diff --git a/elliptic-curve/src/lib.rs b/elliptic-curve/src/lib.rs
index 1f49f1267..3bcd5b974 100644
--- a/elliptic-curve/src/lib.rs
+++ b/elliptic-curve/src/lib.rs
@@ -84,13 +84,17 @@ pub trait Curve: Clone + Debug + Default + Eq + Ord + Send + Sync {
 
 /// Elliptic curve with curve arithmetic support
 pub trait Arithmetic: Curve {
-    /// Scalar type for a given curve
-    type Scalar: ConditionallySelectable
+    /// Scalar type for a given curve.
+    type Scalar: ff::PrimeField
         + ConstantTimeEq
         + Default
         + FromBytes<Size = Self::FieldSize>
         + Into<ElementBytes<Self>>;
 
+    /// Elliptic curve point in projective coordinates.
+    type ProjectivePoint: group::Curve<AffineRepr = Self::AffinePoint>
+        + group::Group<Scalar = Self::Scalar>;
+
     /// Affine point type for a given curve
     type AffinePoint: ConditionallySelectable
         + Mul<scalar::NonZeroScalar<Self>, Output = Self::AffinePoint>