diff --git a/Cargo.toml b/Cargo.toml
index 3bfc782..1ef7abe 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -15,7 +15,7 @@ ark-serialize = { version = "0.4.0", default-features = false, features = [ "der
 rand = { version = "0.8", features = [ "std", "std_rng" ] }
 merlin = { version = "3.0.0" }
 
-ark-crypto-primitives = { version = "^0.4.0", default-features = false, features = [ "r1cs", "snark"] }
+ark-crypto-primitives = { version = "^0.4.0", default-features = false, features = [ "r1cs", "snark", "sponge", "crh" ] }
 ark-r1cs-std = { version = "^0.4.0", default-features = false }
 ark-relations = { version = "^0.4.0", default-features = false }
 ark-snark = { version = "^0.4.0", default-features = false }
diff --git a/README.md b/README.md
index 1247867..e931567 100644
--- a/README.md
+++ b/README.md
@@ -7,3 +7,6 @@ Implementation of [Nova](https://eprint.iacr.org/2021/370.pdf) using [arkworks-r
 This repo is an ongoing implementation, the code will be dirty for a while and not optimized but just to understand and experiment with the internals of the scheme and try experimental combinations.
 
 Thanks to [Levs57](https://twitter.com/levs57), [Nalin Bhardwaj](https://twitter.com/nibnalin) and [Carlos Pérez](https://twitter.com/cperezz19) for clarifications on the Nova paper.
+
+### Details
+Initial impl using a cycle of pairing-friendly curves with Groth16 for the folding proofs (as an example, the tests use MNT4, MNT6 curves), once the full scheme works, will see how many constraints the folding circuits need and might change one of the sides to a non-pairing curve with a non-pairing proof instead of Groth16. Eventually would like to explore also using BN254 with Grumpkin for ending up verifying the proofs in Ethereum.
diff --git a/src/circuits.rs b/src/circuits.rs
index 2a13c04..16df7c1 100644
--- a/src/circuits.rs
+++ b/src/circuits.rs
@@ -1,7 +1,6 @@
-use ark_crypto_primitives::snark::{FromFieldElementsGadget, SNARKGadget, SNARK};
 use ark_ec::AffineRepr;
 use ark_ec::{CurveGroup, Group};
-use ark_ff::{fields::Fp256, Field, PrimeField};
+use ark_ff::{fields::Fp256, BigInteger, Field, PrimeField};
 use ark_r1cs_std::{
     alloc::{AllocVar, AllocationMode},
     bits::uint8::UInt8,
@@ -17,8 +16,20 @@ use ark_r1cs_std::{
     prelude::CurveVar,
     ToBitsGadget, ToBytesGadget, ToConstraintFieldGadget,
 };
+// use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;
 use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystemRef, Namespace, SynthesisError};
-use ark_std::ops::Mul;
+use ark_std::ops::{Add, Mul, Sub};
+
+use ark_crypto_primitives::crh::poseidon::{
+    constraints::{CRHGadget, CRHParametersVar},
+    CRH,
+};
+use ark_crypto_primitives::crh::{CRHScheme, CRHSchemeGadget};
+use ark_crypto_primitives::snark::{FromFieldElementsGadget, SNARKGadget, SNARK};
+use ark_crypto_primitives::sponge::constraints::CryptographicSpongeVar;
+use ark_crypto_primitives::sponge::poseidon::{
+    constraints::PoseidonSpongeVar, PoseidonConfig, PoseidonSponge,
+};
 
 use core::{borrow::Borrow, marker::PhantomData};
 use derivative::Derivative;
@@ -114,34 +125,107 @@ where
     }
 }
 
-////
-
-pub trait Config<Fq: PrimeField, Fr: PrimeField> {
-    type AugmentedFunctionCircuit: SNARK<Fq>; // F'
-    type FunctionCircuit: ConstraintSynthesizer<Fq>; // F
-    type DummyStepCircuit: SNARK<Fr>;
-}
-
-pub struct AugmentedFCircuit<
-    Fq: PrimeField,
-    Fr: PrimeField,
-    C: CurveGroup,
-    GC: CurveVar<C, Fq>,
-    Cfg: Config<Fq, Fr>,
-> {
-    pub dummystep_vk: Option<<Cfg::DummyStepCircuit as SNARK<Fr>>::VerifyingKey>,
+use ark_crypto_primitives::sponge::Absorb;
+pub struct AugmentedFCircuit<C: CurveGroup, GC: CurveVar<C, ConstraintF<C>>>
+where
+    <<C as CurveGroup>::BaseField as Field>::BasePrimeField: Absorb,
+{
     _c: PhantomData<C>,
     _gc: PhantomData<GC>,
+
+    pub poseidon_native: PoseidonSponge<ConstraintF<C>>,
+    pub poseidon_config: PoseidonConfig<ConstraintF<C>>,
+    pub i: Option<C::BaseField>,
+    pub z_0: Option<C::BaseField>,
+    pub z_i: Option<C::BaseField>,
+    pub phi: Option<Phi<C>>, // phi in the paper sometimes appears as phi (φ) and others as 𝗎
+    pub phiBig: Option<Phi<C>>,
+    pub phiOut: Option<Phi<C>>,
+    pub cmT: Option<C>,
+    pub r: Option<C::ScalarField>, // This will not be an input and derived from a hash internally in the circuit (poseidon transcript)
 }
 
