Add affine_xy, affine_x, affine_y functions to CurveVar

src/groups/curves/short_weierstrass/mod.rs

@@ -371,12 +371,14 @@ where
     }
 }
 
-impl<P, F> CurveVar<SWProjective<P>, BasePrimeField<P>, F> for ProjectiveVar<P, F>
+impl<P, F> CurveVar<SWProjective<P>, BasePrimeField<P>> for ProjectiveVar<P, F>
 where
     P: SWCurveConfig,
     F: FieldVar<P::BaseField, BasePrimeField<P>>,
     for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
 {
+    type F = F;
+
     fn constant(g: SWProjective<P>) -> Self {
         let cs = ConstraintSystemRef::None;
         Self::new_variable_omit_on_curve_check(cs, || Ok(g), AllocationMode::Constant).unwrap()

src/groups/curves/twisted_edwards/mod.rs

@@ -395,13 +395,15 @@ where
     }
 }
 
-impl<P, F> CurveVar<TEProjective<P>, BasePrimeField<P>, F> for AffineVar<P, F>
+impl<P, F> CurveVar<TEProjective<P>, BasePrimeField<P>> for AffineVar<P, F>
 where
     P: TECurveConfig,
     F: FieldVar<P::BaseField, BasePrimeField<P>>
         + TwoBitLookupGadget<BasePrimeField<P>, TableConstant = P::BaseField>,
     for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
 {
+    type F = F;
+
     fn constant(g: TEProjective<P>) -> Self {
         let cs = ConstraintSystemRef::None;
         Self::new_variable_omit_on_curve_check(cs, || Ok(g), AllocationMode::Constant).unwrap()

src/groups/mod.rs

@@ -29,7 +29,7 @@ pub trait GroupOpsBounds<'a, G, T: 'a>:
 
 /// A variable that represents a curve point for
 /// the curve `C`.
-pub trait CurveVar<C: CurveGroup, ConstraintF: PrimeField, F: FieldVar<C::BaseField, ConstraintF>>:
+pub trait CurveVar<C: CurveGroup, ConstraintF: PrimeField>:
     'static
     + Sized
     + Clone
@@ -53,6 +53,8 @@ pub trait CurveVar<C: CurveGroup, ConstraintF: PrimeField, F: FieldVar<C::BaseFi
     + for<'a> Mul<&'a EmulatedFpVar<C::ScalarField, ConstraintF>, Output = Self>
     + MulAssign<EmulatedFpVar<C::ScalarField, ConstraintF>>
 {
+    type F: FieldVar<C::BaseField, ConstraintF>;
+
     /// Returns the constant `F::zero()`. This is the identity
     /// of the group.
     fn zero() -> Self;
@@ -69,15 +71,15 @@ pub trait CurveVar<C: CurveGroup, ConstraintF: PrimeField, F: FieldVar<C::BaseFi
     fn constant(other: C) -> Self;
 
     /// Returns the x and y coordinates in Affine representation.
-    fn affine_xy(&self) -> Result<(F, F), SynthesisError>;
+    fn affine_xy(&self) -> Result<(Self::F, Self::F), SynthesisError>;
 
     /// Returns the x coordinate in Affine representation.
-    fn affine_x(&self) -> Result<F, SynthesisError> {
+    fn affine_x(&self) -> Result<Self::F, SynthesisError> {
         self.affine_xy().map(|(x, _)| x)
     }
 
     /// Returns the y coordinate in Affine representation.
-    fn affine_y(&self) -> Result<F, SynthesisError> {
+    fn affine_y(&self) -> Result<Self::F, SynthesisError> {
         self.affine_xy().map(|(_, y)| y)
     }
 

src/pairing/bls12/mod.rs

@@ -59,10 +59,7 @@ impl<P: Bls12Config> PairingVar<P> {
     }
 }
 
-impl<P: Bls12Config>
-    PG<Bls12<P>, FpVar<<P as Bls12Config>::Fp>, Fp2Var<<P as Bls12Config>::Fp2Config>>
-    for PairingVar<P>
-{
+impl<P: Bls12Config> PG<Bls12<P>> for PairingVar<P> {
     type G1Var = G1Var<P>;
     type G2Var = G2Var<P>;
     type G1PreparedVar = G1PreparedVar<P>;

src/pairing/mnt4/mod.rs

@@ -196,9 +196,7 @@ impl<P: MNT4Config> PairingVar<P> {
     }
 }
 
-impl<P: MNT4Config> PG<MNT4<P>, FpVar<<P as MNT4Config>::Fp>, Fp2Var<<P as MNT4Config>::Fp2Config>>
-    for PairingVar<P>
-{
+impl<P: MNT4Config> PG<MNT4<P>> for PairingVar<P> {
     type G1Var = G1Var<P>;
     type G2Var = G2Var<P>;
     type G1PreparedVar = G1PreparedVar<P>;

src/pairing/mnt6/mod.rs

@@ -191,9 +191,7 @@ impl<P: MNT6Config> PairingVar<P> {
     }
 }
 
-impl<P: MNT6Config> PG<MNT6<P>, FpVar<<P as MNT6Config>::Fp>, Fp3Var<<P as MNT6Config>::Fp3Config>>
-    for PairingVar<P>
-{
+impl<P: MNT6Config> PG<MNT6<P>> for PairingVar<P> {
     type G1Var = G1Var<P>;
     type G2Var = G2Var<P>;
     type G1PreparedVar = G1PreparedVar<P>;

src/pairing/mod.rs

@@ -14,19 +14,14 @@ type BasePrimeField<E> = <<E as Pairing>::BaseField as ark_ff::Field>::BasePrime
 
 /// Specifies the constraints for computing a pairing in the yybilinear group
 /// `E`.
-pub trait PairingVar<
-    E: Pairing,
-    F1: FieldVar<<E::G1 as ark_ec::CurveGroup>::BaseField, E::BaseField>,
-    F2: FieldVar<<E::G2 as ark_ec::CurveGroup>::BaseField, E::BaseField>,
->
-{
+pub trait PairingVar<E: Pairing> {
     /// An variable representing an element of `G1`.
     /// This is the R1CS equivalent of `E::G1Projective`.
-    type G1Var: CurveVar<E::G1, BasePrimeField<E>, F1>;
+    type G1Var: CurveVar<E::G1, BasePrimeField<E>>;
 
     /// An variable representing an element of `G2`.
     /// This is the R1CS equivalent of `E::G2Projective`.
-    type G2Var: CurveVar<E::G2, BasePrimeField<E>, F2>;
+    type G2Var: CurveVar<E::G2, BasePrimeField<E>>;
 
     /// An variable representing an element of `GT`.
     /// This is the R1CS equivalent of `E::GT`.