diff --git a/elliptic-curve/src/arithmetic.rs b/elliptic-curve/src/arithmetic.rs
index b69c1a408..fa445f1bc 100644
--- a/elliptic-curve/src/arithmetic.rs
+++ b/elliptic-curve/src/arithmetic.rs
@@ -1,6 +1,8 @@
 //! Elliptic curve arithmetic traits.
 
-use crate::{AffineXCoordinate, Curve, FieldBytes, IsHigh, PrimeCurve, ScalarCore};
+use crate::{
+    ops::LinearCombination, AffineXCoordinate, Curve, FieldBytes, IsHigh, PrimeCurve, ScalarCore,
+};
 use core::fmt::Debug;
 use subtle::{ConditionallySelectable, ConstantTimeEq};
 use zeroize::DefaultIsZeroes;
@@ -54,6 +56,7 @@ pub trait ProjectiveArithmetic: Curve + AffineArithmetic {
         + DefaultIsZeroes
         + From<Self::AffinePoint>
         + Into<Self::AffinePoint>
+        + LinearCombination
         + group::Curve<AffineRepr = Self::AffinePoint>
         + group::Group<Scalar = Self::Scalar>;
 }
diff --git a/elliptic-curve/src/dev.rs b/elliptic-curve/src/dev.rs
index 1da6c6316..5b9ca3781 100644
--- a/elliptic-curve/src/dev.rs
+++ b/elliptic-curve/src/dev.rs
@@ -6,7 +6,7 @@
 use crate::{
     bigint::{Limb, U256},
     error::{Error, Result},
-    ops::Reduce,
+    ops::{LinearCombination, Reduce},
     pkcs8,
     rand_core::RngCore,
     sec1::{FromEncodedPoint, ToEncodedPoint},
@@ -541,6 +541,8 @@ impl group::Curve for ProjectivePoint {
     }
 }
 
+impl LinearCombination for ProjectivePoint {}
+
 impl Add<ProjectivePoint> for ProjectivePoint {
     type Output = ProjectivePoint;
 
diff --git a/elliptic-curve/src/ops.rs b/elliptic-curve/src/ops.rs
index b49e1b335..b5ab2dd8f 100644
--- a/elliptic-curve/src/ops.rs
+++ b/elliptic-curve/src/ops.rs
@@ -6,7 +6,7 @@ use crypto_bigint::{ArrayEncoding, ByteArray, Integer};
 use subtle::CtOption;
 
 #[cfg(feature = "arithmetic")]
-use crate::ProjectiveArithmetic;
+use group::Group;
 
 /// Perform an inversion on a field element (i.e. base field element or scalar)
 pub trait Invert {
@@ -34,14 +34,9 @@ impl<F: ff::Field> Invert for F {
 // TODO(tarcieri): replace this with a trait from the `group` crate? (see zkcrypto/group#25)
 #[cfg(feature = "arithmetic")]
 #[cfg_attr(docsrs, doc(cfg(feature = "arithmetic")))]
-pub trait LinearCombination: ProjectiveArithmetic {
+pub trait LinearCombination: Group {
     /// Calculates `x * k + y * l`.
-    fn lincomb(
-        x: &Self::ProjectivePoint,
-        k: &Self::Scalar,
-        y: &Self::ProjectivePoint,
-        l: &Self::Scalar,
-    ) -> Self::ProjectivePoint {
+    fn lincomb(x: &Self, k: &Self::Scalar, y: &Self, l: &Self::Scalar) -> Self {
         (*x * k) + (*y * l)
     }
 }