diff --git a/src/constraints.rs b/src/constraints.rs
new file mode 100644
index 0000000..28a06e4
--- /dev/null
+++ b/src/constraints.rs
@@ -0,0 +1,126 @@
+use crate::{Parameters, Signature};
+
+use ark_ec::{AffineCurve, ProjectiveCurve};
+use ark_ed_on_bn254::{constraints::EdwardsVar, EdwardsParameters, FqParameters};
+use ark_ff::{
+    fields::{Field, Fp256},
+    to_bytes, ToConstraintField,
+};
+use ark_r1cs_std::{
+    alloc::{AllocVar, AllocationMode},
+    bits::uint8::UInt8,
+    boolean::Boolean,
+    fields::fp::FpVar,
+    groups::{curves::twisted_edwards::AffineVar, GroupOpsBounds},
+    prelude::CurveVar,
+    ToBitsGadget,
+};
+use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystemRef, Namespace, SynthesisError};
+use ark_std::ops::Mul;
+
+use core::{borrow::Borrow, marker::PhantomData};
+use derivative::Derivative;
+
+// hash
+use arkworks_r1cs_gadgets::poseidon;
+use arkworks_r1cs_gadgets::poseidon::{FieldHasherGadget, PoseidonGadget};
+
+// type ConstraintF<C> = <<C as ProjectiveCurve>::BaseField as Field>::BasePrimeField;
+type ConstraintF<C> = <C as ProjectiveCurve>::ScalarField; // Fr
+
+#[derive(Derivative)]
+#[derivative(
+    Debug(bound = "C: ProjectiveCurve, GC: CurveVar<C, ConstraintF<C>>"),
+    Clone(bound = "C: ProjectiveCurve, GC: CurveVar<C, ConstraintF<C>>")
+)]
+pub struct PublicKeyVar<C: ProjectiveCurve, GC: CurveVar<C, ConstraintF<C>>>
+where
+    for<'a> &'a GC: GroupOpsBounds<'a, C, GC>,
+{
+    pub_key: GC,
+    #[doc(hidden)]
+    _group: PhantomData<*const C>,
+}
+
+#[derive(Derivative)]
+#[derivative(
+    Debug(bound = "C: ProjectiveCurve, GC: CurveVar<C, ConstraintF<C>>"),
+    Clone(bound = "C: ProjectiveCurve, GC: CurveVar<C, ConstraintF<C>>")
+)]
+pub struct SignatureVar<C: ProjectiveCurve, GC: CurveVar<C, ConstraintF<C>>>
+where
+    for<'a> &'a GC: GroupOpsBounds<'a, C, GC>,
+{
+    // s: FpVar<ConstraintF>,
+    // s: C::ScalarField,
+    s: Vec<UInt8<ConstraintF<C>>>,
+    r: GC,
+    _curve: PhantomData<C>,
+}
+
+impl<C, GC> AllocVar<Signature<C>, ConstraintF<C>> for SignatureVar<C, GC>
+where
+    C: ProjectiveCurve,
+    // TODO not sure on '+ AllocVarar'
+    GC: CurveVar<C, ConstraintF<C>> + AllocVar<GC, ConstraintF<C>>,
+    for<'a> &'a GC: GroupOpsBounds<'a, C, GC>,
+{
+    fn new_variable<T: Borrow<Signature<C>>>(
+        cs: impl Into<Namespace<ConstraintF<C>>>,
+        f: impl FnOnce() -> Result<T, SynthesisError>,
+        mode: AllocationMode,
+    ) -> Result<Self, SynthesisError> {
+        f().and_then(|val| {
+            let cs = cs.into();
+            // let s = val.borrow().s;
+            let mut s = Vec::<UInt8<ConstraintF<C>>>::new();
+            let s_bytes = to_bytes![val.borrow().s].unwrap();
+            for i in 0..s_bytes.len() {
+                s.push(UInt8::<ConstraintF<C>>::new_variable(
+                    cs.clone(),
+                    || Ok(s_bytes[i].clone()),
+                    mode,
+                )?);
+            }
+
+            let r = GC::new_variable(cs.clone(), || Ok(val.borrow().r), mode)?;
+
+            Ok(Self {
+                s: s, // TODO not sure of FpVar::Constant
+                r: r,
+                _curve: PhantomData,
+            })
+        })
+    }
+}
+
+#[derive(Clone)]
+pub struct ParametersVar<C: ProjectiveCurve, GC: CurveVar<C, ConstraintF<C>>>
+where
+    for<'a> &'a GC: GroupOpsBounds<'a, C, GC>,
+{
+    generator: GC,
+    _curve: PhantomData<C>,
+}
+
+impl<C, GC> AllocVar<Parameters<C>, ConstraintF<C>> for ParametersVar<C, GC>
+where
+    C: ProjectiveCurve,
+    GC: CurveVar<C, ConstraintF<C>>,
+    for<'a> &'a GC: GroupOpsBounds<'a, C, GC>,
+{
+    fn new_variable<T: Borrow<Parameters<C>>>(
+        cs: impl Into<Namespace<ConstraintF<C>>>,
+        f: impl FnOnce() -> Result<T, SynthesisError>,
+        mode: AllocationMode,
+    ) -> Result<Self, SynthesisError> {
+        f().and_then(|val| {
+            let cs = cs.into();
+            let generator = GC::new_variable(cs.clone(), || Ok(val.borrow().generator), mode)?;
+            Ok(Self {
+                generator,
+                _curve: PhantomData,
+            })
+        })
+    }
+}
diff --git a/src/lib.rs b/src/lib.rs
index 30e2939..ce9c0f3 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -126,6 +126,7 @@ where
         let modulus_repr = BigInteger256::try_from(modulus.into()).unwrap();
 
         if !(x_repr >= one && x_repr < modulus_repr) {
+            // TODO maybe add a counter of attempts with a limit
             return Self::new_blind_params(parameters, rng, signer_r);
         }
         u