@@ -60,7 +60,7 @@ run: |
           curl -sSfL https://github.com/ethereum/solidity/releases/download/v0.8.4/solc-static-linux -o /usr/local/bin/solc
           chmod +x /usr/local/bin/solc
       - name: Execute compile.sh to generate .r1cs and .wasm from .circom
-        run: bash ./folding-schemes/src/frontend/circom/test_folder/compile.sh
+        run: ./folding-schemes/src/frontend/circom/test_folder/compile.sh
       - name: Build
         # This build will be reused by nextest,
         # and also checks (--all-targets) that benches don't bit-rot
@@ -90,7 +90,7 @@ run: |
           curl -sSfL https://github.com/ethereum/solidity/releases/download/v0.8.4/solc-static-linux -o /usr/local/bin/solc
           chmod +x /usr/local/bin/solc
       - name: Execute compile.sh to generate .r1cs and .wasm from .circom
-        run: bash ./folding-schemes/src/frontend/circom/test_folder/compile.sh
+        run: ./folding-schemes/src/frontend/circom/test_folder/compile.sh 
       - name: Run examples tests
         run: cargo test --examples
       - name: Run examples

@@ -4,8 +4,9 @@ use ark_std::rand::Rng;
 
 use crate::utils::vec::{hadamard, mat_vec_mul, vec_add, vec_scalar_mul, SparseMatrix};
 use crate::Error;
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 
-#[derive(Debug, Clone, Eq, PartialEq)]
+#[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct R1CS<F: PrimeField> {
     pub l: usize, // io len
     pub A: SparseMatrix<F>,

@@ -14,6 +14,7 @@ };
 use ark_poly_commit::kzg10::{
     Commitment as KZG10Commitment, Proof as KZG10Proof, VerifierKey, KZG10,
 };
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Valid};
 use ark_std::rand::RngCore;
 use ark_std::{borrow::Cow, fmt::Debug};
 use ark_std::{One, Zero};
@@ -33,6 +34,42 @@ /// Group elements of the form `β^i G`, for different values of `i`.
     pub powers_of_g: Cow<'a, [C::Affine]>,
 }
 
+impl<'a, C: CurveGroup> CanonicalSerialize for ProverKey<'a, C> {
+    fn serialize_with_mode<W: std::io::prelude::Write>(
+        &self,
+        mut writer: W,
+        compress: ark_serialize::Compress,
+    ) -> Result<(), ark_serialize::SerializationError> {
+        self.powers_of_g.serialize_with_mode(&mut writer, compress)
+    }
+
+    fn serialized_size(&self, compress: ark_serialize::Compress) -> usize {
+        self.powers_of_g.serialized_size(compress)
+    }
+}
+
+impl<'a, C: CurveGroup> CanonicalDeserialize for ProverKey<'a, C> {
+    fn deserialize_with_mode<R: std::io::prelude::Read>(
+        reader: R,
+        compress: ark_serialize::Compress,
+        validate: ark_serialize::Validate,
+    ) -> Result<Self, ark_serialize::SerializationError> {
+        let powers_of_g_vec = Vec::deserialize_with_mode(reader, compress, validate)?;
+        Ok(ProverKey {
+            powers_of_g: ark_std::borrow::Cow::Owned(powers_of_g_vec),
+        })
+    }
+}
+
+impl<'a, C: CurveGroup> Valid for ProverKey<'a, C> {
+    fn check(&self) -> Result<(), ark_serialize::SerializationError> {
+        match self.powers_of_g.clone() {
+            Cow::Borrowed(powers) => powers.to_vec().check(),
+            Cow::Owned(powers) => powers.check(),
+        }
+    }
+}
+
 #[derive(Debug, Clone, Default, Eq, PartialEq)]
 pub struct Proof<C: CurveGroup> {
     pub eval: C::ScalarField,
@@ -45,6 +82,7 @@ pub struct KZG<'a, E: Pairing, const H: bool = false> {
     _a: PhantomData<&'a ()>,
     _e: PhantomData<E>,
 }
+
 impl<'a, E, const H: bool> CommitmentScheme<E::G1, H> for KZG<'a, E, H>
 where
     E: Pairing,

@@ -2,6 +2,7 @@ use ark_ec::CurveGroup;
 use ark_ff::Field;
 use ark_r1cs_std::{boolean::Boolean, groups::GroupOpsBounds, prelude::CurveVar};
 use ark_relations::r1cs::SynthesisError;
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::Zero;
 use ark_std::{rand::RngCore, UniformRand};
 use core::marker::PhantomData;
@@ -18,7 +19,7 @@ pub u: Vec<C::ScalarField>,
     pub r_u: C::ScalarField, // blind
 }
 
