diff --git a/folding-schemes/src/folding/circuits/cyclefold.rs b/folding-schemes/src/folding/circuits/cyclefold.rs
index c4527d71..9e86651a 100644
--- a/folding-schemes/src/folding/circuits/cyclefold.rs
+++ b/folding-schemes/src/folding/circuits/cyclefold.rs
@@ -16,20 +16,23 @@ use ark_relations::r1cs::{
 };
 use ark_std::fmt::Debug;
 use ark_std::rand::RngCore;
-use ark_std::Zero;
+use ark_std::{One, Zero};
 use core::{borrow::Borrow, marker::PhantomData};
 
 use super::{nonnative::uint::NonNativeUintVar, CF1, CF2};
-use crate::arith::{
-    r1cs::{circuits::R1CSMatricesVar, extract_w_x, R1CS},
-    ArithGadget,
-};
 use crate::commitment::CommitmentScheme;
 use crate::constants::NOVA_N_BITS_RO;
 use crate::folding::nova::{nifs::NIFS, traits::NIFSTrait};
 use crate::transcript::{AbsorbNonNative, AbsorbNonNativeGadget, Transcript, TranscriptVar};
 use crate::utils::gadgets::{EquivalenceGadget, VectorGadget};
 use crate::Error;
+use crate::{
+    arith::{
+        r1cs::{circuits::R1CSMatricesVar, extract_w_x, R1CS},
+        ArithGadget,
+    },
+    folding::traits::Inputize,
+};
 
 /// Re-export the Nova committed instance as `CycleFoldCommittedInstance` and
 /// witness as `CycleFoldWitness`, for clarity and consistency
@@ -37,6 +40,35 @@ pub use crate::folding::nova::{
     CommittedInstance as CycleFoldCommittedInstance, Witness as CycleFoldWitness,
 };
 
+impl<C: CurveGroup, GC: CurveVar<C, CF2<C>>> Inputize<CF2<C>, CycleFoldCommittedInstanceVar<C, GC>>
+    for CycleFoldCommittedInstance<C>
+{
+    fn inputize(&self) -> Vec<CF2<C>> {
+        let zero = (&C::BaseField::zero(), &C::BaseField::zero());
+        let cmE = self.cmE.into_affine();
+        let cmW = self.cmW.into_affine();
+        let (cmE_x, cmE_y) = cmE.xy().unwrap_or(zero);
+        let (cmW_x, cmW_y) = cmW.xy().unwrap_or(zero);
+        self.u
+            .inputize()
+            .into_iter()
+            .chain(self.x.iter().flat_map(|x| x.inputize()))
+            .chain(
+                [
+                    *cmE_x,
+                    *cmE_y,
+                    C::BaseField::one(),
+                    *cmW_x,
+                    *cmW_y,
+                    C::BaseField::one(),
+                ]
+                .into_iter()
+                .flat_map(|x| x.to_base_prime_field_elements()),
+            )
+            .collect()
+    }
+}
+
 /// CycleFoldCommittedInstanceVar is the CycleFold CommittedInstance represented
 /// in folding verifier circuit
 #[derive(Debug, Clone)]
diff --git a/folding-schemes/src/folding/circuits/nonnative/affine.rs b/folding-schemes/src/folding/circuits/nonnative/affine.rs
index da4d9e4f..58f6b2ae 100644
--- a/folding-schemes/src/folding/circuits/nonnative/affine.rs
+++ b/folding-schemes/src/folding/circuits/nonnative/affine.rs
@@ -10,7 +10,10 @@ use ark_serialize::{CanonicalSerialize, CanonicalSerializeWithFlags};
 use ark_std::Zero;
 use core::borrow::Borrow;
 
-use crate::transcript::{AbsorbNonNative, AbsorbNonNativeGadget};
+use crate::{
+    folding::traits::Inputize,
+    transcript::{AbsorbNonNative, AbsorbNonNativeGadget},
+};
 
 use super::uint::{nonnative_field_to_field_elements, NonNativeUintVar};
 
@@ -104,21 +107,19 @@ pub(crate) fn nonnative_affine_to_field_elements<C: CurveGroup>(
     (x, y)
 }
 
