@@ -1,6 +1,8 @@
 use ark_crypto_primitives::sponge::Absorb;
 use ark_ec::CurveGroup;
 use ark_ff::PrimeField;
+use ark_serialize::CanonicalDeserialize;
+use ark_serialize::CanonicalSerialize;
 use ark_std::One;
 use ark_std::Zero;
 use std::sync::Arc;
@@ -17,7 +19,7 @@ use crate::utils::virtual_polynomial::{build_eq_x_r_vec, VirtualPolynomial};
 use crate::Error;
 
 /// Committed CCS instance
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, CanonicalSerialize, CanonicalDeserialize)]
 pub struct CCCS<C: CurveGroup> {
     // Commitment to witness
     pub C: C,

@@ -3,6 +3,7 @@ use ark_crypto_primitives::sponge::Absorb;
 use ark_ec::{CurveGroup, Group};
 use ark_ff::PrimeField;
 use ark_r1cs_std::{groups::GroupOpsBounds, prelude::CurveVar, ToConstraintFieldGadget};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_snark::SNARK;
 use ark_std::rand::{CryptoRng, RngCore};
 use ark_std::{One, Zero};
@@ -14,11 +15,12 @@ use crate::commitment::{
     kzg::Proof as KZGProof, pedersen::Params as PedersenParams, CommitmentScheme,
 };
 use crate::folding::circuits::{nonnative::affine::NonNativeAffineVar, CF2};
+use crate::folding::nova::decider_eth::VerifierParam;
 use crate::frontend::FCircuit;
 use crate::Error;
 use crate::{Decider as DeciderTrait, FoldingScheme};
 
-#[derive(Debug, Clone, Eq, PartialEq)]
+#[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct Proof<C1, CS1, S>
 where
     C1: CurveGroup,
@@ -85,8 +87,7 @@ {
     type PreprocessorParam = (FS::ProverParam, FS::VerifierParam);
     type ProverParam = (S::ProvingKey, CS1::ProverParams);
     type Proof = Proof<C1, CS1, S>;
-    /// VerifierParam = (pp_hash, snark::vk, commitment_scheme::vk)
-    type VerifierParam = (C1::ScalarField, S::VerifyingKey, CS1::VerifierParams);
+    type VerifierParam = VerifierParam<C1, CS1::VerifierParams, S::VerifyingKey>;
     type PublicInput = Vec<C1::ScalarField>;
     type CommittedInstance = ();
 
@@ -120,7 +121,12 @@ >>::VerifierParam = prep_param.1.into();
         let pp_hash = hypernova_vp.pp_hash()?;
 
         let pp = (g16_pk, hypernova_pp.cs_pp);
-        let vp = (pp_hash, g16_vk, hypernova_vp.cs_vp);
+
+        let vp = VerifierParam {
+            pp_hash,
+            snark_vp: g16_vk,
+            cs_vp: hypernova_vp.cs_vp,
+        };
         Ok((pp, vp))
     }
 
@@ -183,7 +189,7 @@ return Err(Error::NotEnoughSteps);
         }
 
         let (pp_hash, snark_vk, cs_vk): (C1::ScalarField, S::VerifyingKey, CS1::VerifierParams) =
-            vp;
+            (vp.pp_hash, vp.snark_vp, vp.cs_vp);
 
         // Note: the NIMFS proof is checked inside the DeciderEthCircuit, which ensures that the
         // 'proof.U_i1' is correctly computed
@@ -223,11 +229,15 @@ pub mod tests {
     use ark_bn254::{constraints::GVar, Bn254, Fr, G1Projective as Projective};
     use ark_groth16::Groth16;
     use ark_grumpkin::{constraints::GVar as GVar2, Projective as Projective2};
-    use std::time::Instant;
+    use ark_serialize::{Compress, Validate};
 
     use super::*;
     use crate::commitment::{kzg::KZG, pedersen::Pedersen};
-    use crate::folding::hypernova::PreprocessorParam;
+    use crate::folding::hypernova::cccs::CCCS;
+    use crate::folding::hypernova::{
+        PreprocessorParam, ProverParams, VerifierParams as HyperNovaVerifierParams,
+    };
+    use crate::folding::nova::decider_eth::VerifierParam;
     use crate::frontend::utils::CubicFCircuit;
     use crate::transcript::poseidon::poseidon_canonical_config;
 
