Add affine_xy, affine_x, affine_y functions to CurveVar (#190)

* Add xy, x, y functions to CurveVar

* Refactor

* Update CHANGELOG.md

* Refactor

* Refactor

* Update mod.rs

---------

Co-authored-by: Weikeng Chen <w.k@berkeley.edu>

Author: dongwook1214

CHANGELOG.md

@@ -38,6 +38,7 @@
     - Add `UInt::{from_bytes_le, from_bytes_be, to_bytes_be}`.
 - [\#143](https://github.com/arkworks-rs/r1cs-std/pull/143) Add `AllocVar::new_variable_with_inferred_mode`.
 - [\#144](https://github.com/arkworks-rs/r1cs-std/pull/144) Add `ToConstraintFieldGadget` bounds to `CurveVar` and `FieldVar`
+- [\#190](https://github.com/arkworks-rs/r1cs-std/pull/190) Add `affine_xy, affine_x, affine_y` functions to `CurveVar`
 
 ### Improvements
 

src/groups/curves/short_weierstrass/mod.rs

@@ -377,6 +377,8 @@ where
     F: FieldVar<P::BaseField, BasePrimeField<P>>,
     for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
 {
+    type BaseFieldVar = F;
+
     fn constant(g: SWProjective<P>) -> Self {
         let cs = ConstraintSystemRef::None;
         Self::new_variable_omit_on_curve_check(cs, || Ok(g), AllocationMode::Constant).unwrap()
@@ -573,6 +575,11 @@ where
         *self += Self::constant(base).scalar_mul_le(bits.iter())?;
         Ok(())
     }
+
+    fn affine_xy(&self) -> Result<(F, F), SynthesisError> {
+        let self_affine = self.to_affine()?;
+        Ok((self_affine.x, self_affine.y))
+    }
 }
 
 impl<P, F> ToConstraintFieldGadget<BasePrimeField<P>> for ProjectiveVar<P, F>

src/groups/curves/twisted_edwards/mod.rs

@@ -402,6 +402,8 @@ where
         + TwoBitLookupGadget<BasePrimeField<P>, TableConstant = P::BaseField>,
     for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
 {
+    type BaseFieldVar = F;
+
     fn constant(g: TEProjective<P>) -> Self {
         let cs = ConstraintSystemRef::None;
         Self::new_variable_omit_on_curve_check(cs, || Ok(g), AllocationMode::Constant).unwrap()
@@ -547,6 +549,10 @@ where
 
         Ok(())
     }
+
+    fn affine_xy(&self) -> Result<(F, F), SynthesisError> {
+        Ok((self.x.clone(), self.y.clone()))
+    }
 }
 
 impl<P, F> AllocVar<TEProjective<P>, BasePrimeField<P>> for AffineVar<P, F>

src/groups/mod.rs

@@ -53,6 +53,9 @@ pub trait CurveVar<C: CurveGroup, ConstraintF: PrimeField>:
     + for<'a> Mul<&'a EmulatedFpVar<C::ScalarField, ConstraintF>, Output = Self>
     + MulAssign<EmulatedFpVar<C::ScalarField, ConstraintF>>
 {
+    /// The base field of the coordinates.
+    type BaseFieldVar: FieldVar<C::BaseField, ConstraintF>;
+
     /// Returns the constant `F::zero()`. This is the identity
     /// of the group.
     fn zero() -> Self;
@@ -68,6 +71,19 @@ pub trait CurveVar<C: CurveGroup, ConstraintF: PrimeField>:
     /// This *should not* allocate any variables.
     fn constant(other: C) -> Self;
 
+    /// Returns the x and y coordinates in Affine representation.
+    fn affine_xy(&self) -> Result<(Self::BaseFieldVar, Self::BaseFieldVar), SynthesisError>;
+
+    /// Returns the x coordinate in Affine representation.
+    fn affine_x(&self) -> Result<Self::BaseFieldVar, SynthesisError> {
+        self.affine_xy().map(|(x, _)| x)
+    }
+
+    /// Returns the y coordinate in Affine representation.
+    fn affine_y(&self) -> Result<Self::BaseFieldVar, SynthesisError> {
+        self.affine_xy().map(|(_, y)| y)
+    }
+
     /// Allocates a variable in the subgroup without checking if it's in the
     /// prime-order subgroup.
     fn new_variable_omit_prime_order_check(