-impl<C: CurveGroup> NonNativeAffineVar<C> {
-    // Extracts a list of field elements of type `C::ScalarField` from the public input
-    // `p`, in exactly the same way as how `NonNativeAffineVar` is represented as limbs of type
-    // `FpVar` in-circuit.
-    #[allow(clippy::type_complexity)]
-    pub fn inputize(p: C) -> Result<(Vec<C::ScalarField>, Vec<C::ScalarField>), SynthesisError> {
-        let affine = p.into_affine();
+impl<C: CurveGroup> Inputize<C::ScalarField, NonNativeAffineVar<C>> for C {
+    fn inputize(&self) -> Vec<C::ScalarField> {
+        let affine = self.into_affine();
         let zero = (&C::BaseField::zero(), &C::BaseField::zero());
         let (x, y) = affine.xy().unwrap_or(zero);
 
-        let x = NonNativeUintVar::inputize(*x);
-        let y = NonNativeUintVar::inputize(*y);
-        Ok((x, y))
+        let x = x.inputize();
+        let y = y.inputize();
+        [x, y].concat()
     }
+}
 
+impl<C: CurveGroup> NonNativeAffineVar<C> {
     pub fn zero() -> Self {
         Self::new_constant(ConstraintSystemRef::None, C::zero()).unwrap()
     }
@@ -179,9 +180,11 @@ mod tests {
         let mut rng = ark_std::test_rng();
         let p = Projective::rand(&mut rng);
         let pVar = NonNativeAffineVar::<Projective>::new_witness(cs.clone(), || Ok(p)).unwrap();
-        let (x, y) = NonNativeAffineVar::inputize(p).unwrap();
+        let xy = p.inputize();
 
-        assert_eq!(pVar.x.0.value().unwrap(), x);
-        assert_eq!(pVar.y.0.value().unwrap(), y);
+        assert_eq!(
+            [pVar.x.0.value().unwrap(), pVar.y.0.value().unwrap()].concat(),
+            xy
+        );
     }
 }
diff --git a/folding-schemes/src/folding/circuits/nonnative/uint.rs b/folding-schemes/src/folding/circuits/nonnative/uint.rs
index 4624cb37..fc3c09e4 100644
--- a/folding-schemes/src/folding/circuits/nonnative/uint.rs
+++ b/folding-schemes/src/folding/circuits/nonnative/uint.rs
@@ -17,6 +17,7 @@ use num_bigint::BigUint;
 use num_integer::Integer;
 
 use crate::{
+    folding::traits::Inputize,
     transcript::{AbsorbNonNative, AbsorbNonNativeGadget},
     utils::gadgets::{EquivalenceGadget, MatrixGadget, SparseMatrixVar, VectorGadget},
 };
@@ -259,15 +260,15 @@ impl<F: PrimeField, G: Field> AllocVar<G, F> for NonNativeUintVar<F> {
     }
 }
 
-impl<F: PrimeField> NonNativeUintVar<F> {
-    pub fn inputize<T: Field>(x: T) -> Vec<F> {
+impl<F: PrimeField, T: Field> Inputize<F, NonNativeUintVar<F>> for T {
+    fn inputize(&self) -> Vec<F> {
         assert_eq!(T::extension_degree(), 1);
-        x.to_base_prime_field_elements()
+        self.to_base_prime_field_elements()
             .next()
             .unwrap()
             .into_bigint()
             .to_bits_le()
-            .chunks(Self::bits_per_limb())
+            .chunks(NonNativeUintVar::<F>::bits_per_limb())
             .map(|chunk| F::from_bigint(F::BigInt::from_bits_le(chunk)).unwrap())
             .collect()
     }
diff --git a/folding-schemes/src/folding/hypernova/cccs.rs b/folding-schemes/src/folding/hypernova/cccs.rs
index 5378a639..cca92def 100644
--- a/folding-schemes/src/folding/hypernova/cccs.rs
+++ b/folding-schemes/src/folding/hypernova/cccs.rs
@@ -10,6 +10,7 @@ use super::Witness;
 use crate::arith::{ccs::CCS, Arith};
 use crate::commitment::CommitmentScheme;
 use crate::folding::circuits::CF1;
+use crate::folding::traits::Inputize;
 use crate::folding::traits::{CommittedInstanceOps, Dummy};
 use crate::transcript::AbsorbNonNative;
 use crate::utils::mle::dense_vec_to_dense_mle;
@@ -152,6 +153,12 @@ impl<C: CurveGroup> CommittedInstanceOps<C> for CCCS<C> {
     }
 }
 
