) =
-                    NIFS::<Projective>::fold_instances(r_Fr, &w_i, &u_i, &W_i, &U_i, &T, cmT)
-                        .unwrap();
+                (W_i1, U_i1) = NIFS::<Projective, Pedersen<Projective>>::fold_instances(
+                    r_Fr, &w_i, &u_i, &W_i, &U_i, &T, cmT,
+                )
+                .unwrap();
 
                 r1cs.check_relaxed_instance_relation(&W_i1, &U_i1).unwrap();
 
@@ -782,7 +783,7 @@ pub mod tests {
                     )
                     .unwrap();
                 let cf_r_Fq = Fq::from_bigint(BigInteger::from_bits_le(&cf_r_bits)).unwrap();
-                let (_, cf_U_i1) = NIFS::<Projective2>::fold_instances(
+                let (_, cf_U_i1) = NIFS::<Projective2, Pedersen<Projective2>>::fold_instances(
                     cf_r_Fq, &cf_W_i, &cf_U_i, &cf_w_i, &cf_u_i, &cf_T, cf_cmT,
                 )
                 .unwrap();
@@ -828,7 +829,9 @@ pub mod tests {
             // compute committed instances, w_{i+1}, u_{i+1}, which will be used as w_i, u_i, so we
             // assign them directly to w_i, u_i.
             w_i = Witness::<Projective>::new(w_i1.clone(), r1cs.A.n_rows);
-            u_i = w_i.commit(&pedersen_params, vec![u_i1_x]).unwrap();
+            u_i = w_i
+                .commit::<Pedersen<Projective>>(&pedersen_params, vec![u_i1_x])
+                .unwrap();
 
             r1cs.check_relaxed_instance_relation(&w_i, &u_i).unwrap();
             r1cs.check_relaxed_instance_relation(&W_i1, &U_i1).unwrap();

src/folding/nova/decider.rs

@@ -18,7 +18,7 @@ use ark_std::{One, Zero};
 use core::{borrow::Borrow, marker::PhantomData};
 
 use crate::ccs::r1cs::R1CS;
-use crate::commitment::pedersen::Params as PedersenParams;
+use crate::commitment::{pedersen::Params as PedersenParams, CommitmentProver};
 use crate::folding::nova::{
     circuits::{CommittedInstanceVar, CF1, CF2},
     ivc::IVC,
@@ -179,17 +179,21 @@ where
 
 /// Circuit that implements the in-circuit checks needed for the onchain (Ethereum's EVM)
 /// verification.
-pub struct DeciderCircuit<C1, GC1, C2, GC2>
+pub struct DeciderCircuit<C1, GC1, C2, GC2, CP1, CP2>
 where
     C1: CurveGroup,
     GC1: CurveVar<C1, CF2<C1>>,
     C2: CurveGroup,
     GC2: CurveVar<C2, CF2<C2>>,
+    CP1: CommitmentProver<C1>,
+    CP2: CommitmentProver<C2>,
 {
     _c1: PhantomData<C1>,
     _gc1: PhantomData<GC1>,
     _c2: PhantomData<C2>,
     _gc2: PhantomData<GC2>,
+    _cp1: PhantomData<CP1>,
+    _cp2: PhantomData<CP2>,
 
     /// E vector's length of the Nova instance witness
     pub E_len: usize,
@@ -199,7 +203,7 @@ where
     pub r1cs: R1CS<C1::ScalarField>,
     /// R1CS of the CycleFold circuit
     pub cf_r1cs: R1CS<C2::ScalarField>,
-    /// CycleFold PedersenParams, over C2
+    /// CycleFold PedersenParams over C2
     pub cf_pedersen_params: PedersenParams<C2>,
     pub poseidon_config: PoseidonConfig<CF1<C1>>,
     pub i: Option<CF1<C1>>,
@@ -216,25 +220,32 @@ where
     pub cf_U_i: Option<CommittedInstance<C2>>,
     pub cf_W_i: Option<Witness<C2>>,
 }
-impl<C1, GC1, C2, GC2> DeciderCircuit<C1, GC1, C2, GC2>
+impl<C1, GC1, C2, GC2, CP1, CP2> DeciderCircuit<C1, GC1, C2, GC2, CP1, CP2>
 where
     C1: CurveGroup,
     C2: CurveGroup,
     GC1: CurveVar<C1, CF2<C1>>,
     GC2: CurveVar<C2, CF2<C2>>,
+    CP1: CommitmentProver<C1>,
+    // enforce that the CP2 is Pedersen commitment, since we're at Ethereum's EVM decider
+    CP2: CommitmentProver<C2, Params = PedersenParams<C2>>,
 {
-    pub fn from_ivc<FC: FCircuit<C1::ScalarField>>(ivc: IVC<C1, GC1, C2, GC2, FC>) -> Self {
+    pub fn from_ivc<FC: FCircuit<C1::ScalarField>>(
+        ivc: IVC<C1, GC1, C2, GC2, FC, CP1, CP2>,
+    ) -> Self {
         Self {
             _c1: PhantomData,
             _gc1: PhantomData,
             _c2: PhantomData,
             _gc2: PhantomData,
+            _cp1: PhantomData,
+            _cp2: PhantomData,
 
