diff --git a/Cargo.toml b/Cargo.toml
index 6c85af4..5913108 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -12,6 +12,7 @@ ark-crypto-primitives = { version = "^0.4.0", default-features = false, features
 ark-poly-commit = "^0.4.0"
 ark-relations = { version = "^0.4.0", default-features = false }
 ark-r1cs-std = { default-features = false } # use latest version from the patch
+ark-snark = { version = "^0.4.0"}
 ark-serialize = "^0.4.0"
 ark-circom = { git = "https://github.com/gakonst/ark-circom.git" }
 thiserror = "1.0"
@@ -26,6 +27,10 @@ espresso_subroutines = {git="https://github.com/EspressoSystems/hyperplonk", pac
 ark-pallas = {version="0.4.0", features=["r1cs"]}
 ark-vesta = {version="0.4.0", features=["r1cs"]}
 ark-bn254 = "0.4.0"
+ark-mnt4-298 = {version="0.4.0", features=["r1cs"]}
+ark-mnt6-298 = {version="0.4.0", features=["r1cs"]}
+ark-groth16 = { version = "^0.4.0" }
+rand = "0.8.5"
 tracing = { version = "0.1", default-features = false, features = [ "attributes" ] }
 tracing-subscriber = { version = "0.2" }
 
@@ -35,7 +40,10 @@ default = ["parallel"]
 parallel = [ 
     "ark-std/parallel", 
     "ark-ff/parallel",  
+    "ark-ec/parallel",  
     "ark-poly/parallel", 
+    "ark-crypto-primitives/parallel",  
+    "ark-r1cs-std/parallel",  
     ]
 
 # The following patch is to use a version of ark-r1cs-std compatible with
diff --git a/src/folding/circuits/nonnative.rs b/src/folding/circuits/nonnative.rs
index 6d964ee..d6b1c99 100644
--- a/src/folding/circuits/nonnative.rs
+++ b/src/folding/circuits/nonnative.rs
@@ -54,12 +54,26 @@ where
     }
 }
 
-/// point_to_nonnative_limbs is used to compute (outside the circuit) the limbs representation of a
-/// point that matches the one used in-circuit.
+/// Wrapper on top of [`point_to_nonnative_limbs_custom_opt`] which always uses
+/// [`OptimizationType::Weight`].
 #[allow(clippy::type_complexity)]
 pub fn point_to_nonnative_limbs<C: CurveGroup>(
     p: C,
 ) -> Result<(Vec<C::ScalarField>, Vec<C::ScalarField>), SynthesisError>
+where
+    <C as ark_ec::CurveGroup>::BaseField: ark_ff::PrimeField,
+{
+    point_to_nonnative_limbs_custom_opt(p, OptimizationType::Weight)
+}
+
+/// Used to compute (outside the circuit) the limbs representation of a point that matches the one
+/// used in-circuit, and in particular this method allows to specify which [`OptimizationType`] to
+/// use.
+#[allow(clippy::type_complexity)]
+pub fn point_to_nonnative_limbs_custom_opt<C: CurveGroup>(
+    p: C,
+    optimization_type: OptimizationType,
+) -> Result<(Vec<C::ScalarField>, Vec<C::ScalarField>), SynthesisError>
 where
     <C as ark_ec::CurveGroup>::BaseField: ark_ff::PrimeField,
 {
@@ -68,12 +82,12 @@ where
         let x =
             AllocatedNonNativeFieldVar::<C::BaseField, C::ScalarField>::get_limbs_representations(
                 &C::BaseField::zero(),
-                OptimizationType::Weight,
+                optimization_type,
             )?;
         let y =
             AllocatedNonNativeFieldVar::<C::BaseField, C::ScalarField>::get_limbs_representations(
                 &C::BaseField::one(),
-                OptimizationType::Weight,
+                optimization_type,
             )?;
         return Ok((x, y));
     }
@@ -81,11 +95,11 @@ where
     let (x, y) = affine.xy().unwrap();
     let x = AllocatedNonNativeFieldVar::<C::BaseField, C::ScalarField>::get_limbs_representations(
         x,
-        OptimizationType::Weight,
+        optimization_type,
     )?;
     let y = AllocatedNonNativeFieldVar::<C::BaseField, C::ScalarField>::get_limbs_representations(
         y,
-        OptimizationType::Weight,
+        optimization_type,
     )?;
     Ok((x, y))
 }
@@ -94,16 +108,24 @@ where
 mod tests {
     use super::*;
     use ark_pallas::{Fr, Projective};
-    use ark_r1cs_std::alloc::AllocVar;
+    use ark_r1cs_std::{alloc::AllocVar, R1CSVar};
     use ark_relations::r1cs::ConstraintSystem;
-    use ark_std::Zero;
+    use ark_std::{UniformRand, Zero};
 