+impl<C: CurveGroup> Inputize<C::ScalarField, CCCSVar<C>> for CCCS<C> {
+    fn inputize(&self) -> Vec<C::ScalarField> {
+        [&self.C.inputize()[..], &self.x].concat()
+    }
+}
+
 #[cfg(test)]
 pub mod tests {
     use ark_pallas::Fr;
diff --git a/folding-schemes/src/folding/hypernova/decider_eth.rs b/folding-schemes/src/folding/hypernova/decider_eth.rs
index 0c4bdd9f..b29baff0 100644
--- a/folding-schemes/src/folding/hypernova/decider_eth.rs
+++ b/folding-schemes/src/folding/hypernova/decider_eth.rs
@@ -14,8 +14,9 @@ use super::{lcccs::LCCCS, HyperNova};
 use crate::commitment::{
     kzg::Proof as KZGProof, pedersen::Params as PedersenParams, CommitmentScheme,
 };
-use crate::folding::circuits::{nonnative::affine::NonNativeAffineVar, CF2};
+use crate::folding::circuits::CF2;
 use crate::folding::nova::decider_eth::VerifierParam;
+use crate::folding::traits::Inputize;
 use crate::frontend::FCircuit;
 use crate::Error;
 use crate::{Decider as DeciderTrait, FoldingScheme};
@@ -192,19 +193,11 @@ where
         // Note: the NIMFS proof is checked inside the DeciderEthCircuit, which ensures that the
         // 'proof.U_i1' is correctly computed
 
-        let (cmC_x, cmC_y) = NonNativeAffineVar::inputize(proof.U_i1.C)?;
-
         let public_input: Vec<C1::ScalarField> = [
             vec![pp_hash, i],
             z_0,
             z_i,
-            // U_i+1:
-            cmC_x,
-            cmC_y,
-            vec![proof.U_i1.u],
-            proof.U_i1.x.clone(),
-            proof.U_i1.r_x.clone(),
-            proof.U_i1.v.clone(),
+            proof.U_i1.inputize(),
             vec![proof.kzg_challenge, proof.kzg_proof.eval, proof.rho],
         ]
         .concat();
diff --git a/folding-schemes/src/folding/hypernova/lcccs.rs b/folding-schemes/src/folding/hypernova/lcccs.rs
index 6d2c2165..8784d21e 100644
--- a/folding-schemes/src/folding/hypernova/lcccs.rs
+++ b/folding-schemes/src/folding/hypernova/lcccs.rs
@@ -14,6 +14,7 @@ use crate::arith::ccs::CCS;
 use crate::arith::Arith;
 use crate::commitment::CommitmentScheme;
 use crate::folding::circuits::CF1;
+use crate::folding::traits::Inputize;
 use crate::folding::traits::{CommittedInstanceOps, Dummy};
 use crate::transcript::AbsorbNonNative;
 use crate::utils::mle::dense_vec_to_dense_mle;
@@ -154,6 +155,19 @@ impl<C: CurveGroup> CommittedInstanceOps<C> for LCCCS<C> {
     }
 }
 