             E_len: ivc.W_i.E.len(),
             cf_E_len: ivc.cf_W_i.E.len(),
             r1cs: ivc.r1cs,
             cf_r1cs: ivc.cf_r1cs,
-            cf_pedersen_params: ivc.cf_pedersen_params,
+            cf_pedersen_params: ivc.cf_cm_params,
             poseidon_config: ivc.poseidon_config,
             i: Some(ivc.i),
             z_0: Some(ivc.z_0),
@@ -249,18 +260,21 @@ where
     }
 }
 
-impl<C1, GC1, C2, GC2> ConstraintSynthesizer<CF1<C1>> for DeciderCircuit<C1, GC1, C2, GC2>
+impl<C1, GC1, C2, GC2, CP1, CP2> ConstraintSynthesizer<CF1<C1>>
+    for DeciderCircuit<C1, GC1, C2, GC2, CP1, CP2>
 where
     C1: CurveGroup,
     C2: CurveGroup,
     GC1: CurveVar<C1, CF2<C1>>,
     GC2: CurveVar<C2, CF2<C2>>,
+    CP1: CommitmentProver<C1>,
+    CP2: CommitmentProver<C2>,
     <C1 as CurveGroup>::BaseField: PrimeField,
     <C2 as CurveGroup>::BaseField: PrimeField,
     <C1 as Group>::ScalarField: Absorb,
     <C2 as Group>::ScalarField: Absorb,
     C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
-    for<'a> &'a GC2: GroupOpsBounds<'a, C2, GC2>,
+    for<'b> &'b GC2: GroupOpsBounds<'b, C2, GC2>,
 {
     fn generate_constraints(self, cs: ConstraintSystemRef<CF1<C1>>) -> Result<(), SynthesisError> {
         let r1cs =
@@ -437,7 +451,8 @@ pub mod tests {
     use ark_relations::r1cs::ConstraintSystem;
     use ark_vesta::{constraints::GVar as GVar2, Projective as Projective2};
 
-    use crate::folding::nova::ivc::IVC;
+    use crate::commitment::pedersen::Pedersen;
+    use crate::folding::nova::ivc::tests::get_pedersen_params_len;
     use crate::frontend::tests::{CubicFCircuit, CustomFCircuit, WrapperCircuit};
     use crate::transcript::poseidon::tests::poseidon_test_config;
 
@@ -604,10 +619,25 @@ pub mod tests {
         let F_circuit = CubicFCircuit::<Fr>::new(());
         let z_0 = vec![Fr::from(3_u32)];
 
+        let (pedersen_len, cf_pedersen_len) =
+            get_pedersen_params_len::<CubicFCircuit<Fr>>(&poseidon_config, F_circuit).unwrap();
+        // generate the Pedersen params
+        let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, pedersen_len);
+        let cf_pedersen_params = Pedersen::<Projective2>::new_params(&mut rng, cf_pedersen_len);
+
         // generate an IVC and do a step of it
-        let mut ivc = IVC::<Projective, GVar, Projective2, GVar2, CubicFCircuit<Fr>>::new(
-            &mut rng,
+        let mut ivc = IVC::<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            CubicFCircuit<Fr>,
+            Pedersen<Projective>,
+            Pedersen<Projective2>,
+        >::new(
             poseidon_config,
+            pedersen_params,
+            cf_pedersen_params,
             F_circuit,
             z_0.clone(),
         )
@@ -616,7 +646,14 @@ pub mod tests {
         ivc.verify(z_0, 1).unwrap();
 
         // load the DeciderCircuit from the generated IVC
-        let decider_circuit = DeciderCircuit::<Projective, GVar, Projective2, GVar2>::from_ivc(ivc);
+        let decider_circuit = DeciderCircuit::<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            Pedersen<Projective>,
+            Pedersen<Projective2>,
+        >::from_ivc(ivc);
 
         let cs = ConstraintSystem::<Fr>::new_ref();
 

src/folding/nova/ivc.rs

@@ -3,7 +3,6 @@ use ark_ec::{AffineRepr, CurveGroup, Group};
 use ark_ff::{BigInteger, PrimeField};
 use ark_r1cs_std::{groups::GroupOpsBounds, prelude::CurveVar};
 use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystem};
-use ark_std::rand::Rng;
 use ark_std::{One, Zero};
 use core::marker::PhantomData;
 