@@ -262,7 +272,7 @@ MU,
             NU,
         >;
 
-        let mut rng = ark_std::test_rng();
+        let mut rng = rand::rngs::OsRng;
         let poseidon_config = poseidon_canonical_config::<Fr>();
 
         let F_circuit = CubicFCircuit::<Fr>::new(()).unwrap();
@@ -271,31 +281,22 @@
         let prep_param = PreprocessorParam::new(poseidon_config, F_circuit);
         let hypernova_params = HN::preprocess(&mut rng, &prep_param).unwrap();
 
-        let start = Instant::now();
         let mut hypernova = HN::init(&hypernova_params, F_circuit, z_0.clone()).unwrap();
-        println!("Nova initialized, {:?}", start.elapsed());
-        let start = Instant::now();
         hypernova
             .prove_step(&mut rng, vec![], Some((vec![], vec![])))
             .unwrap();
-        println!("prove_step, {:?}", start.elapsed());
         hypernova
             .prove_step(&mut rng, vec![], Some((vec![], vec![])))
             .unwrap(); // do a 2nd step
-
-        let mut rng = rand::rngs::OsRng;
 
         // prepare the Decider prover & verifier params
         let (decider_pp, decider_vp) =
             D::preprocess(&mut rng, hypernova_params, hypernova.clone()).unwrap();
 
         // decider proof generation
-        let start = Instant::now();
         let proof = D::prove(rng, decider_pp, hypernova.clone()).unwrap();
-        println!("Decider prove, {:?}", start.elapsed());
 