-impl<Fq: PrimeField, Fr: PrimeField, C: CurveGroup, GC: CurveVar<C, Fq>, Cfg: Config<Fq, Fr>>
-    ConstraintSynthesizer<Fq> for AugmentedFCircuit<Fq, Fr, C, GC, Cfg>
+impl<C: CurveGroup, GC: CurveVar<C, ConstraintF<C>>> ConstraintSynthesizer<ConstraintF<C>>
+    for AugmentedFCircuit<C, GC>
+where
+    C: CurveGroup,
+    GC: CurveVar<C, ConstraintF<C>>,
+    for<'a> &'a GC: GroupOpsBounds<'a, C, GC>,
+    <C as CurveGroup>::BaseField: PrimeField,
+    <<C as CurveGroup>::BaseField as Field>::BasePrimeField: Absorb,
 {
-    fn generate_constraints(self, cs: ConstraintSystemRef<Fq>) -> Result<(), SynthesisError> {
-        unimplemented!();
+    fn generate_constraints(
+        self,
+        cs: ConstraintSystemRef<ConstraintF<C>>,
+    ) -> Result<(), SynthesisError> {
+        let i = FpVar::<ConstraintF<C>>::new_witness(cs.clone(), || Ok(self.i.unwrap()))?;
+        let z_0 = FpVar::<ConstraintF<C>>::new_witness(cs.clone(), || Ok(self.z_0.unwrap()))?;
+        let z_i = FpVar::<ConstraintF<C>>::new_witness(cs.clone(), || Ok(self.z_i.unwrap()))?;
+
+        let phi = PhiVar::<C, GC>::new_witness(cs.clone(), || Ok(self.phi.unwrap()))?;
+        let phiBig = PhiVar::<C, GC>::new_witness(cs.clone(), || Ok(self.phiBig.unwrap()))?;
+        let phiOut = PhiVar::<C, GC>::new_witness(cs.clone(), || Ok(self.phiOut.unwrap()))?;
+
+        let cmT = GC::new_witness(cs.clone(), || Ok(self.cmT.unwrap()))?;
+        let r =
+            NonNativeFieldVar::<C::ScalarField, ConstraintF<C>>::new_witness(cs.clone(), || {
+                Ok(self.r.unwrap())
+            })?; // r will come from transcript
+
+        // 1. phi.x == H(vk_nifs, i, z_0, z_i, phiBig)
+        let mut sponge =
+            PoseidonSpongeVar::<ConstraintF<C>>::new(cs.clone(), &self.poseidon_config);
+        let input = vec![i, z_0, z_i];
+        sponge.absorb(&input)?;
+        let input = vec![
+            phiBig.u.to_constraint_field()?,
+            phiBig.x.to_constraint_field()?,
+        ];
+        sponge.absorb(&input)?;
+        let input = vec![phiBig.cmE.to_bytes()?, phiBig.cmW.to_bytes()?];
+        sponge.absorb(&input)?;
+        let h = sponge.squeeze_field_elements(1).unwrap();
+        let x_CF = phi.x.to_constraint_field()?; // phi.x on the ConstraintF<C>
+        x_CF[0].is_eq(&h[0])?; // review
+
+        // // 2. phi.cmE==0, phi.u==1
+        // <GC as CurveVar<C, ConstraintF<C>>>::is_zero(&phi.cmE)?;
+        phi.cmE.is_zero()?;
+        phi.u.is_one()?;
+
+        // 3. nifs.verify
+        NIFSGadget::<C, GC>::verify(r, cmT, phi, phiBig, phiOut)?;
+
+        // 4. zksnark.V(vk_snark, phi_new, proof_phi)
+
+        Ok(())
     }
 }
 
+//////////
+
+// pub struct Nova<MainField: PrimeField, SecondField: PrimeField, C1: CurveGroup, C2: CurveGroup> {}
+// pub trait SNARKs<MainField: PrimeField, SecondField: PrimeField> {
+//     type AugmentedFunctionSNARK: SNARK<MainField>;
+//     // type FunctionSNARK: ConstraintSynthesizer<Fr>; // F
+//     type DummyStepSNARK: SNARK<SecondField>;
+//
+//     type AugmentedFunctionCircuit: SNARKGadget<MainField, SecondField, Self::AugmentedFunctionSNARK>; // F'
+//     type FunctionCircuit: ConstraintSynthesizer<MainField>; // F
+//     type DummyStepCircuit: SNARKGadget<SecondField, MainField, Self::DummyStepSNARK>;
+// }
+// pub struct TS<
+//     MainField: PrimeField,
+//     SecondField: PrimeField,
+//     Config: SNARKs<MainField, SecondField>,
+// > {
+//     augmentedF_pk: <Config::AugmentedFunctionSNARK as SNARK<MainField>>::ProvingKey,
+//     augmentedF_vk: <Config::AugmentedFunctionSNARK as SNARK<MainField>>::VerifyingKey,
+//
+//     dummy_pk: <Config::DummyStepSNARK as SNARK<SecondField>>::ProvingKey,
+//     dummy_vk: <Config::DummyStepSNARK as SNARK<SecondField>>::VerifyingKey,
+// }
+
 #[cfg(test)]
 mod test {
     use super::*;