     #[test]
-    fn test_alloc_nonnativeaffinevar_zero() {
+    fn test_alloc_nonnativeaffinevar() {
         let cs = ConstraintSystem::<Fr>::new_ref();
 
         // dealing with the 'zero' point should not panic when doing the unwrap
         let p = Projective::zero();
         NonNativeAffineVar::<Fr>::new_witness(cs.clone(), || Ok(p)).unwrap();
+
+        // check that point_to_nonnative_limbs returns the expected values
+        let mut rng = ark_std::test_rng();
+        let p = Projective::rand(&mut rng);
+        let pVar = NonNativeAffineVar::<Fr>::new_witness(cs.clone(), || Ok(p)).unwrap();
+        let (x, y) = point_to_nonnative_limbs(p).unwrap();
+        assert_eq!(pVar.x.value().unwrap(), x);
+        assert_eq!(pVar.y.value().unwrap(), y);
     }
 }
diff --git a/src/folding/nova/decider_eth.rs b/src/folding/nova/decider_eth.rs
new file mode 100644
index 0000000..4aadf15
--- /dev/null
+++ b/src/folding/nova/decider_eth.rs
@@ -0,0 +1,205 @@
+/// This file implements the onchain (Ethereum's EVM) decider.
+use ark_crypto_primitives::sponge::Absorb;
+use ark_ec::{CurveGroup, Group};
+use ark_ff::PrimeField;
+use ark_r1cs_std::{groups::GroupOpsBounds, prelude::CurveVar};
+use ark_snark::SNARK;
+use ark_std::rand::CryptoRng;
+use ark_std::rand::RngCore;
+use core::marker::PhantomData;
+
+pub use super::decider_eth_circuit::DeciderEthCircuit;
+use crate::commitment::{pedersen::Params as PedersenParams, CommitmentProver};
+use crate::folding::circuits::nonnative::point_to_nonnative_limbs_custom_opt;
+use crate::folding::nova::{circuits::CF2, CommittedInstance, Nova};
+use crate::frontend::FCircuit;
+use crate::Error;
+use crate::{Decider as DeciderTrait, FoldingScheme};
+use ark_r1cs_std::fields::nonnative::params::OptimizationType;
+
+/// Onchain Decider, for ethereum use cases
+#[derive(Clone, Debug)]
+pub struct Decider<C1, GC1, C2, GC2, FC, CP1, CP2, S, FS> {
+    _c1: PhantomData<C1>,
+    _gc1: PhantomData<GC1>,
+    _c2: PhantomData<C2>,
+    _gc2: PhantomData<GC2>,
+    _fc: PhantomData<FC>,
+    _cp1: PhantomData<CP1>,
+    _cp2: PhantomData<CP2>,
+    _s: PhantomData<S>,
+    _fs: PhantomData<FS>,
+}
+
+impl<C1, GC1, C2, GC2, FC, CP1, CP2, S, FS> DeciderTrait<C1, C2, FC, FS>
+    for Decider<C1, GC1, C2, GC2, FC, CP1, CP2, S, FS>
+where
+    C1: CurveGroup,
+    C2: CurveGroup,
+    GC1: CurveVar<C1, CF2<C1>>,
+    GC2: CurveVar<C2, CF2<C2>>,
+    FC: FCircuit<C1::ScalarField>,
+    CP1: CommitmentProver<C1>,
+    // enforce that the CP2 is Pedersen commitment, since we're at Ethereum's EVM decider
+    CP2: CommitmentProver<C2, Params = PedersenParams<C2>>,
+    S: SNARK<C1::ScalarField>,
+    FS: FoldingScheme<C1, C2, FC>,
+    <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<'b> &'b GC2: GroupOpsBounds<'b, C2, GC2>,
+    // constrain FS into Nova, since this is a Decider specificly for Nova
+    Nova<C1, GC1, C2, GC2, FC, CP1, CP2>: From<FS>,
+{
+    type ProverParam = S::ProvingKey;
+    type Proof = S::Proof;
+    type VerifierParam = S::VerifyingKey;
+    type PublicInput = Vec<C1::ScalarField>;
+    type CommittedInstanceWithWitness = ();
+    type CommittedInstance = CommittedInstance<C1>;
+
+    fn prove(
+        pp: &Self::ProverParam,
+        mut rng: impl RngCore + CryptoRng,
+        folding_scheme: FS,
+    ) -> Result<Self::Proof, Error> {
+        let circuit =
+            DeciderEthCircuit::<C1, GC1, C2, GC2, CP1, CP2>::from_nova::<FC>(folding_scheme.into());
+
+        let proof = S::prove(pp, circuit.clone(), &mut rng).unwrap();
+
+        Ok(proof)
+    }
+
+    fn verify(
+        vp: &Self::VerifierParam,
+        i: C1::ScalarField,
+        z_0: Vec<C1::ScalarField>,
+        z_i: Vec<C1::ScalarField>,
+        running_instance: &Self::CommittedInstance,
+        proof: Self::Proof,
+    ) -> Result<bool, Error> {
+        let (cmE_x, cmE_y) = point_to_nonnative_limbs_custom_opt::<C1>(
+            running_instance.cmE,
+            OptimizationType::Constraints,
+        )?;
+        let (cmW_x, cmW_y) = point_to_nonnative_limbs_custom_opt::<C1>(
+            running_instance.cmW,
+            OptimizationType::Constraints,
+        )?;
+        let public_input: Vec<C1::ScalarField> = vec![