@@ -12,9 +11,8 @@ use super::{
     cyclefold::{CycleFoldChallengeGadget, CycleFoldCircuit},
 };
 use super::{nifs::NIFS, traits::NovaR1CS, CommittedInstance, Witness};
-use crate::ccs::r1cs::R1CS;
-use crate::ccs::r1cs::{extract_r1cs, extract_w_x};
-use crate::commitment::pedersen::{Params as PedersenParams, Pedersen};
+use crate::ccs::r1cs::{extract_r1cs, extract_w_x, R1CS};
+use crate::commitment::CommitmentProver;
 use crate::frontend::FCircuit;
 use crate::Error;
 
@@ -23,13 +21,15 @@ use super::cyclefold::CF_IO_LEN;
 
 /// Implements the Incremental Verifiable Computation described in sections 1.2 and 5 of
 /// [Nova](https://eprint.iacr.org/2021/370.pdf)
-pub struct IVC<C1, GC1, C2, GC2, FC>
+pub struct IVC<C1, GC1, C2, GC2, FC, CP1, CP2>
 where
     C1: CurveGroup,
     GC1: CurveVar<C1, CF2<C1>>,
     C2: CurveGroup,
     GC2: CurveVar<C2, CF2<C2>>,
     FC: FCircuit<C1::ScalarField>,
+    CP1: CommitmentProver<C1>,
+    CP2: CommitmentProver<C2>,
 {
     _gc1: PhantomData<GC1>,
     _c2: PhantomData<C2>,
@@ -39,10 +39,10 @@ where
     /// R1CS of the CycleFold circuit
     pub cf_r1cs: R1CS<C2::ScalarField>,
     pub poseidon_config: PoseidonConfig<C1::ScalarField>,
-    /// PedersenParams over C1
-    pub pedersen_params: PedersenParams<C1>,
-    /// CycleFold PedersenParams, over C2
-    pub cf_pedersen_params: PedersenParams<C2>,
+    /// CommitmentProver::Params over C1
+    pub cm_params: CP1::Params,
+    /// CycleFold CommitmentProver::Params, over C2
+    pub cf_cm_params: CP2::Params,
     /// F circuit, the circuit that is being folded
     pub F: FC,
     pub i: C1::ScalarField,
@@ -61,13 +61,15 @@ where
     pub cf_U_i: CommittedInstance<C2>,
 }
 
-impl<C1, GC1, C2, GC2, FC> IVC<C1, GC1, C2, GC2, FC>
+impl<C1, GC1, C2, GC2, FC, CP1, CP2> IVC<C1, GC1, C2, GC2, FC, CP1, CP2>
 where
     C1: CurveGroup,
     GC1: CurveVar<C1, CF2<C1>>,
     C2: CurveGroup,
     GC2: CurveVar<C2, CF2<C2>>,
     FC: FCircuit<C1::ScalarField>,
+    CP1: CommitmentProver<C1>,
+    CP2: CommitmentProver<C2>,
     <C1 as CurveGroup>::BaseField: PrimeField,
     <C2 as CurveGroup>::BaseField: PrimeField,
     <C1 as Group>::ScalarField: Absorb,
@@ -77,9 +79,10 @@ where
     for<'a> &'a GC2: GroupOpsBounds<'a, C2, GC2>,
 {
     /// Initializes the IVC for the given parameters and initial state `z_0`.
-    pub fn new<R: Rng>(
-        rng: &mut R,
+    pub fn new(
         poseidon_config: PoseidonConfig<C1::ScalarField>,
+        cm_params: CP1::Params,
+        cf_cm_params: CP2::Params,
         F: FC,
         z_0: Vec<C1::ScalarField>,
     ) -> Result<Self, Error> {
@@ -100,11 +103,6 @@ where
         let cs2 = cs2.into_inner().ok_or(Error::NoInnerConstraintSystem)?;
         let cf_r1cs = extract_r1cs::<C1::BaseField>(&cs2);
 
-        // this will not be randomly generated in this method, and will come from above levels, so
-        // the same params can be loaded on multiple instances
-        let pedersen_params = Pedersen::<C1>::new_params(rng, r1cs.A.n_rows);
-        let cf_pedersen_params = Pedersen::<C2>::new_params(rng, cf_r1cs.A.n_rows);
-
         // setup the dummy instances
         let (w_dummy, u_dummy) = r1cs.dummy_instance();
         let (cf_w_dummy, cf_u_dummy) = cf_r1cs.dummy_instance();
@@ -118,8 +116,8 @@ where
             r1cs,
             cf_r1cs,
             poseidon_config,
-            pedersen_params,
-            cf_pedersen_params,
+            cm_params,
+            cf_cm_params,
             F,
             i: C1::ScalarField::zero(),
             z_0: z_0.clone(),
@@ -154,8 +152,9 @@ where
             .ok_or(Error::OutOfBounds)?;
 