+impl<C: CurveGroup> Inputize<C::ScalarField, LCCCSVar<C>> for LCCCS<C> {
+    fn inputize(&self) -> Vec<C::ScalarField> {
+        [
+            &self.C.inputize(),
+            &[self.u][..],
+            &self.x,
+            &self.r_x,
+            &self.v,
+        ]
+        .concat()
+    }
+}
+
 #[cfg(test)]
 pub mod tests {
     use ark_pallas::{Fr, Projective};
diff --git a/folding-schemes/src/folding/nova/decider.rs b/folding-schemes/src/folding/nova/decider.rs
index 901f152a..e67d77da 100644
--- a/folding-schemes/src/folding/nova/decider.rs
+++ b/folding-schemes/src/folding/nova/decider.rs
@@ -3,7 +3,7 @@
 /// More details can be found at the documentation page:
 /// https://privacy-scaling-explorations.github.io/sonobe-docs/design/nova-decider-offchain.html
 use ark_crypto_primitives::sponge::Absorb;
-use ark_ec::{AffineRepr, CurveGroup, Group};
+use ark_ec::{CurveGroup, Group};
 use ark_ff::{BigInteger, PrimeField};
 use ark_r1cs_std::{groups::GroupOpsBounds, prelude::CurveVar, ToConstraintFieldGadget};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
@@ -16,10 +16,10 @@ use super::decider_circuits::{DeciderCircuit1, DeciderCircuit2};
 use super::{nifs::NIFS, traits::NIFSTrait, CommittedInstance, Nova};
 use crate::commitment::CommitmentScheme;
 use crate::folding::circuits::{
-    cyclefold::CycleFoldCommittedInstance,
-    nonnative::{affine::NonNativeAffineVar, uint::NonNativeUintVar},
+    cyclefold::{CycleFoldCommittedInstance, CycleFoldCommittedInstanceVar},
     CF2,
 };
+use crate::folding::traits::Inputize;
 use crate::frontend::FCircuit;
 use crate::Error;
 use crate::{Decider as DeciderTrait, FoldingScheme};
@@ -288,50 +288,21 @@ where
         // compute U = U_{d+1}= NIFS.V(U_d, u_d, cmT)
         let U = NIFS::<C1, CS1>::verify(proof.r, running_instance, incoming_instance, &proof.cmT);
 
-        let (cmE_x, cmE_y) = NonNativeAffineVar::inputize(U.cmE)?;
-        let (cmW_x, cmW_y) = NonNativeAffineVar::inputize(U.cmW)?;
-        let (cmT_x, cmT_y) = NonNativeAffineVar::inputize(proof.cmT)?;
-
-        let zero = (&C2::BaseField::zero(), &C2::BaseField::zero());
-        let cmE_affine = proof.cf_U_i.cmE.into_affine();
-        let cmW_affine = proof.cf_U_i.cmW.into_affine();
-        let (cf_cmE_x, cf_cmE_y) = cmE_affine.xy().unwrap_or(zero);
-        let cf_cmE_z = C1::ScalarField::one();
-        let (cf_cmW_x, cf_cmW_y) = cmW_affine.xy().unwrap_or(zero);
-        let cf_cmW_z = C1::ScalarField::one();
-
         // snark proof 1
         let c1_public_input: Vec<C1::ScalarField> = [
             vec![vp.pp_hash, i],
             z_0,
             z_i,
-            // U_{i+1} values:
-            vec![U.u],
-            U.x.clone(),
-            cmE_x,
-            cmE_y,
-            cmW_x,
-            cmW_y,
+            U.inputize(),
             // CS1 values:
             proof.cs1_challenges.to_vec(), // c_W, c_E
             vec![
                 proof.cs1_proofs[0].eval, // eval_W
                 proof.cs1_proofs[1].eval, // eval_E
             ],
-            // cf_U_i values
-            NonNativeUintVar::<CF2<C2>>::inputize(proof.cf_U_i.u),
-            proof
-                .cf_U_i
-                .x
-                .iter()
-                .flat_map(|&x_i| NonNativeUintVar::<CF2<C2>>::inputize(x_i))
-                .collect::<Vec<C1::ScalarField>>(),
-            vec![
-                *cf_cmE_x, *cf_cmE_y, cf_cmE_z, *cf_cmW_x, *cf_cmW_y, cf_cmW_z,
-            ],
+            Inputize::<CF2<C2>, CycleFoldCommittedInstanceVar<C2, GC2>>::inputize(&proof.cf_U_i),
             // NIFS values:
-            cmT_x,
-            cmT_y,
+            proof.cmT.inputize(),
             vec![proof.r],
         ]
         .concat();
@@ -342,21 +313,13 @@ where
             return Err(Error::SNARKVerificationFail);
         }
 