         // decider proof verification
-        let start = Instant::now();
         let verified = D::verify(
             decider_vp,
             hypernova.i,
@@ -307,6 +308,189 @@ &proof,
         )
         .unwrap();
         assert!(verified);
-        println!("Decider verify, {:?}", start.elapsed());
+    }
+
+    #[test]
+    fn test_decider_serialization() {
+        const MU: usize = 1;
+        const NU: usize = 1;
+        // use HyperNova as FoldingScheme
+        type HN = HyperNova<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            CubicFCircuit<Fr>,
+            KZG<'static, Bn254>,
+            Pedersen<Projective2>,
+            MU,
+            NU,
+            false,
+        >;
+        type D = Decider<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            CubicFCircuit<Fr>,
+            KZG<'static, Bn254>,
+            Pedersen<Projective2>,
+            Groth16<Bn254>, // here we define the Snark to use in the decider
+            HN,             // here we define the FoldingScheme to use
+            MU,
+            NU,
+        >;
+
+        let mut rng = ark_std::test_rng();
+        let poseidon_config = poseidon_canonical_config::<Fr>();
+
+        let F_circuit = CubicFCircuit::<Fr>::new(()).unwrap();
+        let z_0 = vec![Fr::from(3_u32)];
+
+        let prep_param = PreprocessorParam::new(poseidon_config.clone(), F_circuit);
+        let hypernova_params = HN::preprocess(&mut rng, &prep_param).unwrap();
+
+        let hypernova = HN::init(&hypernova_params, F_circuit, z_0.clone()).unwrap();
+
+        let mut rng = rand::rngs::OsRng;
+
+        // prepare the Decider prover & verifier params
+        let (decider_pp, decider_vp) =
+            D::preprocess(&mut rng, hypernova_params.clone(), hypernova.clone()).unwrap();
+
+        let mut hypernova_pp_serialized = vec![];
+        hypernova_params
+            .0
+            .clone()
+            .serialize_compressed(&mut hypernova_pp_serialized)
+            .unwrap();
+        let mut hypernova_vp_serialized = vec![];
+        hypernova_params
+            .1
+            .clone()
+            .serialize_compressed(&mut hypernova_vp_serialized)
+            .unwrap();
+
+        let hypernova_pp_deserialized = ProverParams::<
+            Projective,
+            Projective2,
+            KZG<'static, Bn254>,
+            Pedersen<Projective2>,
+            false,
+        >::deserialize_prover_params(
+            hypernova_pp_serialized.as_slice(),
+            Compress::Yes,
+            Validate::No,
+            &hypernova_params.0.ccs,
+            &poseidon_config,
+        )
+        .unwrap();
+
+        let hypernova_vp_deserialized = HyperNovaVerifierParams::<
+            Projective,
+            Projective2,
+            KZG<'static, Bn254>,
+            Pedersen<Projective2>,
+            false,
+        >::deserialize_verifier_params(
+            hypernova_vp_serialized.as_slice(),
+            Compress::Yes,
+            Validate::No,
+            &hypernova_params.0.ccs.unwrap(),
+            &poseidon_config,
+        )
+        .unwrap();
+
+        let hypernova_params = (hypernova_pp_deserialized, hypernova_vp_deserialized);
+        let mut hypernova = HN::init(&hypernova_params, F_circuit, z_0.clone()).unwrap();
+
+        hypernova
+            .prove_step(&mut rng, vec![], Some((vec![], vec![])))
+            .unwrap();
+        hypernova
+            .prove_step(&mut rng, vec![], Some((vec![], vec![])))
+            .unwrap();
+
+        // decider proof generation
+        let proof = D::prove(rng, decider_pp, hypernova.clone()).unwrap();
+
+        let verified = D::verify(
+            decider_vp.clone(),
+            hypernova.i.clone(),
+            hypernova.z_0.clone(),
+            hypernova.z_i.clone(),
+            &(),
+            &(),
+            &proof,
+        )
+        .unwrap();
+        assert!(verified);
+
+        // The rest of this test will serialize the data and deserialize it back, and use it to
+        // verify the proof:
+
+        // serialize the verifier_params, proof and public inputs
+        let mut decider_vp_serialized = vec![];
+        decider_vp
+            .serialize_compressed(&mut decider_vp_serialized)
+            .unwrap();
+        let mut proof_serialized = vec![];
+        proof.serialize_compressed(&mut proof_serialized).unwrap();
+        // serialize the public inputs in a single packet
+        let mut public_inputs_serialized = vec![];
+        hypernova
+            .i
+            .serialize_compressed(&mut public_inputs_serialized)
+            .unwrap();
+        hypernova
+            .z_0
+            .serialize_compressed(&mut public_inputs_serialized)
+            .unwrap();
+        hypernova
+            .z_i
+            .serialize_compressed(&mut public_inputs_serialized)
+            .unwrap();
+        hypernova
+            .U_i
+            .serialize_compressed(&mut public_inputs_serialized)
+            .unwrap();
+        hypernova
+            .u_i
+            .serialize_compressed(&mut public_inputs_serialized)
+            .unwrap();
+
+        // deserialize back the verifier_params, proof and public inputs
+        let decider_vp_deserialized =
+            VerifierParam::<
+                Projective,
+                <KZG<'static, Bn254> as CommitmentScheme<Projective>>::VerifierParams,
+                <Groth16<Bn254> as SNARK<Fr>>::VerifyingKey,
+            >::deserialize_compressed(&mut decider_vp_serialized.as_slice())
+            .unwrap();
+
+        let proof_deserialized =
+            Proof::<Projective, KZG<'static, Bn254>, Groth16<Bn254>>::deserialize_compressed(
+                &mut proof_serialized.as_slice(),
+            )
+            .unwrap();
+
+        let mut reader = public_inputs_serialized.as_slice();
+        let i_deserialized = Fr::deserialize_compressed(&mut reader).unwrap();
+        let z_0_deserialized = Vec::<Fr>::deserialize_compressed(&mut reader).unwrap();
+        let z_i_deserialized = Vec::<Fr>::deserialize_compressed(&mut reader).unwrap();
+        let _U_i = LCCCS::<Projective>::deserialize_compressed(&mut reader).unwrap();
+        let _u_i = CCCS::<Projective>::deserialize_compressed(&mut reader).unwrap();
+
+        let verified = D::verify(
+            decider_vp_deserialized,
+            i_deserialized.clone(),
+            z_0_deserialized.clone(),
+            z_i_deserialized.clone(),
+            &(),
+            &(),
+            &proof_deserialized,
+        )
+        .unwrap();
+        assert!(verified);
     }
 }