+            vec![i],
+            z_0,
+            z_i,
+            vec![running_instance.u],
+            running_instance.x.clone(),
+            cmE_x,
+            cmE_y,
+            cmW_x,
+            cmW_y,
+        ]
+        .concat();
+        S::verify(vp, &public_input, &proof).map_err(|e| Error::Other(e.to_string()))
+    }
+}
+
+#[cfg(test)]
+pub mod tests {
+    use super::*;
+    use ark_groth16::Groth16;
+    use ark_mnt4_298::{constraints::G1Var as GVar, Fr, G1Projective as Projective, MNT4_298};
+    use ark_mnt6_298::{constraints::G1Var as GVar2, G1Projective as Projective2};
+    use std::time::Instant;
+
+    use crate::commitment::pedersen::Pedersen;
+    use crate::folding::nova::{get_pedersen_params_len, ProverParams};
+    use crate::frontend::tests::CubicFCircuit;
+    use crate::transcript::poseidon::poseidon_test_config;
+
+    // Note: since we're testing a big circuit, this test takes a bit more of computation and time,
+    // do not run in the normal CI.
+    // To run the test use `--ignored` flag, eg. `cargo test -- --ignored`
+    #[test]
+    #[ignore]
+    fn test_decider() {
+        type NOVA = Nova<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            CubicFCircuit<Fr>,
+            Pedersen<Projective>,
+            Pedersen<Projective2>,
+        >;
+        type DECIDER = Decider<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            CubicFCircuit<Fr>,
+            Pedersen<Projective>,
+            Pedersen<Projective2>,
+            Groth16<MNT4_298>, // here we define the Snark to use in the decider
+            NOVA,              // here we define the FoldingScheme to use
+        >;
+
+        let mut rng = ark_std::test_rng();
+        let poseidon_config = poseidon_test_config::<Fr>();
+
+        let F_circuit = CubicFCircuit::<Fr>::new(());
+        let z_0 = vec![Fr::from(3_u32)];
+
+        let (cm_len, cf_cm_len) =
+            get_pedersen_params_len::<Projective, GVar, Projective2, GVar2, CubicFCircuit<Fr>>(
+                &poseidon_config,
+                F_circuit,
+            )
+            .unwrap();
+        let pedersen_params = Pedersen::<Projective>::new_params(&mut rng, cm_len);
+        let cf_pedersen_params = Pedersen::<Projective2>::new_params(&mut rng, cf_cm_len);
+
+        let start = Instant::now();
+        let prover_params =
+            ProverParams::<Projective, Projective2, Pedersen<Projective>, Pedersen<Projective2>> {
+                poseidon_config: poseidon_config.clone(),
+                cm_params: pedersen_params,
+                cf_cm_params: cf_pedersen_params,
+            };
+        println!("generating pedersen params, {:?}", start.elapsed());
+
+        // use Nova as FoldingScheme
+        let start = Instant::now();
+        let mut nova = NOVA::init(&prover_params, F_circuit, z_0.clone()).unwrap();
+        println!("Nova initialized, {:?}", start.elapsed());
+        let start = Instant::now();
+        nova.prove_step().unwrap();
+        println!("prove_step, {:?}", start.elapsed());
+
+        // generate Groth16 setup
+        let circuit = DeciderEthCircuit::<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            Pedersen<Projective>,
+            Pedersen<Projective2>,
+        >::from_nova::<CubicFCircuit<Fr>>(nova.clone());
+        let mut rng = rand::rngs::OsRng;
+
+        let start = Instant::now();
+        let (pk, vk) =
+            Groth16::<MNT4_298>::circuit_specific_setup(circuit.clone(), &mut rng).unwrap();
+        println!("Groth16 setup, {:?}", start.elapsed());
+
+        // decider proof generation
+        let start = Instant::now();
+        let proof = DECIDER::prove(&pk, rng, nova.clone()).unwrap();
+        println!("Decider Groth16 prove, {:?}", start.elapsed());
+
+        // decider proof verification
+        let verified = DECIDER::verify(&vk, nova.i, nova.z_0, nova.z_i, &nova.U_i, proof).unwrap();
+        assert!(verified);
+    }
+}
diff --git a/src/folding/nova/decider_eth_circuit.rs b/src/folding/nova/decider_eth_circuit.rs
index b79bc26..12fb98b 100644
--- a/src/folding/nova/decider_eth_circuit.rs
+++ b/src/folding/nova/decider_eth_circuit.rs
@@ -178,6 +178,7 @@ where
 