-#[derive(Debug, Clone, Eq, PartialEq)]
+#[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct Params<C: CurveGroup> {
     pub h: C,
     pub generators: Vec<C::Affine>,

@@ -7,11 +7,12 @@ };
 use ark_ec::{AffineRepr, CurveGroup, Group};
 use ark_ff::{BigInteger, Field, PrimeField, ToConstraintField};
 use ark_r1cs_std::{groups::GroupOpsBounds, prelude::CurveVar, ToConstraintFieldGadget};
+use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystem};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::fmt::Debug;
 use ark_std::{One, Zero};
 use core::marker::PhantomData;
-
-use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystem};
+use std::usize;
 
 use crate::ccs::r1cs::{extract_r1cs, extract_w_x, R1CS};
 use crate::commitment::CommitmentScheme;
@@ -31,6 +32,7 @@ pub mod cyclefold;
 pub mod decider_eth;
 pub mod decider_eth_circuit;
 pub mod nifs;
+pub mod serialize;
 pub mod traits;
 
 use circuits::{AugmentedFCircuit, ChallengeGadget};
@@ -41,7 +43,7 @@
 #[cfg(test)]
 use cyclefold::CF_IO_LEN;
 
-#[derive(Debug, Clone, Eq, PartialEq)]
+#[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct CommittedInstance<C: CurveGroup> {
     pub cmE: C,
     pub u: C::ScalarField,
@@ -148,7 +150,7 @@ .map_err(|e| Error::Other(e.to_string()))
     }
 }
 
-#[derive(Debug, Clone, Eq, PartialEq)]
+#[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct Witness<C: CurveGroup> {
     pub E: Vec<C::ScalarField>,
     pub rE: C::ScalarField,