         // fold Nova instances
-        let (W_i1, U_i1): (Witness<C1>, CommittedInstance<C1>) =
-            NIFS::<C1>::fold_instances(r_Fr, &self.w_i, &self.u_i, &self.W_i, &self.U_i, &T, cmT)?;
+        let (W_i1, U_i1): (Witness<C1>, CommittedInstance<C1>) = NIFS::<C1, CP1>::fold_instances(
+            r_Fr, &self.w_i, &self.u_i, &self.W_i, &self.U_i, &T, cmT,
+        )?;
 
         // folded instance output (public input, x)
         // u_{i+1}.x = H(i+1, z_0, z_{i+1}, U_{i+1})
@@ -188,7 +187,7 @@ where
             };
 
             #[cfg(test)]
-            NIFS::verify_folded_instance(r_Fr, &self.u_i, &self.U_i, &U_i1, &cmT)?;
+            NIFS::<C1, CP1>::verify_folded_instance(r_Fr, &self.u_i, &self.U_i, &U_i1, &cmT)?;
         } else {
             // CycleFold part:
             // get the vector used as public inputs 'x' in the CycleFold circuit
@@ -226,7 +225,7 @@ where
             // fold cyclefold instances
             let cf_w_i = Witness::<C2>::new(cf_w_i.clone(), self.cf_r1cs.A.n_rows);
             let cf_u_i: CommittedInstance<C2> =
-                cf_w_i.commit(&self.cf_pedersen_params, cf_x_i.clone())?;
+                cf_w_i.commit::<CP2>(&self.cf_cm_params, cf_x_i.clone())?;
 
             // compute T* and cmT* for CycleFoldCircuit
             let (cf_T, cf_cmT) = self.compute_cf_cmT(&cf_w_i, &cf_u_i)?;
@@ -240,7 +239,7 @@ where
             let cf_r_Fq = C1::BaseField::from_bigint(BigInteger::from_bits_le(&cf_r_bits))
                 .ok_or(Error::OutOfBounds)?;
 
-            let (cf_W_i1, cf_U_i1) = NIFS::<C2>::fold_instances(
+            let (cf_W_i1, cf_U_i1) = NIFS::<C2, CP2>::fold_instances(
                 cf_r_Fq,
                 &self.cf_W_i,
                 &self.cf_U_i,
@@ -300,7 +299,7 @@ where
         self.i += C1::ScalarField::one();
         self.z_i = z_i1.clone();
         self.w_i = Witness::<C1>::new(w_i1, self.r1cs.A.n_rows);
-        self.u_i = self.w_i.commit(&self.pedersen_params, vec![u_i1_x])?;
+        self.u_i = self.w_i.commit::<CP1>(&self.cm_params, vec![u_i1_x])?;
         self.W_i = W_i1.clone();
         self.U_i = U_i1.clone();
 
@@ -353,8 +352,8 @@ where
 
     // computes T and cmT for the AugmentedFCircuit
     fn compute_cmT(&self) -> Result<(Vec<C1::ScalarField>, C1), Error> {
-        NIFS::<C1>::compute_cmT(
-            &self.pedersen_params,
+        NIFS::<C1, CP1>::compute_cmT(
+            &self.cm_params,
             &self.r1cs,
             &self.w_i,
             &self.u_i,
@@ -368,8 +367,8 @@ where
         cf_w_i: &Witness<C2>,
         cf_u_i: &CommittedInstance<C2>,
     ) -> Result<(Vec<C2::ScalarField>, C2), Error> {
-        NIFS::<C2>::compute_cyclefold_cmT(
-            &self.cf_pedersen_params,
+        NIFS::<C2, CP2>::compute_cyclefold_cmT(
+            &self.cf_cm_params,
             &self.cf_r1cs,
             cf_w_i,
             cf_u_i,
@@ -393,14 +392,43 @@ pub(crate) fn get_committed_instance_coordinates(
 }
 
 #[cfg(test)]
-mod tests {
+pub mod tests {
     use super::*;
     use ark_pallas::{constraints::GVar, Fr, Projective};
     use ark_vesta::{constraints::GVar as GVar2, Projective as Projective2};
 
+    use crate::commitment::pedersen::Pedersen;
     use crate::frontend::tests::CubicFCircuit;
     use crate::transcript::poseidon::tests::poseidon_test_config;
 