 /// Circuit that implements the in-circuit checks needed for the onchain (Ethereum's EVM)
 /// verification.
+#[derive(Clone, Debug)]
 pub struct DeciderEthCircuit<C1, GC1, C2, GC2, CP1, CP2>
 where
     C1: CurveGroup,
@@ -281,13 +282,12 @@ where
                 Ok(self.r1cs.clone())
             })?;
 
-        let i = FpVar::<CF1<C1>>::new_witness(cs.clone(), || {
-            Ok(self.i.unwrap_or_else(CF1::<C1>::zero))
-        })?;
-        let z_0 = Vec::<FpVar<CF1<C1>>>::new_witness(cs.clone(), || {
+        let i =
+            FpVar::<CF1<C1>>::new_input(cs.clone(), || Ok(self.i.unwrap_or_else(CF1::<C1>::zero)))?;
+        let z_0 = Vec::<FpVar<CF1<C1>>>::new_input(cs.clone(), || {
             Ok(self.z_0.unwrap_or(vec![CF1::<C1>::zero()]))
         })?;
-        let z_i = Vec::<FpVar<CF1<C1>>>::new_witness(cs.clone(), || {
+        let z_i = Vec::<FpVar<CF1<C1>>>::new_input(cs.clone(), || {
             Ok(self.z_i.unwrap_or(vec![CF1::<C1>::zero()]))
         })?;
 
@@ -303,7 +303,7 @@ where
         let w_i = WitnessVar::<C1>::new_witness(cs.clone(), || {
             Ok(self.w_i.unwrap_or(w_dummy_native.clone()))
         })?;
-        let U_i = CommittedInstanceVar::<C1>::new_witness(cs.clone(), || {
+        let U_i = CommittedInstanceVar::<C1>::new_input(cs.clone(), || {
             Ok(self.U_i.unwrap_or(u_dummy_native.clone()))
         })?;
         let W_i = WitnessVar::<C1>::new_witness(cs.clone(), || {
@@ -367,7 +367,7 @@ where
         #[cfg(not(test))]
         {
             // imports here instead of at the top of the file, so we avoid having multiple
-            // `#[cfg(not(test))]
+            // `#[cfg(not(test))]`
             use crate::commitment::pedersen::PedersenGadget;
             use crate::folding::nova::cyclefold::{CycleFoldCommittedInstanceVar, CF_IO_LEN};
             use ark_r1cs_std::ToBitsGadget;
diff --git a/src/folding/nova/mod.rs b/src/folding/nova/mod.rs
index d9efa2d..203b023 100644
--- a/src/folding/nova/mod.rs
+++ b/src/folding/nova/mod.rs
@@ -1,4 +1,5 @@
-/// Implements the scheme described in [Nova](https://eprint.iacr.org/2021/370.pdf)
+/// Implements the scheme described in [Nova](https://eprint.iacr.org/2021/370.pdf) and
+/// [CycleFold](https://eprint.iacr.org/2023/1192.pdf).
 use ark_crypto_primitives::{
     crh::{poseidon::CRH, CRHScheme},
     sponge::{poseidon::PoseidonConfig, Absorb},
@@ -22,6 +23,7 @@ use crate::FoldingScheme;
 