@@ -0,0 +1,266 @@
+use super::{circuits::AugmentedFCircuit, cyclefold::CycleFoldCircuit, Nova, ProverParams};
+pub use super::{CommittedInstance, Witness};
+pub use crate::folding::circuits::CF2;
+use crate::{
+    ccs::r1cs::extract_r1cs, commitment::CommitmentScheme, folding::circuits::CF1,
+    frontend::FCircuit,
+};
+use ark_crypto_primitives::sponge::{poseidon::PoseidonConfig, Absorb};
+use ark_ec::{CurveGroup, Group};
+use ark_ff::PrimeField;
+use ark_r1cs_std::{
+    groups::{CurveVar, GroupOpsBounds},
+    ToConstraintFieldGadget,
+};
+use ark_relations::r1cs::ConstraintSynthesizer;
+use ark_relations::r1cs::ConstraintSystem;
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, SerializationError, Write};
+use std::marker::PhantomData;
+
+impl<C1, GC1, C2, GC2, FC, CS1, CS2> CanonicalSerialize for Nova<C1, GC1, C2, GC2, FC, CS1, CS2>
+where
+    C1: CurveGroup,
+    C2: CurveGroup,
+    FC: FCircuit<C1::ScalarField>,
+    CS1: CommitmentScheme<C1>,
+    CS2: CommitmentScheme<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 GC1: GroupOpsBounds<'a, C1, GC1>,
+    for<'a> &'a GC2: GroupOpsBounds<'a, C2, GC2>,
+    GC1: CurveVar<C1, <C2 as Group>::ScalarField>,
+    GC1: ToConstraintFieldGadget<<C2 as Group>::ScalarField>,
+    GC2: CurveVar<C2, <C2 as CurveGroup>::BaseField>,
+{
+    fn serialize_with_mode<W: Write>(
+        &self,
+        mut writer: W,
+        compress: ark_serialize::Compress,
+    ) -> Result<(), ark_serialize::SerializationError> {
+        self.i.serialize_with_mode(&mut writer, compress)?;
+        self.z_0.serialize_with_mode(&mut writer, compress)?;
+        self.z_i.serialize_with_mode(&mut writer, compress)?;
+        self.w_i.serialize_with_mode(&mut writer, compress)?;
+        self.u_i.serialize_with_mode(&mut writer, compress)?;
+        self.W_i.serialize_with_mode(&mut writer, compress)?;
+        self.U_i.serialize_with_mode(&mut writer, compress)?;
+        self.cf_W_i.serialize_with_mode(&mut writer, compress)?;
+        self.cf_U_i.serialize_with_mode(&mut writer, compress)
+    }
+
+    fn serialized_size(&self, compress: ark_serialize::Compress) -> usize {
+        self.i.serialized_size(compress)
+            + self.z_0.serialized_size(compress)
+            + self.z_i.serialized_size(compress)
+            + self.w_i.serialized_size(compress)
+            + self.u_i.serialized_size(compress)
+            + self.W_i.serialized_size(compress)
+            + self.U_i.serialized_size(compress)
+            + self.cf_W_i.serialized_size(compress)
+            + self.cf_U_i.serialized_size(compress)
+    }
+
+    fn serialize_compressed<W: Write>(
+        &self,
+        writer: W,
+    ) -> Result<(), ark_serialize::SerializationError> {
+        self.serialize_with_mode(writer, ark_serialize::Compress::Yes)
+    }
+
+    fn compressed_size(&self) -> usize {
+        self.serialized_size(ark_serialize::Compress::Yes)
+    }
+
+    fn serialize_uncompressed<W: Write>(
+        &self,
+        writer: W,
+    ) -> Result<(), ark_serialize::SerializationError> {
+        self.serialize_with_mode(writer, ark_serialize::Compress::No)
+    }
+
+    fn uncompressed_size(&self) -> usize {
+        self.serialized_size(ark_serialize::Compress::No)
+    }
+}
+
+// Note that we can't derive or implement `CanonicalDeserialize` directly.
+// This is because `CurveVar` notably does not implement the `Sync` trait.
+impl<C1, GC1, C2, GC2, FC, CS1, CS2> Nova<C1, GC1, C2, GC2, FC, CS1, CS2>
+where
+    C1: CurveGroup,
+    C2: CurveGroup,
+    FC: FCircuit<CF1<C1>, Params = ()>,
+    CS1: CommitmentScheme<C1>,
+    CS2: CommitmentScheme<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 GC1: GroupOpsBounds<'a, C1, GC1>,
+    for<'a> &'a GC2: GroupOpsBounds<'a, C2, GC2>,
+    GC1: CurveVar<C1, <C2 as Group>::ScalarField>,
+    GC1: ToConstraintFieldGadget<<C2 as Group>::ScalarField>,
+    GC2: CurveVar<C2, CF2<C2>>,
+    GC2: ToConstraintFieldGadget<<C2 as CurveGroup>::BaseField>,
+{
+    pub fn deserialize_nova<R: std::io::prelude::Read>(
+        mut reader: R,
+        compress: ark_serialize::Compress,
+        validate: ark_serialize::Validate,
+        prover_params: ProverParams<C1, C2, CS1, CS2>,
+        poseidon_config: PoseidonConfig<C1::ScalarField>,
+    ) -> Result<Self, ark_serialize::SerializationError> {
+        let i = C1::ScalarField::deserialize_with_mode(&mut reader, compress, validate)?;
+        let z_0 = Vec::<C1::ScalarField>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let z_i = Vec::<C1::ScalarField>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let w_i = Witness::<C1>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let u_i = CommittedInstance::<C1>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let W_i = Witness::<C1>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let U_i = CommittedInstance::<C1>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let cf_W_i = Witness::<C2>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let cf_U_i =
+            CommittedInstance::<C2>::deserialize_with_mode(&mut reader, compress, validate)?;
+
+        let f_circuit = FC::new(()).unwrap();
+        let cs = ConstraintSystem::<C1::ScalarField>::new_ref();