+    /// helper method to get the r1cs from the circuit
+    pub fn get_r1cs<F: PrimeField>(
+        circuit: impl ConstraintSynthesizer<F>,
+    ) -> Result<R1CS<F>, Error> {
+        let cs = ConstraintSystem::<F>::new_ref();
+        circuit.generate_constraints(cs.clone())?;
+        cs.finalize();
+        let cs = cs.into_inner().ok_or(Error::NoInnerConstraintSystem)?;
+        let r1cs = extract_r1cs::<F>(&cs);
+        Ok(r1cs)
+    }
+
+    /// helper method to get the pedersen params length for both the AugmentedFCircuit and the
+    /// CycleFold circuit
+    pub fn get_pedersen_params_len<FC: FCircuit<Fr>>(
+        poseidon_config: &PoseidonConfig<Fr>,
+        F_circuit: FC,
+    ) -> Result<(usize, usize), Error> {
+        let augmented_F_circuit = AugmentedFCircuit::<Projective, Projective2, GVar2, FC>::empty(
+            poseidon_config,
+            F_circuit,
+        );
+        let cf_circuit = CycleFoldCircuit::<Projective, GVar>::empty();
+        let r1cs = get_r1cs(augmented_F_circuit)?;
+        let cf_r1cs = get_r1cs(cf_circuit)?;
+        Ok((r1cs.A.n_rows, cf_r1cs.A.n_rows))
+    }
+
     #[test]
     fn test_ivc() {
         let mut rng = ark_std::test_rng();
@@ -409,9 +437,24 @@ mod tests {
         let F_circuit = CubicFCircuit::<Fr>::new(());
         let z_0 = vec![Fr::from(3_u32)];
 
-        let mut ivc = IVC::<Projective, GVar, Projective2, GVar2, CubicFCircuit<Fr>>::new(
-            &mut rng,
+        let (pedersen_len, cf_pedersen_len) =
+            get_pedersen_params_len::<CubicFCircuit<Fr>>(&poseidon_config, F_circuit).unwrap();
+        // generate the Pedersen params
+        let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, pedersen_len);
+        let cf_pedersen_params = Pedersen::<Projective2>::new_params(&mut rng, cf_pedersen_len);
+
+        let mut ivc = IVC::<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            CubicFCircuit<Fr>,
+            Pedersen<Projective>,
+            Pedersen<Projective2>,
+        >::new(
             poseidon_config,
+            pedersen_params,
+            cf_pedersen_params,
             F_circuit,
             z_0.clone(),
         )

src/folding/nova/mod.rs

@@ -7,10 +7,7 @@ use ark_ec::{CurveGroup, Group};
 use ark_std::fmt::Debug;
 use ark_std::{One, Zero};
 
-use crate::commitment::{
-    pedersen::{Params as PedersenParams, Pedersen},
-    CommitmentProver,
-};
+use crate::commitment::CommitmentProver;
 use crate::folding::circuits::nonnative::point_to_nonnative_limbs;
 use crate::utils::vec::is_zero_vec;
 use crate::Error;
@@ -101,16 +98,16 @@ where
             rW: C::ScalarField::zero(),
         }
     }
-    pub fn commit(
+    pub fn commit<CP: CommitmentProver<C>>(
         &self,
-        params: &PedersenParams<C>,
+        params: &CP::Params,
         x: Vec<C::ScalarField>,
     ) -> Result<CommittedInstance<C>, Error> {
         let mut cmE = C::zero();
         if !is_zero_vec::<C::ScalarField>(&self.E) {
-            cmE = Pedersen::commit(params, &self.E, &self.rE)?;
+            cmE = CP::commit(params, &self.E, &self.rE)?;
         }
-        let cmW = Pedersen::commit(params, &self.W, &self.rW)?;
+        let cmW = CP::commit(params, &self.W, &self.rW)?;
         Ok(CommittedInstance {
             cmE,
             u: C::ScalarField::one(),

src/folding/nova/nifs.rs

@@ -5,21 +5,19 @@ use std::marker::PhantomData;
 
 use super::{CommittedInstance, Witness};
 use crate::ccs::r1cs::R1CS;
-use crate::commitment::{
-    pedersen::{Params as PedersenParams, Pedersen, Proof as PedersenProof},
-    CommitmentProver,
-};
+use crate::commitment::CommitmentProver;
 use crate::transcript::Transcript;
 use crate::utils::vec::*;
 use crate::Error;
 
 /// Implements the Non-Interactive Folding Scheme described in section 4 of
 /// [Nova](https://eprint.iacr.org/2021/370.pdf)
-pub struct NIFS<C: CurveGroup> {
-    _phantom: PhantomData<C>,
+pub struct NIFS<C: CurveGroup, CP: CommitmentProver<C>> {
+    _c: PhantomData<C>,
+    _cp: PhantomData<CP>,
 }
 
-impl<C: CurveGroup> NIFS<C>
+impl<C: CurveGroup, CP: CommitmentProver<C>> NIFS<C, CP>
 where
     <C as Group>::ScalarField: Absorb,
 {
@@ -92,7 +90,7 @@ where
 