 pub mod circuits;
 pub mod cyclefold;
+pub mod decider_eth;
 pub mod decider_eth_circuit;
 pub mod nifs;
 pub mod traits;
@@ -216,10 +218,8 @@ where
     type PreprocessorParam = (Self::ProverParam, FC);
     type ProverParam = ProverParams<C1, C2, CP1, CP2>;
     type VerifierParam = VerifierParams<C1, C2>;
-    type Witness = Witness<C1>;
     type CommittedInstanceWithWitness = (CommittedInstance<C1>, Witness<C1>);
     type CFCommittedInstanceWithWitness = (CommittedInstance<C2>, Witness<C2>);
-    type CommittedInstance = CommittedInstance<C1>;
 
     fn preprocess(
         prep_param: &Self::PreprocessorParam,
diff --git a/src/lib.rs b/src/lib.rs
index 7e32f94..c8b967c 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -5,18 +5,18 @@
 
 use ark_ec::CurveGroup;
 use ark_ff::PrimeField;
+use ark_std::rand::CryptoRng;
 use ark_std::{fmt::Debug, rand::RngCore};
 use thiserror::Error;
 
 use crate::frontend::FCircuit;
 
-pub mod transcript;
-use transcript::Transcript;
 pub mod ccs;
 pub mod commitment;
 pub mod constants;
 pub mod folding;
 pub mod frontend;
+pub mod transcript;
 pub mod utils;
 
 #[derive(Debug, Error)]
@@ -82,10 +82,8 @@ where
     type PreprocessorParam: Debug;
     type ProverParam: Debug;
     type VerifierParam: Debug;
-    type Witness: Debug;
     type CommittedInstanceWithWitness: Debug;
     type CFCommittedInstanceWithWitness: Debug; // CycleFold CommittedInstance & Witness
-    type CommittedInstance: Clone + Debug;
 
     fn preprocess(
         prep_param: &Self::PreprocessorParam,
@@ -123,26 +121,36 @@ where
     ) -> Result<(), Error>;
 }
 
-pub trait Decider<C: CurveGroup>: Clone + Debug {
-    type PreprocessorParam: Debug;
-    type ProverParam: Debug;
-    type VerifierParam: Debug;
-    type FreshInstance: Debug;
+pub trait Decider<
+    C1: CurveGroup,
+    C2: CurveGroup,
+    FC: FCircuit<C1::ScalarField>,
+    FS: FoldingScheme<C1, C2, FC>,
+> where
+    C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
+    C2::BaseField: PrimeField,
+{
+    type ProverParam: Clone;
+    type Proof: Clone;
+    type VerifierParam;
     type PublicInput: Debug;
     type CommittedInstanceWithWitness: Debug;
     type CommittedInstance: Clone + Debug;
 
     fn prove(
         pp: &Self::ProverParam,
-        running_instance: &Self::CommittedInstanceWithWitness,
-        transcript: &mut impl Transcript<C>,
-        rng: impl RngCore,
-    ) -> Result<(), Error>;
+        rng: impl RngCore + CryptoRng,
+        folding_scheme: FS,
+    ) -> Result<Self::Proof, Error>;
 
     fn verify(
         vp: &Self::VerifierParam,
+        i: C1::ScalarField,
+        z_0: Vec<C1::ScalarField>,
+        z_i: Vec<C1::ScalarField>,
         running_instance: &Self::CommittedInstance,
-        transcript: &mut impl Transcript<C>,
-        rng: impl RngCore,
-    ) -> Result<(), Error>;
+        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.
+    ) -> Result<bool, Error>;
 }