Introduce `Group` for generic group operations.

src/curves/bls381/ec.rs

@@ -43,6 +43,18 @@ macro_rules! curve_impl {
             }
         }
 
+        impl Group<$engine> for $name {
+            fn group_mul_assign(&mut self, e: &$engine, scalar: &$scalarfield) {
+                self.mul_assign(e, scalar);
+            }
+            fn group_add_assign(&mut self, e: &$engine, other: &Self) {
+                self.add_assign(e, other);
+            }
+            fn group_sub_assign(&mut self, e: &$engine, other: &Self) {
+                self.sub_assign(e, other);
+            }
+        }
+
         impl CurveAffine<$engine, $name> for $name_affine {
             type Uncompressed = $name_uncompressed;
 

src/curves/bls381/mod.rs

@@ -5,6 +5,7 @@ use std::borrow::Borrow;
 use super::{
     WindowTable,
     Engine,
+    Group,
     Curve,
     CurveAffine,
     CurveRepresentation,
@@ -95,6 +96,18 @@ fp_impl!(
     inv = 0xfffffffeffffffff
 );
 
+impl Group<Bls381> for Fr {
+    fn group_mul_assign(&mut self, e: &Bls381, scalar: &Fr) {
+        self.mul_assign(e, scalar);
+    }
+    fn group_add_assign(&mut self, e: &Bls381, other: &Self) {
+        self.add_assign(e, other);
+    }
+    fn group_sub_assign(&mut self, e: &Bls381, other: &Self) {
+        self.sub_assign(e, other);
+    }
+}
+
 curve_impl!(Bls381, G1, G1Affine, G1Affine, G1Uncompressed, G1Params, g1params, Fq, Fr);
 curve_impl!(Bls381, G2, G2Affine, G2Prepared, G2Uncompressed, G2Params, g2params, Fq2, Fr);
 

src/curves/mod.rs

@@ -46,13 +46,21 @@ pub trait Engine: Sized + Clone
     fn batch_baseexp<G: Curve<Self>, S: AsRef<[Self::Fr]>>(&self, table: &WindowTable<Self, G, Vec<G>>, scalars: S) -> Vec<G::Affine>;
 }
 
+pub trait Group<E: Engine>
+{
+    fn group_mul_assign(&mut self, &E, scalar: &E::Fr);
+    fn group_add_assign(&mut self, &E, other: &Self);
+    fn group_sub_assign(&mut self, &E, other: &Self);
+}
+
 pub trait Curve<E: Engine>: Sized +
                             Copy +
                             Clone +
                             Send +
                             Sync +
                             fmt::Debug +
-                            'static
+                            'static +
+                            Group<E>
 {
     type Affine: CurveAffine<E, Self>;
     type Prepared: Clone + Send + Sync + 'static;
@@ -193,7 +201,7 @@ pub trait PrimeField<E: Engine>: SqrtField<E> + Convert<[u64], E>
     fn capacity(&E) -> usize;
 }
 
-pub trait SnarkField<E: Engine>: PrimeField<E>
+pub trait SnarkField<E: Engine>: PrimeField<E> + Group<E>
 {
     fn s(&E) -> u64;
     fn multiplicative_generator(&E) -> Self;