diff --git a/Cargo.toml b/Cargo.toml
index 7724955..ca5a9f2 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -14,7 +14,8 @@ ark-r1cs-std = { version = "^0.4.0", default-features = false }
 thiserror = "1.0"
 
 [dev-dependencies]
-ark-bls12-381 = "0.4.0"
+ark-bls12-377 = "0.4.0"
+ark-bw6-761 = "0.4.0"
 
 [features]
 default = []
diff --git a/src/lib.rs b/src/lib.rs
index 44aeb0b..de53ca6 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -8,6 +8,8 @@ use thiserror::Error;
 
 pub mod transcript;
 use transcript::Transcript;
+pub mod pedersen;
+pub mod utils;
 
 #[derive(Debug, Error)]
 pub enum Error {
@@ -19,23 +21,21 @@ pub enum Error {
 /// over a cycle of curves (C1, C2), where:
 /// - C1 is the main curve, which ScalarField we use as our F for al the field operations
 /// - C2 is the auxiliary curve, which we use for the commitments, whose BaseField (for point
-/// coordinates) are in the C1::ScalarField
+/// coordinates) are in the C1::ScalarField.
+/// In other words, C1.Fq == C2.Fr, and C1.Fr == C2.Fq.
 pub trait FoldingScheme<C1: CurveGroup, C2: CurveGroup>: Clone + Debug
 where
     C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
     C2::BaseField: PrimeField,
 {
-    // type PCS: PolynomialCommitmentScheme<C>; // maybe not needed, just PedersenCommitment
     type PreprocessorParam: Debug;
     type ProverParam: Debug;
     type VerifierParam: Debug;
-    type FreshInstance: Debug;
-    type PublicInput: Debug;
+    type Witness: Debug;
     type CommittedInstanceWithWitness: Debug;
     type CommittedInstance: Clone + Debug;
 
     fn preprocess(
-        // pcs_param: &<Self::CS as PolynomialCommitmentScheme<C>>::Param,
         prep_param: &Self::PreprocessorParam,
     ) -> Result<(Self::ProverParam, Self::VerifierParam), Error>;
 
@@ -46,17 +46,15 @@ where
     fn prove(
         pp: &Self::ProverParam,
         running_instance: &mut Self::CommittedInstanceWithWitness,
-        incomming_instances: &[Self::FreshInstance],
-        transcript: &mut impl Transcript<C1::ScalarField>,
-        rng: impl RngCore,
+        incomming_instances: &[Self::Witness],
+        transcript: &mut impl Transcript<C1>,
     ) -> Result<(), Error>;
 
     fn verify(
         vp: &Self::VerifierParam,
         running_instance: &mut Self::CommittedInstance,
-        incomming_instances: &[Self::PublicInput],
-        transcript: &mut impl Transcript<C1::ScalarField>,
-        rng: impl RngCore,
+        incomming_instances: &[Self::CommittedInstance],
+        transcript: &mut impl Transcript<C1>,
     ) -> Result<(), Error>;
 }
 
@@ -72,14 +70,14 @@ pub trait Decider<C: CurveGroup>: Clone + Debug {
     fn prove(
         pp: &Self::ProverParam,
         running_instance: &Self::CommittedInstanceWithWitness,
-        transcript: &mut impl Transcript<C::ScalarField>,
+        transcript: &mut impl Transcript<C>,
         rng: impl RngCore,
     ) -> Result<(), Error>;
 