@@ -3,6 +3,8 @@ use ark_ec::{CurveGroup, Group};
 use ark_ff::PrimeField;
 use ark_poly::DenseMultilinearExtension;
 use ark_poly::MultilinearExtension;
+use ark_serialize::CanonicalDeserialize;
+use ark_serialize::CanonicalSerialize;
 use ark_std::rand::Rng;
 use ark_std::Zero;
 
@@ -15,7 +17,7 @@ use crate::utils::vec::mat_vec_mul;
 use crate::Error;
 
 /// Linearized Committed CCS instance
-#[derive(Debug, Clone, Eq, PartialEq)]
+#[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct LCCCS<C: CurveGroup> {
     // Commitment to witness
     pub C: C,

@@ -6,6 +6,7 @@ };
 use ark_ec::{CurveGroup, Group};
 use ark_ff::{BigInteger, PrimeField};
 use ark_r1cs_std::{groups::GroupOpsBounds, prelude::CurveVar, ToConstraintFieldGadget};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::{fmt::Debug, marker::PhantomData, rand::RngCore, One, Zero};
 
 pub mod cccs;
@@ -14,6 +15,7 @@ pub mod decider_eth;
 pub mod decider_eth_circuit;
 pub mod lcccs;
 pub mod nimfs;
+pub mod serialize;
 pub mod utils;
 
 use cccs::CCCS;
@@ -62,7 +64,7 @@ pub type HyperNovaCycleFoldCircuit<C, GC, const MU: usize, const NU: usize> =
     CycleFoldCircuit<HyperNovaCycleFoldConfig<C, MU, NU>, GC>;
 
 /// Witness for the LCCCS & CCCS, containing the w vector, and the r_w used as randomness in the Pedersen commitment.
-#[derive(Debug, Clone, Eq, PartialEq)]
+#[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct Witness<F: PrimeField> {
     pub w: Vec<F>,
     pub r_w: F,
@@ -939,13 +941,25 @@ test_ivc_opt::<KZG<Bn254>, Pedersen<Projective2>, false>(poseidon_config, F_circuit);
     }
 
     // test_ivc allowing to choose the CommitmentSchemes
-    fn test_ivc_opt<
+    pub fn test_ivc_opt<
         CS1: CommitmentScheme<Projective, H>,
         CS2: CommitmentScheme<Projective2, H>,
         const H: bool,
     >(
         poseidon_config: PoseidonConfig<Fr>,
         F_circuit: CubicFCircuit<Fr>,
+    ) -> (
+        HyperNova<Projective, GVar, Projective2, GVar2, CubicFCircuit<Fr>, CS1, CS2, 2, 3, H>,
+        (
+            ProverParams<Projective, Projective2, CS1, CS2, H>,
+            VerifierParams<Projective, Projective2, CS1, CS2, H>,
+        ),
+        (LCCCS<Projective>, Witness<Fr>),
+        (CCCS<Projective>, Witness<Fr>),
+        (
+            CycleFoldCommittedInstance<Projective2>,
+            CycleFoldWitness<Projective2>,
+        ),
     ) {
         let mut rng = ark_std::test_rng();
 
