Fix the incorrect Affine - Projective implementation (#822)

* Fix the subtraction between Affine and Projective points

* Add unit test for Affine - Projective

* Update changelog

* Faster subtraction

---------

Co-authored-by: Pratyush Mishra <pratyush795@gmail.com>

CHANGELOG.md

@@ -45,6 +45,7 @@
 - [\#747](https://github.com/arkworks-rs/algebra/pull/747) (`ark-ff-macros`) Fix fetching attributes in `MontConfig` macro.
 - [\#803](https://github.com/arkworks-rs/algebra/pull/803) (`ark-ec`, `ark-test-template`) Fix incorrect decomposition in GLV.
 - [\#806](https://github.com/arkworks-rs/algebra/pull/806) (`ark-ff`) Fix the impl for `Display`ing zero element in Fp.
+- [\#822](https://github.com/arkworks-rs/algebra/pull/822) (`ark-ec`, `ark-test-template`) Fix the incorrect `Affine - Projective` implementation
 
 ## v0.4.2
 

ec/src/models/short_weierstrass/affine.rs

@@ -305,14 +305,14 @@ impl<P: SWCurveConfig, T: Borrow<Self>> Sub<T> for Affine<P> {
 impl<P: SWCurveConfig> Sub<Projective<P>> for Affine<P> {
     type Output = Projective<P>;
     fn sub(self, other: Projective<P>) -> Projective<P> {
-        other - self
+        self + (-other)
     }
 }
 
 impl<'a, P: SWCurveConfig> Sub<&'a Projective<P>> for Affine<P> {
     type Output = Projective<P>;
     fn sub(self, other: &'a Projective<P>) -> Projective<P> {
-        *other - self
+        self + (-*other)
     }
 }
 

ec/src/models/twisted_edwards/affine.rs

@@ -255,14 +255,14 @@ impl<P: TECurveConfig, T: Borrow<Self>> Sub<T> for Affine<P> {
 impl<P: TECurveConfig> Sub<Projective<P>> for Affine<P> {
     type Output = Projective<P>;
     fn sub(self, other: Projective<P>) -> Projective<P> {
-        other - self
+        self + (-other)
     }
 }
 
 impl<'a, P: TECurveConfig> Sub<&'a Projective<P>> for Affine<P> {
     type Output = Projective<P>;
     fn sub(self, other: &'a Projective<P>) -> Projective<P> {
-        *other - self
+        self + (-*other)
     }
 }
 

test-templates/src/groups.rs

@@ -67,6 +67,9 @@ macro_rules! __test_group {
 
                 assert_eq!(a - zero, a);
                 assert_eq!(b - zero, b);
+
+                // Affine - Projective
+                assert_eq!(a.into_affine() - b, a - b);
             }
         }