     /// compute_cmT is part of the NIFS.P logic
     pub fn compute_cmT(
-        pedersen_params: &PedersenParams<C>,
+        cm_prover_params: &CP::Params,
         r1cs: &R1CS<C::ScalarField>,
         w1: &Witness<C>,
         ci1: &CommittedInstance<C>,
@@ -105,11 +103,11 @@ where
         // compute cross terms
         let T = Self::compute_T(r1cs, ci1.u, ci2.u, &z1, &z2)?;
         // use r_T=1 since we don't need hiding property for cm(T)
-        let cmT = Pedersen::commit(pedersen_params, &T, &C::ScalarField::one())?;
+        let cmT = CP::commit(cm_prover_params, &T, &C::ScalarField::one())?;
         Ok((T, cmT))
     }
     pub fn compute_cyclefold_cmT(
-        pedersen_params: &PedersenParams<C>,
+        cm_prover_params: &CP::Params,
         r1cs: &R1CS<C::ScalarField>, // R1CS over C2.Fr=C1.Fq (here C=C2)
         w1: &Witness<C>,
         ci1: &CommittedInstance<C>,
@@ -125,7 +123,7 @@ where
         // compute cross terms
         let T = Self::compute_T(r1cs, ci1.u, ci2.u, &z1, &z2)?;
         // use r_T=1 since we don't need hiding property for cm(T)
-        let cmT = Pedersen::commit(pedersen_params, &T, &C::ScalarField::one())?;
+        let cmT = CP::commit(cm_prover_params, &T, &C::ScalarField::one())?;
         Ok((T, cmT))
     }
 
@@ -143,10 +141,10 @@ where
     ) -> Result<(Witness<C>, CommittedInstance<C>), Error> {
         // fold witness
         // use r_T=1 since we don't need hiding property for cm(T)
-        let w3 = NIFS::<C>::fold_witness(r, w1, w2, T, C::ScalarField::one())?;
+        let w3 = NIFS::<C, CP>::fold_witness(r, w1, w2, T, C::ScalarField::one())?;
 
         // fold committed instancs
-        let ci3 = NIFS::<C>::fold_committed_instance(r, ci1, ci2, &cmT);
+        let ci3 = NIFS::<C, CP>::fold_committed_instance(r, ci1, ci2, &cmT);
 
         Ok((w3, ci3))
     }
@@ -160,7 +158,7 @@ where
         ci2: &CommittedInstance<C>,
         cmT: &C,
     ) -> CommittedInstance<C> {
-        NIFS::<C>::fold_committed_instance(r, ci1, ci2, cmT)
+        NIFS::<C, CP>::fold_committed_instance(r, ci1, ci2, cmT)
     }
 
     /// Verify commited folded instance (ci) relations. Notice that this method does not open the
@@ -184,50 +182,35 @@ where
         Ok(())
     }
 
-    pub fn open_commitments(
+    pub fn prove_commitments(
         tr: &mut impl Transcript<C>,
-        pedersen_params: &PedersenParams<C>,
+        cm_prover_params: &CP::Params,
         w: &Witness<C>,
         ci: &CommittedInstance<C>,
         T: Vec<C::ScalarField>,
         cmT: &C,
-    ) -> Result<[PedersenProof<C>; 3], Error> {
-        let cmE_proof = Pedersen::prove(pedersen_params, tr, &ci.cmE, &w.E, &w.rE)?;
-        let cmW_proof = Pedersen::prove(pedersen_params, tr, &ci.cmW, &w.W, &w.rW)?;
-        let cmT_proof = Pedersen::prove(pedersen_params, tr, cmT, &T, &C::ScalarField::one())?; // cm(T) is committed with rT=1
+    ) -> Result<[CP::Proof; 3], Error> {
+        let cmE_proof = CP::prove(cm_prover_params, tr, &ci.cmE, &w.E, &w.rE)?;
+        let cmW_proof = CP::prove(cm_prover_params, tr, &ci.cmW, &w.W, &w.rW)?;
+        let cmT_proof = CP::prove(cm_prover_params, tr, cmT, &T, &C::ScalarField::one())?; // cm(T) is committed with rT=1
         Ok([cmE_proof, cmW_proof, cmT_proof])
     }
-    pub fn verify_commitments(
-        tr: &mut impl Transcript<C>,
-        pedersen_params: &PedersenParams<C>,
-        ci: CommittedInstance<C>,
-        cmT: C,
-        cm_proofs: [PedersenProof<C>; 3],
-    ) -> Result<(), Error> {
-        if cm_proofs.len() != 3 {
-            // cm_proofs should have length 3: [cmE_proof, cmW_proof, cmT_proof]
-            return Err(Error::NotExpectedLength(cm_proofs.len(), 3));
-        }
-        Pedersen::verify(pedersen_params, tr, ci.cmE, cm_proofs[0].clone())?;
-        Pedersen::verify(pedersen_params, tr, ci.cmW, cm_proofs[1].clone())?;
-        Pedersen::verify(pedersen_params, tr, cmT, cm_proofs[2].clone())?;
-        Ok(())
-    }
 }
 