+        let cs2 = ConstraintSystem::<C1::BaseField>::new_ref();
+        let augmented_F_circuit =
+            AugmentedFCircuit::<C1, C2, GC2, FC>::empty(&poseidon_config, f_circuit.clone());
+        let cf_circuit = CycleFoldCircuit::<C1, GC1>::empty();
+
+        augmented_F_circuit
+            .generate_constraints(cs.clone())
+            .map_err(|_| SerializationError::InvalidData)?;
+        cs.finalize();
+        let cs = cs.into_inner().ok_or(SerializationError::InvalidData)?;
+        let r1cs = extract_r1cs::<C1::ScalarField>(&cs);
+
+        cf_circuit
+            .generate_constraints(cs2.clone())
+            .map_err(|_| SerializationError::InvalidData)?;
+        cs2.finalize();
+        let cs2 = cs2.into_inner().ok_or(SerializationError::InvalidData)?;
+        let cf_r1cs = extract_r1cs::<C1::BaseField>(&cs2);
+
+        Ok(Nova {
+            _gc1: PhantomData,
+            _c2: PhantomData,
+            _gc2: PhantomData,
+            cs_params: prover_params.cs_params,
+            cf_cs_params: prover_params.cf_cs_params,
+            i,
+            z_0,
+            z_i,
+            w_i,
+            u_i,
+            W_i,
+            U_i,
+            cf_W_i,
+            cf_U_i,
+            r1cs,
+            cf_r1cs,
+            poseidon_config,
+            F: f_circuit,
+        })
+    }
+}
+
+#[cfg(test)]
+pub mod tests {
+    use crate::{
+        commitment::{
+            kzg::{ProverKey as KZGProverKey, KZG},
+            pedersen::Pedersen,
+            CommitmentScheme,
+        },
+        folding::nova::{get_cs_params_len, Nova, ProverParams},
+        frontend::{tests::CubicFCircuit, FCircuit},
+        transcript::poseidon::poseidon_canonical_config,
+        FoldingScheme,
+    };
+    use ark_bn254::{constraints::GVar, Bn254, Fr, G1Projective as Projective};
+    use ark_grumpkin::{constraints::GVar as GVar2, Projective as Projective2};
+    use ark_poly_commit::kzg10::VerifierKey as KZGVerifierKey;
+    use ark_serialize::{CanonicalSerialize, Compress, Validate};
+    use std::{fs, io::Write};
+
+    #[test]
+    fn test_serde_nova() {
+        let mut rng = ark_std::test_rng();
+        let poseidon_config = poseidon_canonical_config::<Fr>();
+        let F_circuit = CubicFCircuit::<Fr>::new(()).unwrap();
+        let (cs_len, cf_cs_len) =
+            get_cs_params_len::<Projective, GVar, Projective2, GVar2, CubicFCircuit<Fr>>(
+                &poseidon_config,
+                F_circuit,
+            )
+            .unwrap();
+        let (kzg_pk, _): (KZGProverKey<Projective>, KZGVerifierKey<Bn254>) =
+            KZG::<Bn254>::setup(&mut rng, cs_len).unwrap();
+        let (cf_pedersen_params, _) = Pedersen::<Projective2>::setup(&mut rng, cf_cs_len).unwrap();
+
+        // Initialize nova and make multiple `prove_step()`
+        type NOVA<CS1, CS2> =
+            Nova<Projective, GVar, Projective2, GVar2, CubicFCircuit<Fr>, CS1, CS2>;
+        let prover_params =
+            ProverParams::<Projective, Projective2, KZG<Bn254>, Pedersen<Projective2>> {
+                poseidon_config: poseidon_config.clone(),
+                cs_params: kzg_pk.clone(),
+                cf_cs_params: cf_pedersen_params.clone(),
+            };
+
+        let z_0 = vec![Fr::from(3_u32)];
+        let mut nova = NOVA::init(&prover_params, F_circuit, z_0.clone()).unwrap();
+
+        let num_steps: usize = 3;
+        for _ in 0..num_steps {
+            nova.prove_step(vec![]).unwrap();
+        }
+
+        let mut writer = vec![];
+        assert!(nova
+            .serialize_with_mode(&mut writer, ark_serialize::Compress::No)
+            .is_ok());
+
+        let mut file = fs::OpenOptions::new()
+            .create(true)
+            .write(true)
+            .open("./nova.serde")
+            .unwrap();
+
+        file.write_all(&writer).unwrap();
+
+        let bytes = fs::read("./nova.serde").unwrap();
+
+        let mut deserialized_nova = Nova::<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            CubicFCircuit<Fr>,
+            KZG<Bn254>,
+            Pedersen<Projective2>,
+        >::deserialize_nova(
+            bytes.as_slice(),
+            Compress::No,
+            Validate::No,
+            prover_params,
+            poseidon_config,
+        )
+        .unwrap();
+
+        assert_eq!(nova.i, deserialized_nova.i);
+
+        let num_steps: usize = 3;
+        for _ in 0..num_steps {
+            deserialized_nova.prove_step(vec![]).unwrap();
+            nova.prove_step(vec![]).unwrap();
+        }
+
+        assert_eq!(deserialized_nova.w_i, nova.w_i);
+    }
+}

@@ -3,13 +3,14 @@ use ark_poly::{
     univariate::DensePolynomial, EvaluationDomain, Evaluations, GeneralEvaluationDomain,
 };
 pub use ark_relations::r1cs::Matrix as R1CSMatrix;
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::cfg_iter;
 use ark_std::rand::Rng;
 use rayon::iter::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator};
 
 use crate::Error;
 
-#[derive(Clone, Debug, Eq, PartialEq)]
+#[derive(Clone, Debug, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct SparseMatrix<F: PrimeField> {
     pub n_rows: usize,
     pub n_cols: usize,