     fn verify(
         vp: &Self::VerifierParam,
         running_instance: &Self::CommittedInstance,
-        transcript: &mut impl Transcript<C::ScalarField>,
+        transcript: &mut impl Transcript<C>,
         rng: impl RngCore,
     ) -> Result<(), Error>;
 }
diff --git a/src/pedersen.rs b/src/pedersen.rs
new file mode 100644
index 0000000..e21406a
--- /dev/null
+++ b/src/pedersen.rs
@@ -0,0 +1,127 @@
+use ark_ec::{CurveGroup, Group};
+use ark_std::{rand::Rng, UniformRand};
+use std::marker::PhantomData;
+
+use crate::utils::vec::{vec_add, vec_scalar_mul};
+
+use crate::transcript::Transcript;
+use ark_crypto_primitives::sponge::Absorb;
+
+#[derive(Debug, Clone, Eq, PartialEq)]
+pub struct Proof<C: CurveGroup> {
+    R: C,
+    u: Vec<C::ScalarField>,
+    r_u: C::ScalarField,
+}
+
+#[derive(Debug, Clone, Eq, PartialEq)]
+pub struct Params<C: CurveGroup> {
+    h: C,
+    pub generators: Vec<C::Affine>,
+}
+
+#[derive(Debug, Clone, Eq, PartialEq)]
+pub struct Pedersen<C: CurveGroup>
+where
+    <C as Group>::ScalarField: Absorb,
+{
+    _c: PhantomData<C>,
+}
+
+impl<C: CurveGroup> Pedersen<C>
+where
+    <C as Group>::ScalarField: Absorb,
+{
+    pub fn new_params<R: Rng>(rng: &mut R, max: usize) -> Params<C> {
+        let generators: Vec<C::Affine> = std::iter::repeat_with(|| C::Affine::rand(rng))
+            .take(max.next_power_of_two())
+            .collect();
+        let params: Params<C> = Params::<C> {
+            h: C::rand(rng),
+            generators,
+        };
+        params
+    }
+
+    pub fn commit(params: &Params<C>, v: &Vec<C::ScalarField>, r: &C::ScalarField) -> C {
+        // h⋅r + <g, v>
+        params.h.mul(r) + C::msm(&params.generators[..v.len()], v).unwrap()
+    }
+
+    pub fn prove(
+        params: &Params<C>,
+        transcript: &mut impl Transcript<C>,
+        cm: &C,
+        v: &Vec<C::ScalarField>,
+        r: &C::ScalarField,
+    ) -> Proof<C> {
+        transcript.absorb_point(cm);
+        let r1 = transcript.get_challenge();
+        let d = transcript.get_challenges(v.len());
+
+        // R = h⋅r_1 + <g, d>
+        let R: C = params.h.mul(r1) + C::msm(&params.generators[..d.len()], &d).unwrap();
+
+        transcript.absorb_point(&R);
+        let e = transcript.get_challenge();
+
+        // u = d + v⋅e
+        let u = vec_add(&vec_scalar_mul(v, &e), &d);
+        // r_u = e⋅r + r_1
+        let r_u = e * r + r1;
+
+        Proof::<C> { R, u, r_u }
+    }
+
+    pub fn verify(
+        params: &Params<C>,
+        transcript: &mut impl Transcript<C>,
+        cm: C,
+        proof: Proof<C>,
+    ) -> bool {
+        transcript.absorb_point(&cm);
+        transcript.get_challenge(); // r_1
+        transcript.get_challenges(proof.u.len()); // d
+        transcript.absorb_point(&proof.R);
+        let e = transcript.get_challenge();
+
+        // check that: R + cm == h⋅r_u + <g, u>
+        let lhs = proof.R + cm.mul(e);
+        let rhs = params.h.mul(proof.r_u)
+            + C::msm(&params.generators[..proof.u.len()], &proof.u).unwrap();
+        if lhs != rhs {
+            return false;
+        }
+        true
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::transcript::poseidon::{tests::poseidon_test_config, PoseidonTranscript};
+
+    use ark_bls12_377::{Fr, G1Projective};
+
+    #[test]
+    fn test_pedersen_vector() {
+        let mut rng = ark_std::test_rng();
+
+        const n: usize = 10;
+        // setup params
+        let params = Pedersen::<G1Projective>::new_params(&mut rng, n);
+        let poseidon_config = poseidon_test_config::<Fr>();
+
+        // init Prover's transcript
+        let mut transcript_p = PoseidonTranscript::<G1Projective>::new(&poseidon_config);
+        // init Verifier's transcript
+        let mut transcript_v = PoseidonTranscript::<G1Projective>::new(&poseidon_config);
+
+        let v: Vec<Fr> = vec![Fr::rand(&mut rng); n];
+        let r: Fr = Fr::rand(&mut rng);
+        let cm = Pedersen::<G1Projective>::commit(&params, &v, &r);
+        let proof = Pedersen::<G1Projective>::prove(&params, &mut transcript_p, &cm, &v, &r);
+        let v = Pedersen::<G1Projective>::verify(&params, &mut transcript_v, cm, proof);
+        assert!(v);
+    }
+}
diff --git a/src/transcript/mod.rs b/src/transcript/mod.rs
index cc1424f..420e6bc 100644
--- a/src/transcript/mod.rs
+++ b/src/transcript/mod.rs
@@ -1,14 +1,15 @@
-use ark_ff::PrimeField;
+use ark_ec::CurveGroup;
 use ark_std::fmt::Debug;
 
 pub mod poseidon;
 