-        let (cf2_cmE_x, cf2_cmE_y) = NonNativeAffineVar::inputize(proof.cf_U_i.cmE)?;
-        let (cf2_cmW_x, cf2_cmW_y) = NonNativeAffineVar::inputize(proof.cf_U_i.cmW)?;
-
         // snark proof 2
         // migrate pp_hash from C1::Fr to C1::Fq
         let pp_hash_Fq =
             C2::ScalarField::from_le_bytes_mod_order(&vp.pp_hash.into_bigint().to_bytes_le());
         let c2_public_input: Vec<C2::ScalarField> = [
             vec![pp_hash_Fq],
-            vec![proof.cf_U_i.u],
-            proof.cf_U_i.x.clone(),
-            cf2_cmE_x,
-            cf2_cmE_y,
-            cf2_cmW_x,
-            cf2_cmW_y,
+            proof.cf_U_i.inputize(),
             proof.cs2_challenges.to_vec(),
             vec![
                 proof.cs2_proofs[0].eval, // eval_W
diff --git a/folding-schemes/src/folding/nova/decider_eth.rs b/folding-schemes/src/folding/nova/decider_eth.rs
index 64f1a7cd..7bc73f5e 100644
--- a/folding-schemes/src/folding/nova/decider_eth.rs
+++ b/folding-schemes/src/folding/nova/decider_eth.rs
@@ -22,7 +22,8 @@ use crate::commitment::{
     pedersen::Params as PedersenParams,
     CommitmentScheme,
 };
-use crate::folding::circuits::{nonnative::affine::NonNativeAffineVar, CF2};
+use crate::folding::circuits::CF2;
+use crate::folding::traits::Inputize;
 use crate::frontend::FCircuit;
 use crate::Error;
 use crate::{Decider as DeciderTrait, FoldingScheme};
@@ -212,27 +213,17 @@ where
         // compute U = U_{d+1}= NIFS.V(U_d, u_d, cmT)
         let U = NIFS::<C1, CS1>::verify(proof.r, running_instance, incoming_instance, &proof.cmT);
 
-        let (cmE_x, cmE_y) = NonNativeAffineVar::inputize(U.cmE)?;
-        let (cmW_x, cmW_y) = NonNativeAffineVar::inputize(U.cmW)?;
-        let (cmT_x, cmT_y) = NonNativeAffineVar::inputize(proof.cmT)?;
-
         let public_input: Vec<C1::ScalarField> = [
             vec![vp.pp_hash, i],
             z_0,
             z_i,
-            vec![U.u],
-            U.x.clone(),
-            cmE_x,
-            cmE_y,
-            cmW_x,
-            cmW_y,
+            U.inputize(),
             proof.kzg_challenges.to_vec(),
             vec![
                 proof.kzg_proofs[0].eval, // eval_W
                 proof.kzg_proofs[1].eval, // eval_E
             ],
-            cmT_x,
-            cmT_y,
+            proof.cmT.inputize(),
             vec![proof.r],
         ]
         .concat();
diff --git a/folding-schemes/src/folding/nova/mod.rs b/folding-schemes/src/folding/nova/mod.rs
index 1c1985fe..e0fb818a 100644
--- a/folding-schemes/src/folding/nova/mod.rs
+++ b/folding-schemes/src/folding/nova/mod.rs
@@ -53,7 +53,7 @@ pub mod decider_circuits;
 pub mod decider_eth;
 pub mod decider_eth_circuit;
 
-use super::traits::{CommittedInstanceOps, WitnessOps};
+use super::traits::{CommittedInstanceOps, Inputize, WitnessOps};
 
 /// Configuration for Nova's CycleFold circuit
 pub struct NovaCycleFoldConfig<C: CurveGroup> {
@@ -134,6 +134,18 @@ impl<C: CurveGroup> CommittedInstanceOps<C> for CommittedInstance<C> {
     }
 }
 
