diff --git a/build.rs b/build.rs
index 2c30435..6b6e652 100644
--- a/build.rs
+++ b/build.rs
@@ -26,6 +26,11 @@ extern crate serde;
 #[cfg(feature = "yolocrypto")]
 extern crate stdsimd;
 
+// Macros come first!
+#[path="src/macros.rs"]
+#[macro_use]
+mod macros;
+
 // Public modules
 
 #[path="src/scalar.rs"]
diff --git a/src/edwards.rs b/src/edwards.rs
index 5fca4e9..4af3ec5 100644
--- a/src/edwards.rs
+++ b/src/edwards.rs
@@ -378,12 +378,16 @@ impl<'a, 'b> Add<&'b ExtendedPoint> for &'a ExtendedPoint {
     }
 }
 
+define_add_variants!(LHS = ExtendedPoint, RHS = ExtendedPoint, Output = ExtendedPoint);
+
 impl<'b> AddAssign<&'b ExtendedPoint> for ExtendedPoint {
     fn add_assign(&mut self, _rhs: &'b ExtendedPoint) {
         *self = (self as &ExtendedPoint) + _rhs;
     }
 }
 
+define_add_assign_variants!(LHS = ExtendedPoint, RHS = ExtendedPoint);
+
 impl<'a, 'b> Sub<&'b ExtendedPoint> for &'a ExtendedPoint {
     type Output = ExtendedPoint;
     fn sub(self, other: &'b ExtendedPoint) -> ExtendedPoint {
@@ -391,12 +395,16 @@ impl<'a, 'b> Sub<&'b ExtendedPoint> for &'a ExtendedPoint {
     }
 }
 
+define_sub_variants!(LHS = ExtendedPoint, RHS = ExtendedPoint, Output = ExtendedPoint);
+
 impl<'b> SubAssign<&'b ExtendedPoint> for ExtendedPoint {
     fn sub_assign(&mut self, _rhs: &'b ExtendedPoint) {
         *self = (self as &ExtendedPoint) - _rhs;
     }
 }
 
+define_sub_assign_variants!(LHS = ExtendedPoint, RHS = ExtendedPoint);
+
 // ------------------------------------------------------------------------
 // Negation
 // ------------------------------------------------------------------------
@@ -414,6 +422,14 @@ impl<'a> Neg for &'a ExtendedPoint {
     }
 }
 
+impl Neg for ExtendedPoint {
+    type Output = ExtendedPoint;
+
+    fn neg(self) -> ExtendedPoint {
+        -&self
+    }
+}
+
 // ------------------------------------------------------------------------
 // Scalar multiplication
 // ------------------------------------------------------------------------
@@ -425,6 +441,11 @@ impl<'b> MulAssign<&'b Scalar> for ExtendedPoint {
     }
 }
 
+define_mul_assign_variants!(LHS = ExtendedPoint, RHS = Scalar);
+
+define_mul_variants!(LHS = ExtendedPoint, RHS = Scalar, Output = ExtendedPoint);
+define_mul_variants!(LHS = Scalar, RHS = ExtendedPoint, Output = ExtendedPoint);
+
 impl<'a, 'b> Mul<&'b Scalar> for &'a ExtendedPoint {
     type Output = ExtendedPoint;
     /// Scalar multiplication: compute `scalar * self`.
@@ -478,7 +499,7 @@ impl<'a, 'b> Mul<&'b ExtendedPoint> for &'a Scalar {
     /// For scalar multiplication of a basepoint,
     /// `EdwardsBasepointTable` is approximately 4x faster.
     fn mul(self, point: &'b ExtendedPoint) -> ExtendedPoint {
-        point * &self
+        point * self
     }
 }
 
diff --git a/src/lib.rs b/src/lib.rs
index 6c4ed32..0baf368 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -68,6 +68,10 @@ extern crate serde;
 #[cfg(all(test, feature = "serde"))]
 extern crate serde_cbor;
 