-pub trait Transcript<F: PrimeField> {
+pub trait Transcript<C: CurveGroup> {
     type TranscriptConfig: Debug;
 
     fn new(config: &Self::TranscriptConfig) -> Self;
-    fn absorb(&mut self, v: &F);
-    fn absorb_vec(&mut self, v: &[F]);
-    fn get_challenge(&mut self) -> F;
-    fn get_challenges(&mut self, n: usize) -> Vec<F>;
+    fn absorb(&mut self, v: &C::ScalarField);
+    fn absorb_vec(&mut self, v: &[C::ScalarField]);
+    fn absorb_point(&mut self, v: &C);
+    fn get_challenge(&mut self) -> C::ScalarField;
+    fn get_challenges(&mut self, n: usize) -> Vec<C::ScalarField>;
 }
diff --git a/src/transcript/poseidon.rs b/src/transcript/poseidon.rs
index 4636ca3..29f2e4d 100644
--- a/src/transcript/poseidon.rs
+++ b/src/transcript/poseidon.rs
@@ -3,42 +3,75 @@ use ark_crypto_primitives::sponge::{
     poseidon::{constraints::PoseidonSpongeVar, PoseidonConfig, PoseidonSponge},
     Absorb, CryptographicSponge,
 };
-use ark_ff::PrimeField;
+use ark_ec::{AffineRepr, CurveGroup, Group};
+use ark_ff::{BigInteger, Field, PrimeField};
 use ark_r1cs_std::fields::fp::FpVar;
 use ark_relations::r1cs::{ConstraintSystemRef, SynthesisError};
 
 use crate::transcript::Transcript;
 
 /// PoseidonTranscript implements the Transcript trait using the Poseidon hash
-pub struct PoseidonTranscript<F: PrimeField + Absorb> {
-    sponge: PoseidonSponge<F>,
+pub struct PoseidonTranscript<C: CurveGroup>
+where
+    <C as Group>::ScalarField: Absorb,
+{
+    sponge: PoseidonSponge<C::ScalarField>,
 }
 
-impl<F: PrimeField + Absorb> Transcript<F> for PoseidonTranscript<F> {
-    type TranscriptConfig = PoseidonConfig<F>;
+impl<C: CurveGroup> Transcript<C> for PoseidonTranscript<C>
+where
+    <C as Group>::ScalarField: Absorb,
+{
+    type TranscriptConfig = PoseidonConfig<C::ScalarField>;
 
     fn new(poseidon_config: &Self::TranscriptConfig) -> Self {
-        let sponge = PoseidonSponge::<F>::new(poseidon_config);
+        let sponge = PoseidonSponge::<C::ScalarField>::new(poseidon_config);
         Self { sponge }
     }
-    fn absorb(&mut self, v: &F) {
+    fn absorb(&mut self, v: &C::ScalarField) {
         self.sponge.absorb(&v);
     }
-    fn absorb_vec(&mut self, v: &[F]) {
+    fn absorb_vec(&mut self, v: &[C::ScalarField]) {
         self.sponge.absorb(&v);
     }
-    fn get_challenge(&mut self) -> F {
+    fn absorb_point(&mut self, p: &C) {
+        self.sponge.absorb(&prepare_point(p));
+    }
+    fn get_challenge(&mut self) -> C::ScalarField {
         let c = self.sponge.squeeze_field_elements(1);
         self.sponge.absorb(&c[0]);
         c[0]
     }
-    fn get_challenges(&mut self, n: usize) -> Vec<F> {
+    fn get_challenges(&mut self, n: usize) -> Vec<C::ScalarField> {
         let c = self.sponge.squeeze_field_elements(n);
         self.sponge.absorb(&c);
         c
     }
 }
 
+// Returns the point coordinates in Fr, so it can be absrobed by the transcript. It does not work
+// over bytes in order to have a logic that can be reproduced in-circuit.
+fn prepare_point<C: CurveGroup>(p: &C) -> Vec<C::ScalarField> {
+    let binding = p.into_affine();
+    let p_coords = &binding.xy().unwrap();
+    let x_bi = p_coords
+        .0
+        .to_base_prime_field_elements()
+        .next()
+        .expect("a")
+        .into_bigint();
+    let y_bi = p_coords
+        .1
+        .to_base_prime_field_elements()
+        .next()
+        .expect("a")
+        .into_bigint();
+    vec![
+        C::ScalarField::from_le_bytes_mod_order(x_bi.to_bytes_le().as_ref()),
+        C::ScalarField::from_le_bytes_mod_order(y_bi.to_bytes_le().as_ref()),
+    ]
+}
+
 /// PoseidonTranscriptVar implements the gadget compatible with PoseidonTranscript
 pub struct PoseidonTranscriptVar<F: PrimeField> {
     sponge: PoseidonSpongeVar<F>,
@@ -67,9 +100,9 @@ impl<F: PrimeField> PoseidonTranscriptVar<F> {
 }
 