@@ -1001,14 +1015,22 @@ assert_eq!(Fr::from(num_steps as u32), hypernova.i);
 
         let (running_instance, incoming_instance, cyclefold_instance) = hypernova.instances();
         HN::verify(
-            hypernova_params.1, // verifier_params
+            hypernova_params.1.clone(), // verifier_params
             z_0,
-            hypernova.z_i,
-            hypernova.i,
+            hypernova.z_i.clone(),
+            hypernova.i.clone(),
+            running_instance.clone(),
+            incoming_instance.clone(),
+            cyclefold_instance.clone(),
+        )
+        .unwrap();
+
+        (
+            hypernova,
+            hypernova_params,
             running_instance,
             incoming_instance,
             cyclefold_instance,
         )
-        .unwrap();
     }
 }

@@ -0,0 +1,420 @@
+use crate::arith::ccs::CCS;
+use crate::arith::r1cs::R1CS;
+use crate::folding::hypernova::ProverParams;
+use crate::folding::hypernova::VerifierParams;
+use ark_crypto_primitives::sponge::poseidon::PoseidonConfig;
+use ark_crypto_primitives::sponge::Absorb;
+use ark_ec::{CurveGroup, Group};
+use ark_ff::PrimeField;
+use ark_r1cs_std::groups::{CurveVar, GroupOpsBounds};
+use ark_r1cs_std::ToConstraintFieldGadget;
+use ark_serialize::CanonicalDeserialize;
+use ark_serialize::{CanonicalSerialize, Compress, SerializationError, Validate};
+use ark_std::marker::PhantomData;
+
+use crate::folding::hypernova::cccs::CCCS;
+use crate::folding::hypernova::lcccs::LCCCS;
+use crate::folding::hypernova::Witness;
+use crate::folding::nova::{
+    CommittedInstance as CycleFoldCommittedInstance, Witness as CycleFoldWitness,
+};
+use crate::FoldingScheme;
+use crate::{
+    commitment::CommitmentScheme,
+    folding::{circuits::CF2, nova::PreprocessorParam},
+    frontend::FCircuit,
+};
+
+use super::HyperNova;
+
+impl<C1, GC1, C2, GC2, FC, CS1, CS2, const MU: usize, const NU: usize, const H: bool>
+    CanonicalSerialize for HyperNova<C1, GC1, C2, GC2, FC, CS1, CS2, MU, NU, H>
+where
+    C1: CurveGroup,
+    GC1: CurveVar<C1, CF2<C1>> + ToConstraintFieldGadget<CF2<C1>>,
+    C2: CurveGroup,
+    GC2: CurveVar<C2, CF2<C2>>,
+    FC: FCircuit<C1::ScalarField>,
+    CS1: CommitmentScheme<C1, H>,
+    CS2: CommitmentScheme<C2, H>,
+{
+    fn serialize_compressed<W: std::io::prelude::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: std::io::prelude::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)
+    }
+
+    fn serialize_with_mode<W: std::io::prelude::Write>(
+        &self,
+        mut writer: W,
+        compress: ark_serialize::Compress,
+    ) -> Result<(), ark_serialize::SerializationError> {
+        self.pp_hash.serialize_with_mode(&mut writer, compress)?;
+        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.pp_hash.serialized_size(compress)
+            + 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)
+    }
+}
+
+impl<C1, GC1, C2, GC2, FC, CS1, CS2, const MU: usize, const NU: usize, const H: bool>
+    HyperNova<C1, GC1, C2, GC2, FC, CS1, CS2, MU, NU, H>
+where
+    C1: CurveGroup,
+    GC1: CurveVar<C1, CF2<C1>> + ToConstraintFieldGadget<CF2<C1>>,
+    C2: CurveGroup,
+    GC2: CurveVar<C2, CF2<C2>> + ToConstraintFieldGadget<CF2<C2>>,
+    FC: FCircuit<C1::ScalarField, Params = ()>,
+    CS1: CommitmentScheme<C1, H>,
+    CS2: CommitmentScheme<C2, H>,
+    <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>,