 #[cfg(test)]
 pub mod tests {
     use super::*;
+    use ark_crypto_primitives::sponge::poseidon::PoseidonConfig;
     use ark_ff::{BigInteger, PrimeField};
     use ark_pallas::{Fr, Projective};
     use ark_std::{ops::Mul, UniformRand, Zero};
 
     use crate::ccs::r1cs::tests::{get_test_r1cs, get_test_z};
+    use crate::commitment::pedersen::{Params as PedersenParams, Pedersen};
     use crate::folding::nova::circuits::ChallengeGadget;
     use crate::folding::nova::traits::NovaR1CS;
     use crate::transcript::poseidon::{tests::poseidon_test_config, PoseidonTranscript};
     use crate::utils::vec::vec_scalar_mul;
-    use ark_crypto_primitives::sponge::poseidon::PoseidonConfig;
 
     #[allow(clippy::type_complexity)]
     pub(crate) fn prepare_simple_fold_inputs() -> (
@@ -258,12 +241,23 @@ pub mod tests {
         let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, r1cs.A.n_cols);
 
         // compute committed instances
-        let ci1 = w1.commit(&pedersen_params, x1.clone()).unwrap();
-        let ci2 = w2.commit(&pedersen_params, x2.clone()).unwrap();
+        let ci1 = w1
+            .commit::<Pedersen<Projective>>(&pedersen_params, x1.clone())
+            .unwrap();
+        let ci2 = w2
+            .commit::<Pedersen<Projective>>(&pedersen_params, x2.clone())
+            .unwrap();
 
         // NIFS.P
-        let (T, cmT) =
-            NIFS::<Projective>::compute_cmT(&pedersen_params, &r1cs, &w1, &ci1, &w2, &ci2).unwrap();
+        let (T, cmT) = NIFS::<Projective, Pedersen<Projective>>::compute_cmT(
+            &pedersen_params,
+            &r1cs,
+            &w1,
+            &ci1,
+            &w2,
+            &ci2,
+        )
+        .unwrap();
 
         let poseidon_config = poseidon_test_config::<Fr>();
 
@@ -276,8 +270,10 @@ pub mod tests {
         .unwrap();
         let r_Fr = Fr::from_bigint(BigInteger::from_bits_le(&r_bits)).unwrap();
 
-        let (w3, ci3) =
-            NIFS::<Projective>::fold_instances(r_Fr, &w1, &ci1, &w2, &ci2, &T, cmT).unwrap();
+        let (w3, ci3) = NIFS::<Projective, Pedersen<Projective>>::fold_instances(
+            r_Fr, &w1, &ci1, &w2, &ci2, &T, cmT,
+        )
+        .unwrap();
 
         (
             pedersen_params,
@@ -309,7 +305,7 @@ pub mod tests {
         // dummy instance, witness and public inputs zeroes
         let w_dummy = Witness::<Projective>::new(vec![Fr::zero(); w1.len()], r1cs.A.n_rows);
         let mut u_dummy = w_dummy
-            .commit(&pedersen_params, vec![Fr::zero(); x1.len()])
+            .commit::<Pedersen<Projective>>(&pedersen_params, vec![Fr::zero(); x1.len()])
             .unwrap();
         u_dummy.u = Fr::zero();
 
@@ -322,11 +318,19 @@ pub mod tests {
 
         let r_Fr = Fr::from(3_u32);
 
-        let (T, cmT) =
-            NIFS::<Projective>::compute_cmT(&pedersen_params, &r1cs, &w_i, &u_i, &W_i, &U_i)
-                .unwrap();
-        let (W_i1, U_i1) =
-            NIFS::<Projective>::fold_instances(r_Fr, &w_i, &u_i, &W_i, &U_i, &T, cmT).unwrap();
+        let (T, cmT) = NIFS::<Projective, Pedersen<Projective>>::compute_cmT(
+            &pedersen_params,
+            &r1cs,
+            &w_i,
+            &u_i,
+            &W_i,
+            &U_i,
+        )
+        .unwrap();
+        let (W_i1, U_i1) = NIFS::<Projective, Pedersen<Projective>>::fold_instances(
+            r_Fr, &w_i, &u_i, &W_i, &U_i, &T, cmT,
+        )
+        .unwrap();
         r1cs.check_relaxed_instance_relation(&W_i1, &U_i1).unwrap();
     }
 
@@ -337,7 +341,7 @@ pub mod tests {
             prepare_simple_fold_inputs();
 
         // NIFS.V
-        let ci3_v = NIFS::<Projective>::verify(r, &ci1, &ci2, &cmT);
+        let ci3_v = NIFS::<Projective, Pedersen<Projective>>::verify(r, &ci1, &ci2, &cmT);
         assert_eq!(ci3_v, ci3);
 
         // check that relations hold for the 2 inputted instances and the folded one
@@ -347,7 +351,9 @@ pub mod tests {
 