+impl<C: CurveGroup> Inputize<C::ScalarField, CommittedInstanceVar<C>> for CommittedInstance<C> {
+    fn inputize(&self) -> Vec<C::ScalarField> {
+        [
+            &[self.u][..],
+            &self.x,
+            &self.cmE.inputize(),
+            &self.cmW.inputize(),
+        ]
+        .concat()
+    }
+}
+
 #[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct Witness<C: CurveGroup> {
     pub E: Vec<C::ScalarField>,
diff --git a/folding-schemes/src/folding/protogalaxy/circuits.rs b/folding-schemes/src/folding/protogalaxy/circuits.rs
index 57cba2a9..136e1238 100644
--- a/folding-schemes/src/folding/protogalaxy/circuits.rs
+++ b/folding-schemes/src/folding/protogalaxy/circuits.rs
@@ -503,12 +503,8 @@ mod tests {
             &witnesses,
         )?;
 
-        let folded_instance = Folding::<Projective>::verify(
-            &mut transcript_v,
-            &instance,
-            &instances,
-            proof.clone(),
-        )?;
+        let folded_instance =
+            Folding::<Projective>::verify(&mut transcript_v, &instance, &instances, proof.clone())?;
 
         let cs = ConstraintSystem::new_ref();
         let mut transcript_var = PoseidonSpongeVar::new(cs.clone(), &poseidon_config);
diff --git a/folding-schemes/src/folding/protogalaxy/mod.rs b/folding-schemes/src/folding/protogalaxy/mod.rs
index 356c959f..28c1f0b9 100644
--- a/folding-schemes/src/folding/protogalaxy/mod.rs
+++ b/folding-schemes/src/folding/protogalaxy/mod.rs
@@ -50,7 +50,7 @@ use circuits::AugmentedFCircuit;
 use folding::Folding;
 
 use super::traits::{
-    CommittedInstanceOps, CommittedInstanceVarOps, Dummy, WitnessOps, WitnessVarOps,
+    CommittedInstanceOps, CommittedInstanceVarOps, Dummy, Inputize, WitnessOps, WitnessVarOps,
 };
 
 /// Configuration for ProtoGalaxy's CycleFold circuit
@@ -119,6 +119,14 @@ impl<C: CurveGroup, const TYPE: bool> CommittedInstanceOps<C> for CommittedInsta
     }
 }
 
+impl<C: CurveGroup, const TYPE: bool> Inputize<C::ScalarField, CommittedInstanceVar<C, TYPE>>
+    for CommittedInstance<C, TYPE>
+{
+    fn inputize(&self) -> Vec<C::ScalarField> {
+        [&self.phi.inputize(), &self.betas, &[self.e][..], &self.x].concat()
+    }
+}
+
 #[derive(Clone, Debug)]
 pub struct CommittedInstanceVar<C: CurveGroup, const TYPE: bool> {
     phi: NonNativeAffineVar<C>,
diff --git a/folding-schemes/src/folding/traits.rs b/folding-schemes/src/folding/traits.rs
index 3890554b..1cae1865 100644
--- a/folding-schemes/src/folding/traits.rs
+++ b/folding-schemes/src/folding/traits.rs
@@ -12,7 +12,7 @@ use crate::{transcript::Transcript, Error};
 
 use super::circuits::CF1;
 
-pub trait CommittedInstanceOps<C: CurveGroup> {
+pub trait CommittedInstanceOps<C: CurveGroup>: Inputize<CF1<C>, Self::Var> {
     /// The in-circuit representation of the committed instance.
     type Var: AllocVar<Self, CF1<C>> + CommittedInstanceVarOps<C>;
     /// `hash` implements the committed instance hash compatible with the
@@ -129,3 +129,10 @@ impl<T: Default + Clone> Dummy<usize> for Vec<T> {
         vec![Default::default(); cfg]
     }
 }
+
+/// Converts a value `self` into a vector of field elements, ordered in the same
+/// way as how a variable of type `Var` would be represented in the circuit.
+/// This is useful for the verifier to compute the public inputs.
+pub trait Inputize<F, Var> {
+    fn inputize(&self) -> Vec<F>;
+}