+{
+    #[allow(clippy::too_many_arguments)]
+    pub fn deserialize_hypernova<R: std::io::prelude::Read>(
+        mut reader: R,
+        compress: Compress,
+        validate: Validate,
+        poseidon_config: PoseidonConfig<C1::ScalarField>,
+        cs_pp: CS1::ProverParams,
+        cs_vp: CS1::VerifierParams,
+        cf_cs_pp: CS2::ProverParams,
+        cf_cs_vp: CS2::VerifierParams,
+    ) -> Result<Self, SerializationError> {
+        let f_circuit = FC::new(()).unwrap();
+        let prep_param = PreprocessorParam {
+            poseidon_config: poseidon_config.clone(),
+            F: f_circuit.clone(),
+            cs_pp: Some(cs_pp.clone()),
+            cs_vp: Some(cs_vp.clone()),
+            cf_cs_pp: Some(cf_cs_pp.clone()),
+            cf_cs_vp: Some(cf_cs_vp.clone()),
+        };
+        // `test_rng` won't be used in `preprocess`, since parameters have already been initialized
+        let (prover_params, verifier_params) = Self::preprocess(ark_std::test_rng(), &prep_param)
+            .or(Err(SerializationError::InvalidData))?;
+        let pp_hash = C1::ScalarField::deserialize_with_mode(&mut reader, compress, validate)?;
+        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::ScalarField>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let U_i = LCCCS::<C1>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let w_i =
+            Witness::<C1::ScalarField>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let u_i = CCCS::<C1>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let cf_W_i =
+            CycleFoldWitness::<C2>::deserialize_with_mode(&mut reader, compress, validate)?;
+        let cf_U_i = CycleFoldCommittedInstance::<C2>::deserialize_with_mode(
+            &mut reader,
+            compress,
+            validate,
+        )?;
+        let ccs = prover_params.ccs.ok_or(SerializationError::InvalidData)?;
+
+        Ok(HyperNova {
+            _gc1: PhantomData,
+            _c2: PhantomData,
+            _gc2: PhantomData,
+            ccs,
+            cf_r1cs: verifier_params.cf_r1cs,
+            poseidon_config,
+            cs_pp,
+            cf_cs_pp,
+            F: f_circuit,
+            pp_hash,
+            i,
+            z_0,
+            z_i,
+            W_i,
+            U_i,
+            w_i,
+            u_i,
+            cf_W_i,
+            cf_U_i,
+        })
+    }
+}
+
+impl<
+        C1: CurveGroup,
+        C2: CurveGroup,
+        CS1: CommitmentScheme<C1, H>,
+        CS2: CommitmentScheme<C2, H>,
+        const H: bool,
+    > CanonicalSerialize for ProverParams<C1, C2, CS1, CS2, H>
+{
+    fn serialize_compressed<W: std::io::prelude::Write>(
+        &self,
+        writer: W,
+    ) -> Result<(), SerializationError> {
+        self.serialize_with_mode(writer, Compress::Yes)
+    }
+
+    fn compressed_size(&self) -> usize {
+        self.serialized_size(Compress::Yes)
+    }
+
+    fn serialize_uncompressed<W: std::io::prelude::Write>(
+        &self,
+        writer: W,
+    ) -> Result<(), SerializationError> {
+        self.serialize_with_mode(writer, Compress::No)
+    }
+
+    fn uncompressed_size(&self) -> usize {
+        self.serialized_size(Compress::No)
+    }
+
+    fn serialize_with_mode<W: std::io::prelude::Write>(
+        &self,
+        mut writer: W,
+        compress: Compress,
+    ) -> Result<(), SerializationError> {