         // check that folded commitments from folded instance (ci) are equal to folding the
         // use folded rE, rW to commit w3
-        let ci3_expected = w3.commit(&pedersen_params, ci3.x.clone()).unwrap();
+        let ci3_expected = w3
+            .commit::<Pedersen<Projective>>(&pedersen_params, ci3.x.clone())
+            .unwrap();
         assert_eq!(ci3_expected.cmE, ci3.cmE);
         assert_eq!(ci3_expected.cmW, ci3.cmW);
 
@@ -356,15 +362,16 @@ pub mod tests {
         assert_eq!(w3.E, vec_scalar_mul(&T, &r));
 
         // NIFS.Verify_Folded_Instance:
-        NIFS::<Projective>::verify_folded_instance(r, &ci1, &ci2, &ci3, &cmT).unwrap();
+        NIFS::<Projective, Pedersen<Projective>>::verify_folded_instance(r, &ci1, &ci2, &ci3, &cmT)
+            .unwrap();
 
         // init Prover's transcript
         let mut transcript_p = PoseidonTranscript::<Projective>::new(&poseidon_config);
         // init Verifier's transcript
         let mut transcript_v = PoseidonTranscript::<Projective>::new(&poseidon_config);
 
-        // check openings of ci3.cmE, ci3.cmW and cmT
-        let cm_proofs = NIFS::<Projective>::open_commitments(
+        // prove the ci3.cmE, ci3.cmW, cmT commitments
+        let cm_proofs = NIFS::<Projective, Pedersen<Projective>>::prove_commitments(
             &mut transcript_p,
             &pedersen_params,
             &w3,
@@ -374,12 +381,27 @@ pub mod tests {
         )
         .unwrap();
 
-        NIFS::<Projective>::verify_commitments(
+        // verify the ci3.cmE, ci3.cmW, cmT commitments
+        assert_eq!(cm_proofs.len(), 3);
+        Pedersen::<Projective>::verify(
+            &pedersen_params,
             &mut transcript_v,
+            ci3.cmE,
+            cm_proofs[0].clone(),
+        )
+        .unwrap();
+        Pedersen::<Projective>::verify(
             &pedersen_params,
-            ci3,
+            &mut transcript_v,
+            ci3.cmW,
+            cm_proofs[1].clone(),
+        )
+        .unwrap();
+        Pedersen::<Projective>::verify(
+            &pedersen_params,
+            &mut transcript_v,
             cmT,
-            cm_proofs,
+            cm_proofs[2].clone(),
         )
         .unwrap();
     }
@@ -395,8 +417,9 @@ pub mod tests {
 
         // prepare the running instance
         let mut running_instance_w = Witness::<Projective>::new(w.clone(), r1cs.A.n_rows);
-        let mut running_committed_instance =
-            running_instance_w.commit(&pedersen_params, x).unwrap();
+        let mut running_committed_instance = running_instance_w
+            .commit::<Pedersen<Projective>>(&pedersen_params, x)
+            .unwrap();
 
         r1cs.check_relaxed_instance_relation(&running_instance_w, &running_committed_instance)
             .unwrap();
@@ -407,8 +430,9 @@ pub mod tests {
             let incomming_instance_z = get_test_z(i + 4);
             let (w, x) = r1cs.split_z(&incomming_instance_z);
             let incomming_instance_w = Witness::<Projective>::new(w.clone(), r1cs.A.n_rows);
-            let incomming_committed_instance =
-                incomming_instance_w.commit(&pedersen_params, x).unwrap();
+            let incomming_committed_instance = incomming_instance_w
+                .commit::<Pedersen<Projective>>(&pedersen_params, x)
+                .unwrap();
             r1cs.check_relaxed_instance_relation(
                 &incomming_instance_w,
                 &incomming_committed_instance,
@@ -418,7 +442,7 @@ pub mod tests {
             let r = Fr::rand(&mut rng); // folding challenge would come from the RO
 
             // NIFS.P
-            let (T, cmT) = NIFS::<Projective>::compute_cmT(
+            let (T, cmT) = NIFS::<Projective, Pedersen<Projective>>::compute_cmT(
                 &pedersen_params,
                 &r1cs,
                 &running_instance_w,
@@ -427,7 +451,7 @@ pub mod tests {
                 &incomming_committed_instance,
             )
             .unwrap();
-            let (folded_w, _) = NIFS::<Projective>::fold_instances(
+            let (folded_w, _) = NIFS::<Projective, Pedersen<Projective>>::fold_instances(
                 r,
                 &running_instance_w,
                 &running_committed_instance,
@@ -439,7 +463,7 @@ pub mod tests {
             .unwrap();
 
             // NIFS.V
-            let folded_committed_instance = NIFS::<Projective>::verify(
+            let folded_committed_instance = NIFS::<Projective, Pedersen<Projective>>::verify(
                 r,
                 &running_committed_instance,
                 &incomming_committed_instance,