+// Internal macros. Must come first!
+#[macro_use]
+pub(crate) mod macros;
+
 //------------------------------------------------------------------------
 // curve25519-dalek public modules
 //------------------------------------------------------------------------
diff --git a/src/macros.rs b/src/macros.rs
new file mode 100644
index 0000000..448d32c
--- /dev/null
+++ b/src/macros.rs
@@ -0,0 +1,123 @@
+// -*- mode: rust; -*-
+//
+// This file is part of curve25519-dalek.
+// Copyright (c) 2016-2017 Isis Lovecruft, Henry de Valence
+// See LICENSE for licensing information.
+//
+// Authors:
+// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
+// - Henry de Valence <hdevalence@hdevalence.ca>
+
+//! Internal macros.
+
+/// Define borrow and non-borrow variants of `Add`.
+macro_rules! define_add_variants {
+    (LHS = $lhs:ty, RHS = $rhs:ty, Output = $out:ty) => {
+        impl<'b> Add<&'b $rhs> for $lhs {
+            type Output = $out;
+            fn add(self, rhs: &'b $rhs) -> $out {
+                &self + rhs
+            }
+        }
+
+        impl<'a> Add<$rhs> for &'a $lhs {
+            type Output = $out;
+            fn add(self, rhs: $rhs) -> $out {
+                self + &rhs
+            }
+        }
+
+        impl Add<$rhs> for $lhs {
+            type Output = $out;
+            fn add(self, rhs: $rhs) -> $out {
+                &self + &rhs
+            }
+        }
+    }
+}
+
+/// Define non-borrow variants of `AddAssign`.
+macro_rules! define_add_assign_variants {
+    (LHS = $lhs:ty, RHS = $rhs:ty) => {
+        impl AddAssign<$rhs> for $lhs {
+            fn add_assign(&mut self, rhs: $rhs) {
+                *self += &rhs;
+            }
+        }
+    }
+}
+
+/// Define borrow and non-borrow variants of `Sub`.
+macro_rules! define_sub_variants {
+    (LHS = $lhs:ty, RHS = $rhs:ty, Output = $out:ty) => {
+        impl<'b> Sub<&'b $rhs> for $lhs {
+            type Output = $out;
+            fn sub(self, rhs: &'b $rhs) -> $out {
+                &self - rhs
+            }
+        }
+
+        impl<'a> Sub<$rhs> for &'a $lhs {
+            type Output = $out;
+            fn sub(self, rhs: $rhs) -> $out {
+                self - &rhs
+            }
+        }
+
+        impl Sub<$rhs> for $lhs {
+            type Output = $out;
+            fn sub(self, rhs: $rhs) -> $out {
+                &self - &rhs
+            }
+        }
+    }
+}
+
+/// Define non-borrow variants of `SubAssign`.
+macro_rules! define_sub_assign_variants {
+    (LHS = $lhs:ty, RHS = $rhs:ty) => {
+        impl SubAssign<$rhs> for $lhs {
+            fn sub_assign(&mut self, rhs: $rhs) {
+                *self -= &rhs;
+            }
+        }
+    }
+}
+
+/// Define borrow and non-borrow variants of `Mul`.
+macro_rules! define_mul_variants {
+    (LHS = $lhs:ty, RHS = $rhs:ty, Output = $out:ty) => {
+        impl<'b> Mul<&'b $rhs> for $lhs {
+            type Output = $out;
+            fn mul(self, rhs: &'b $rhs) -> $out {
+                &self * rhs
+            }
+        }
+
+        impl<'a> Mul<$rhs> for &'a $lhs {
+            type Output = $out;
+            fn mul(self, rhs: $rhs) -> $out {
+                self * &rhs
+            }
+        }
+
+        impl Mul<$rhs> for $lhs {
+            type Output = $out;
+            fn mul(self, rhs: $rhs) -> $out {
+                &self * &rhs
+            }
+        }
+    }
+}
+
+/// Define non-borrow variants of `MulAssign`.
+macro_rules! define_mul_assign_variants {
+    (LHS = $lhs:ty, RHS = $rhs:ty) => {
+        impl MulAssign<$rhs> for $lhs {
+            fn mul_assign(&mut self, rhs: $rhs) {
+                *self *= &rhs;
+            }
+        }
+    }
+}
+
diff --git a/src/ristretto.rs b/src/ristretto.rs
index ee6260e..40d667b 100644
--- a/src/ristretto.rs
+++ b/src/ristretto.rs
@@ -925,12 +925,16 @@ impl<'a, 'b> Add<&'b RistrettoPoint> for &'a RistrettoPoint {
     }
 }
 
+define_add_variants!(LHS = RistrettoPoint, RHS = RistrettoPoint, Output = RistrettoPoint);
+
 impl<'b> AddAssign<&'b RistrettoPoint> for RistrettoPoint {
     fn add_assign(&mut self, _rhs: &RistrettoPoint) {
         *self = (self as &RistrettoPoint) + _rhs;
     }
 }
 
+define_add_assign_variants!(LHS = RistrettoPoint, RHS = RistrettoPoint);
+
 impl<'a, 'b> Sub<&'b RistrettoPoint> for &'a RistrettoPoint {
     type Output = RistrettoPoint;
 
@@ -939,12 +943,16 @@ impl<'a, 'b> Sub<&'b RistrettoPoint> for &'a RistrettoPoint {
     }
 }
 