+        self.cs_pp.serialize_with_mode(&mut writer, compress)?;
+        self.cf_cs_pp.serialize_with_mode(&mut writer, compress)
+    }
+
+    fn serialized_size(&self, compress: Compress) -> usize {
+        self.cs_pp.serialized_size(compress) + self.cf_cs_pp.serialized_size(compress)
+    }
+}
+
+impl<
+        C1: CurveGroup,
+        C2: CurveGroup,
+        CS1: CommitmentScheme<C1, H>,
+        CS2: CommitmentScheme<C2, H>,
+        const H: bool,
+    > ProverParams<C1, C2, CS1, CS2, H>
+{
+    pub fn deserialize_prover_params<R: std::io::prelude::Read>(
+        mut reader: R,
+        compress: Compress,
+        validate: Validate,
+        ccs: &Option<CCS<C1::ScalarField>>,
+        poseidon_config: &PoseidonConfig<C1::ScalarField>,
+    ) -> Result<Self, SerializationError> {
+        let cs_pp = CS1::ProverParams::deserialize_with_mode(&mut reader, compress, validate)?;
+        let cf_cs_pp = CS2::ProverParams::deserialize_with_mode(&mut reader, compress, validate)?;
+
+        Ok(ProverParams {
+            cs_pp,
+            cf_cs_pp,
+            ccs: ccs.clone(),
+            poseidon_config: poseidon_config.clone(),
+        })
+    }
+}
+
+impl<
+        C1: CurveGroup,
+        C2: CurveGroup,
+        CS1: CommitmentScheme<C1, H>,
+        CS2: CommitmentScheme<C2, H>,
+        const H: bool,
+    > CanonicalSerialize for VerifierParams<C1, C2, CS1, CS2, H>
+{
+    fn serialize_compressed<W: std::io::prelude::Write>(
+        &self,
+        writer: W,
+    ) -> Result<(), SerializationError> {
+        self.serialize_with_mode(writer, Compress::Yes)
+    }
+
+    fn compressed_size(&self) -> usize {
+        self.serialized_size(Compress::Yes)
+    }
+
+    fn serialize_uncompressed<W: std::io::prelude::Write>(
+        &self,
+        writer: W,
+    ) -> Result<(), SerializationError> {
+        self.serialize_with_mode(writer, Compress::No)
+    }
+
+    fn uncompressed_size(&self) -> usize {
+        self.serialized_size(Compress::No)
+    }
+
+    fn serialize_with_mode<W: std::io::prelude::Write>(
+        &self,
+        mut writer: W,
+        compress: Compress,
+    ) -> Result<(), SerializationError> {
+        self.cf_r1cs.serialize_with_mode(&mut writer, compress)?;
+        self.cs_vp.serialize_with_mode(&mut writer, compress)?;
+        self.cf_cs_vp.serialize_with_mode(&mut writer, compress)
+    }
+
+    fn serialized_size(&self, compress: Compress) -> usize {
+        self.cf_r1cs.serialized_size(compress)
+            + self.cs_vp.serialized_size(compress)
+            + self.cf_cs_vp.serialized_size(compress)
+    }
+}
+
+impl<
+        C1: CurveGroup,
+        C2: CurveGroup,
+        CS1: CommitmentScheme<C1, H>,
+        CS2: CommitmentScheme<C2, H>,
+        const H: bool,
+    > VerifierParams<C1, C2, CS1, CS2, H>
+{
+    pub fn deserialize_verifier_params<R: std::io::Read>(
+        mut reader: R,
+        compress: Compress,
+        validate: Validate,
+        ccs: &CCS<C1::ScalarField>,
+        poseidon_config: &PoseidonConfig<C1::ScalarField>,
+    ) -> Result<Self, SerializationError> {
+        let cf_r1cs = R1CS::deserialize_with_mode(&mut reader, compress, validate)?;
+        let cs_vp = CS1::VerifierParams::deserialize_with_mode(&mut reader, compress, validate)?;
+        let cf_cs_vp = CS2::VerifierParams::deserialize_with_mode(&mut reader, compress, validate)?;
+        Ok(VerifierParams {
