diff --git a/elliptic-curve/src/lib.rs b/elliptic-curve/src/lib.rs
index dbb6292e9..31ee72515 100644
--- a/elliptic-curve/src/lib.rs
+++ b/elliptic-curve/src/lib.rs
@@ -30,10 +30,7 @@ pub mod secret_key;
 #[cfg_attr(docsrs, doc(cfg(feature = "weierstrass")))]
 pub mod weierstrass;
 
-pub use self::{
-    error::Error,
-    secret_key::{FromSecretKey, SecretKey},
-};
+pub use self::{error::Error, secret_key::SecretKey};
 pub use generic_array::{self, typenum::consts};
 pub use subtle;
 
@@ -42,6 +39,7 @@ pub use rand_core;
 
 use core::{fmt::Debug, ops::Add};
 use generic_array::{typenum::Unsigned, ArrayLength, GenericArray};
+use subtle::ConditionallySelectable;
 
 #[cfg(feature = "rand_core")]
 use rand_core::{CryptoRng, RngCore};
@@ -65,10 +63,13 @@ 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: FromSecretKey<Self>;
+    type Scalar: ConditionallySelectable
+        + Default
+        + secret_key::FromSecretKey<Self>
+        + ops::MulBase<Output = Self::AffinePoint>;
 
     /// Affine point type for a given curve
-    type AffinePoint;
+    type AffinePoint: ConditionallySelectable;
 }
 
 /// Randomly generate a value.
diff --git a/elliptic-curve/src/ops.rs b/elliptic-curve/src/ops.rs
index 09f811d7e..4d8f09523 100644
--- a/elliptic-curve/src/ops.rs
+++ b/elliptic-curve/src/ops.rs
@@ -10,3 +10,12 @@ pub trait Invert {
     /// Invert a field element.
     fn invert(&self) -> CtOption<Self::Output>;
 }
+
+/// Fixed-base scalar multiplication
+pub trait MulBase {
+    /// Affine point type
+    type Output;
+
+    /// Multiply this value by the generator point for the elliptic curve
+    fn mul_base(&self) -> CtOption<Self::Output>;
+}
diff --git a/elliptic-curve/src/weierstrass.rs b/elliptic-curve/src/weierstrass.rs
index 424f28fbb..d98cc3791 100644
--- a/elliptic-curve/src/weierstrass.rs
+++ b/elliptic-curve/src/weierstrass.rs
@@ -8,16 +8,5 @@ pub use self::{
     public_key::{FromPublicKey, PublicKey},
 };
 
-use crate::{Arithmetic, ScalarBytes};
-use subtle::CtOption;
-
 /// Marker trait for elliptic curves in short Weierstrass form
 pub trait Curve: super::Curve {}
-
-/// Fixed-base scalar multiplication
-pub trait FixedBaseScalarMul: Curve + Arithmetic {
-    /// Multiply the given scalar by the generator point for this elliptic
-    /// curve.
-    // TODO(tarcieri): use `Self::Scalar` for the `scalar` param
-    fn mul_base(scalar: &ScalarBytes<Self>) -> CtOption<Self::AffinePoint>;
-}
diff --git a/elliptic-curve/src/weierstrass/public_key.rs b/elliptic-curve/src/weierstrass/public_key.rs
index 3aaaa520d..b369e8f2d 100644
--- a/elliptic-curve/src/weierstrass/public_key.rs
+++ b/elliptic-curve/src/weierstrass/public_key.rs
@@ -3,9 +3,9 @@
 
 use super::{
     point::{CompressedPoint, CompressedPointSize, UncompressedPoint, UncompressedPointSize},
-    Curve, FixedBaseScalarMul,
+    Curve,
 };
-use crate::{Error, SecretKey};
+use crate::{ops::MulBase, secret_key::FromSecretKey, Arithmetic, Error, SecretKey};
 use core::fmt::{self, Debug};
 use core::ops::Add;
 use generic_array::{
@@ -104,9 +104,9 @@ where
     }
 }
 
-impl<C: Curve> PublicKey<C>
+impl<C> PublicKey<C>
 where
-    C: FixedBaseScalarMul,
+    C: Curve + Arithmetic,
     C::ElementSize: Add<U1>,
     <C::ElementSize as Add>::Output: Add<U1>,
     CompressedPoint<C>: From<C::AffinePoint>,
@@ -118,18 +118,18 @@ where
     ///
     /// The `compress` flag requests point compression.
     pub fn from_secret_key(secret_key: &SecretKey<C>, compress: bool) -> Result<Self, Error> {
-        let ct_option = C::mul_base(secret_key.secret_scalar());
+        let ct_option = C::Scalar::from_secret_key(&secret_key).and_then(|s| s.mul_base());
+
+        if ct_option.is_none().into() {
+            return Err(Error);
+        }
 
-        if ct_option.is_some().into() {
-            let affine_point = ct_option.unwrap();
+        let affine_point = ct_option.unwrap();
 
-            if compress {
-                Ok(PublicKey::Compressed(affine_point.into()))
-            } else {
-                Ok(PublicKey::Uncompressed(affine_point.into()))
-            }
+        if compress {
+            Ok(PublicKey::Compressed(affine_point.into()))
         } else {
-            Err(Error)
+            Ok(PublicKey::Uncompressed(affine_point.into()))
         }
     }
 }