+define_sub_variants!(LHS = RistrettoPoint, RHS = RistrettoPoint, Output = RistrettoPoint);
+
 impl<'b> SubAssign<&'b RistrettoPoint> for RistrettoPoint {
     fn sub_assign(&mut self, _rhs: &RistrettoPoint) {
         *self = (self as &RistrettoPoint) - _rhs;
     }
 }
 
+define_sub_assign_variants!(LHS = RistrettoPoint, RHS = RistrettoPoint);
+
 impl<'a> Neg for &'a RistrettoPoint {
     type Output = RistrettoPoint;
 
@@ -953,6 +961,14 @@ impl<'a> Neg for &'a RistrettoPoint {
     }
 }
 
+impl Neg for RistrettoPoint {
+    type Output = RistrettoPoint;
+
+    fn neg(self) -> RistrettoPoint {
+        -&self
+    }
+}
+
 impl<'b> MulAssign<&'b Scalar> for RistrettoPoint {
     fn mul_assign(&mut self, scalar: &'b Scalar) {
         let result = (self as &RistrettoPoint) * scalar;
@@ -977,6 +993,12 @@ impl<'a, 'b> Mul<&'b RistrettoPoint> for &'a Scalar {
     }
 }
 
+define_mul_assign_variants!(LHS = RistrettoPoint, RHS = Scalar);
+
+define_mul_variants!(LHS = RistrettoPoint, RHS = Scalar, Output = RistrettoPoint);
+define_mul_variants!(LHS = Scalar, RHS = RistrettoPoint, Output = RistrettoPoint);
+
+
 /// Given a vector of (possibly secret) scalars and a vector of
 /// (possibly secret) points, compute `c_1 P_1 + ... + c_n P_n`.
 ///
diff --git a/src/scalar.rs b/src/scalar.rs
index 8d12b4e..64a59bc 100644
--- a/src/scalar.rs
+++ b/src/scalar.rs
@@ -186,6 +186,8 @@ impl<'b> MulAssign<&'b Scalar> for Scalar {
     }
 }
 
+define_mul_assign_variants!(LHS = Scalar, RHS = Scalar);
+
 impl<'a, 'b> Mul<&'b Scalar> for &'a Scalar {
     type Output = Scalar;
     fn mul(self, _rhs: &'b Scalar) -> Scalar {
@@ -193,12 +195,16 @@ impl<'a, 'b> Mul<&'b Scalar> for &'a Scalar {
     }
 }
 
+define_mul_variants!(LHS = Scalar, RHS = Scalar, Output = Scalar);
+
 impl<'b> AddAssign<&'b Scalar> for Scalar {
     fn add_assign(&mut self, _rhs: &'b Scalar) {
         *self = UnpackedScalar::add(&self.unpack(), &_rhs.unpack()).pack();
     }
 }
 
+define_add_assign_variants!(LHS = Scalar, RHS = Scalar);
+
 impl<'a, 'b> Add<&'b Scalar> for &'a Scalar {
     type Output = Scalar;
     fn add(self, _rhs: &'b Scalar) -> Scalar {
@@ -206,12 +212,16 @@ impl<'a, 'b> Add<&'b Scalar> for &'a Scalar {
     }
 }
 
+define_add_variants!(LHS = Scalar, RHS = Scalar, Output = Scalar);
+
 impl<'b> SubAssign<&'b Scalar> for Scalar {
     fn sub_assign(&mut self, _rhs: &'b Scalar) {
         *self = UnpackedScalar::sub(&self.unpack(), &_rhs.unpack()).pack();
     }
 }
 
+define_sub_assign_variants!(LHS = Scalar, RHS = Scalar);
+
 impl<'a, 'b> Sub<&'b Scalar> for &'a Scalar {
     type Output = Scalar;
     fn sub(self, _rhs: &'b Scalar) -> Scalar {
@@ -219,6 +229,8 @@ impl<'a, 'b> Sub<&'b Scalar> for &'a Scalar {
     }
 }
 
+define_sub_variants!(LHS = Scalar, RHS = Scalar, Output = Scalar);
+
 impl<'a> Neg for &'a Scalar {
     type Output = Scalar;
     fn neg(self) -> Scalar {
@@ -226,6 +238,13 @@ impl<'a> Neg for &'a Scalar {
     }
 }
 
+impl<'a> Neg for Scalar {
+    type Output = Scalar;
+    fn neg(self) -> Scalar {
+        -&self
+    }
+}
+
 impl ConditionallyAssignable for Scalar {
     /// Conditionally assign another Scalar to this one.
     ///