+            ccs: ccs.clone(),
+            poseidon_config: poseidon_config.clone(),
+            cf_r1cs,
+            cs_vp,
+            cf_cs_vp,
+        })
+    }
+}
+
+#[cfg(test)]
+pub mod tests {
+    use crate::FoldingScheme;
+    use crate::MultiFolding;
+    use ark_serialize::{Compress, Validate, Write};
+    use std::fs;
+
+    use crate::{
+        commitment::{kzg::KZG, pedersen::Pedersen},
+        folding::hypernova::{tests::test_ivc_opt, HyperNova},
+        frontend::{utils::CubicFCircuit, FCircuit},
+        transcript::poseidon::poseidon_canonical_config,
+    };
+    use ark_bn254::{constraints::GVar, Bn254, Fr, G1Projective as Projective};
+    use ark_grumpkin::{constraints::GVar as GVar2, Projective as Projective2};
+    use ark_serialize::CanonicalSerialize;
+
+    #[test]
+    fn test_serde_hypernova() {
+        let poseidon_config = poseidon_canonical_config::<Fr>();
+        let F_circuit = CubicFCircuit::<Fr>::new(()).unwrap();
+        let (mut hn, (_, verifier_params), _, _, _) = test_ivc_opt::<
+            KZG<Bn254>,
+            Pedersen<Projective2>,
+            false,
+        >(poseidon_config.clone(), F_circuit);
+
+        let mut writer = vec![];
+        assert!(hn.serialize_compressed(&mut writer).is_ok());
+        let mut writer = vec![];
+        assert!(hn.serialize_uncompressed(&mut writer).is_ok());
+
+        let mut file = fs::OpenOptions::new()
+            .create(true)
+            .write(true)
+            .open("./hypernova.serde")
+            .unwrap();
+
+        file.write_all(&writer).unwrap();
+
+        let bytes = fs::read("./hypernova.serde").unwrap();
+
+        let mut hn_deserialized = HyperNova::<
+            Projective,
+            GVar,
+            Projective2,
+            GVar2,
+            CubicFCircuit<Fr>,
+            KZG<Bn254>,
+            Pedersen<Projective2>,
+            2,
+            3,
+            false,
+        >::deserialize_hypernova(
+            bytes.as_slice(),
+            Compress::No,
+            Validate::No,
+            poseidon_config,
+            hn.cs_pp.clone(),
+            verifier_params.cs_vp,
+            hn.cf_cs_pp.clone(),
+            verifier_params.cf_cs_vp,
+        )
+        .unwrap();
+
+        assert_eq!(hn.i, hn_deserialized.i);
+
+        let mut rng = ark_std::test_rng();
+        for _ in 0..3 {
+            // prepare some new instances to fold in the multifolding step
+            let mut lcccs = vec![];
+            for j in 0..1 {
+                let instance_state = vec![Fr::from(j as u32 + 85_u32)];
+                let (U, W) = hn
+                    .new_running_instance(&mut rng, instance_state, vec![])
+                    .unwrap();
+                lcccs.push((U, W));
+            }
+            let mut cccs = vec![];
+            for j in 0..2 {
+                let instance_state = vec![Fr::from(j as u32 + 15_u32)];
+                let (u, w) = hn
+                    .new_incoming_instance(&mut rng, instance_state, vec![])
+                    .unwrap();
+                cccs.push((u, w));
+            }
+
+            hn.prove_step(&mut rng, vec![], Some((lcccs.clone(), cccs.clone())))
+                .unwrap();
+            hn_deserialized
+                .prove_step(&mut rng, vec![], Some((lcccs, cccs)))
+                .unwrap();
+        }
+
+        assert_eq!(hn.z_i, hn_deserialized.z_i);
+    }
+}