 #[cfg(test)]
-mod tests {
+pub mod tests {
     use super::*;
-    use ark_bls12_381::Fr;
+    use ark_bls12_377::{Fr, G1Projective};
     use ark_crypto_primitives::sponge::poseidon::find_poseidon_ark_and_mds;
     use ark_r1cs_std::{alloc::AllocVar, fields::fp::FpVar, R1CSVar};
     use ark_relations::r1cs::ConstraintSystem;
@@ -105,7 +138,7 @@ mod tests {
     fn test_transcript_and_transcriptvar() {
         // use 'native' transcript
         let config = poseidon_test_config::<Fr>();
-        let mut tr = PoseidonTranscript::<Fr>::new(&config);
+        let mut tr = PoseidonTranscript::<G1Projective>::new(&config);
         tr.absorb(&Fr::from(42_u32));
         let c = tr.get_challenge();
 
diff --git a/src/utils/mod.rs b/src/utils/mod.rs
new file mode 100644
index 0000000..63e55ca
--- /dev/null
+++ b/src/utils/mod.rs
@@ -0,0 +1 @@
+pub mod vec;
diff --git a/src/utils/vec.rs b/src/utils/vec.rs
new file mode 100644
index 0000000..1b3d1b5
--- /dev/null
+++ b/src/utils/vec.rs
@@ -0,0 +1,86 @@
+use ark_ff::PrimeField;
+use ark_std::cfg_iter;
+
+#[derive(Clone, Debug, Eq, PartialEq)]
+pub struct SparseMatrix<F: PrimeField> {
+    pub n_rows: usize,
+    pub n_cols: usize,
+    pub coeffs: Vec<(usize, usize, F)>,
+}
+
+pub fn dense_matrix_to_sparse<F: PrimeField>(m: Vec<Vec<F>>) -> SparseMatrix<F> {
+    let mut r = SparseMatrix::<F> {
+        n_rows: m.len(),
+        n_cols: m[0].len(),
+        coeffs: Vec::new(),
+    };
+    for (i, m_i) in m.iter().enumerate() {
+        for (j, m_ij) in m_i.iter().enumerate() {
+            if !m_ij.is_zero() {
+                r.coeffs.push((i, j, *m_ij));
+            }
+        }
+    }
+    r
+}
+
+pub fn vec_add<F: PrimeField>(a: &[F], b: &[F]) -> Vec<F> {
+    assert_eq!(a.len(), b.len());
+    let mut r: Vec<F> = vec![F::zero(); a.len()];
+    for i in 0..a.len() {
+        r[i] = a[i] + b[i];
+    }
+    r
+}
+
+pub fn vec_sub<F: PrimeField>(a: &[F], b: &[F]) -> Vec<F> {
+    assert_eq!(a.len(), b.len());
+    let mut r: Vec<F> = vec![F::zero(); a.len()];
+    for i in 0..a.len() {
+        r[i] = a[i] - b[i];
+    }
+    r
+}
+
+pub fn vec_scalar_mul<F: PrimeField>(vec: &[F], c: &F) -> Vec<F> {
+    let mut result = vec![F::zero(); vec.len()];
+    for (i, a) in vec.iter().enumerate() {
+        result[i] = *a * c;
+    }
+    result
+}
+
+pub fn is_zero_vec<F: PrimeField>(vec: &[F]) -> bool {
+    for e in vec {
+        if !e.is_zero() {
+            return false;
+        }
+    }
+    true
+}
+
+pub fn mat_vec_mul<F: PrimeField>(M: &Vec<Vec<F>>, z: &[F]) -> Vec<F> {
+    assert!(!M.is_empty());
+    assert_eq!(M[0].len(), z.len());
+
+    let mut r: Vec<F> = vec![F::zero(); M.len()];
+    for (i, M_i) in M.iter().enumerate() {
+        for (j, M_ij) in M_i.iter().enumerate() {
+            r[i] += *M_ij * z[j];
+        }
+    }
+    r
+}
+
+pub fn mat_vec_mul_sparse<F: PrimeField>(matrix: &SparseMatrix<F>, vector: &[F]) -> Vec<F> {
+    let mut res = vec![F::zero(); matrix.n_cols];
+    for &(row, col, value) in matrix.coeffs.iter() {
+        res[row] += value * vector[col];
+    }
+    res
+}
+
+pub fn hadamard<F: PrimeField>(a: &[F], b: &[F]) -> Vec<F> {
+    assert_eq!(a.len(), b.len());
+    cfg_iter!(a).zip(b).map(|(a, b)| *a * b).collect()
+}