diff --git a/elliptic-curve/src/lib.rs b/elliptic-curve/src/lib.rs
index 1c55378fe..d13365992 100644
--- a/elliptic-curve/src/lib.rs
+++ b/elliptic-curve/src/lib.rs
@@ -69,6 +69,7 @@ extern crate alloc;
 extern crate std;
 
 pub mod ops;
+pub mod point;
 pub mod scalar;
 
 #[cfg(feature = "dev")]
@@ -83,7 +84,6 @@ pub mod sec1;
 pub mod weierstrass;
 
 mod error;
-mod point;
 mod secret_key;
 
 #[cfg(feature = "arithmetic")]
diff --git a/elliptic-curve/src/point/non_identity.rs b/elliptic-curve/src/point/non_identity.rs
index 075e3a94d..81c31cd19 100644
--- a/elliptic-curve/src/point/non_identity.rs
+++ b/elliptic-curve/src/point/non_identity.rs
@@ -1,6 +1,6 @@
 //! Non-identity point type.
 
-use core::ops::Deref;
+use core::ops::{Deref, Mul};
 
 use group::{prime::PrimeCurveAffine, Curve, GroupEncoding};
 use rand_core::{CryptoRng, RngCore};
@@ -9,6 +9,8 @@ use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 #[cfg(feature = "serde")]
 use serdect::serde::{de, ser, Deserialize, Serialize};
 
+use crate::{CurveArithmetic, NonZeroScalar, Scalar};
+
 /// Non-identity point type.
 ///
 /// This type ensures that its value is not the identity point, ala `core::num::NonZero*`.
@@ -22,13 +24,22 @@ pub struct NonIdentity<P> {
 
 impl<P> NonIdentity<P>
 where
-    P: ConditionallySelectable + ConstantTimeEq + Default + GroupEncoding,
+    P: ConditionallySelectable + ConstantTimeEq + Default,
 {
     /// Create a [`NonIdentity`] from a point.
     pub fn new(point: P) -> CtOption<Self> {
         CtOption::new(Self { point }, !point.ct_eq(&P::default()))
     }
 
+    pub(crate) fn new_unchecked(point: P) -> Self {
+        Self { point }
+    }
+}
+
+impl<P> NonIdentity<P>
+where
+    P: ConditionallySelectable + ConstantTimeEq + Default + GroupEncoding,
+{
     /// Decode a [`NonIdentity`] from its encoding.
     pub fn from_repr(repr: &P::Repr) -> CtOption<Self> {
         Self::from_bytes(repr)
@@ -44,7 +55,7 @@ impl<P: Copy> NonIdentity<P> {
 
 impl<P> NonIdentity<P>
 where
-    P: ConditionallySelectable + ConstantTimeEq + Curve + Default + GroupEncoding,
+    P: ConditionallySelectable + ConstantTimeEq + Curve + Default,
 {
     /// Generate a random `NonIdentity<ProjectivePoint>`.
     pub fn random(mut rng: impl CryptoRng + RngCore) -> Self {
@@ -129,6 +140,32 @@ where
     }
 }
 
+impl<C, P> Mul<NonZeroScalar<C>> for NonIdentity<P>
+where
+    C: CurveArithmetic,
+    P: Copy + Mul<Scalar<C>, Output = P>,
+{
+    type Output = NonIdentity<P>;
+
+    fn mul(self, rhs: NonZeroScalar<C>) -> Self::Output {
+        &self * &rhs
+    }
+}
+
+impl<C, P> Mul<&NonZeroScalar<C>> for &NonIdentity<P>
+where
+    C: CurveArithmetic,
+    P: Copy + Mul<Scalar<C>, Output = P>,
+{
+    type Output = NonIdentity<P>;
+
+    fn mul(self, rhs: &NonZeroScalar<C>) -> Self::Output {
+        NonIdentity {
+            point: self.point * *rhs.as_ref(),
+        }
+    }
+}
+
 #[cfg(feature = "serde")]
 impl<P> Serialize for NonIdentity<P>
 where
diff --git a/elliptic-curve/src/public_key.rs b/elliptic-curve/src/public_key.rs
index a916cd8a8..045a1aa6a 100644
--- a/elliptic-curve/src/public_key.rs
+++ b/elliptic-curve/src/public_key.rs
@@ -155,6 +155,11 @@ where
         self.point.into()
     }
 
+    /// Convert this [`PublicKey`] to a [`NonIdentity`] of the inner [`AffinePoint`]
+    pub fn to_non_identity(&self) -> NonIdentity<AffinePoint<C>> {
+        NonIdentity::new_unchecked(self.point)
+    }
+
     /// Parse a [`JwkEcKey`] JSON Web Key (JWK) into a [`PublicKey`].
     #[cfg(feature = "jwk")]
     pub fn from_jwk(jwk: &JwkEcKey) -> Result<Self>
@@ -271,7 +276,7 @@ where
     P: Copy + Into<AffinePoint<C>>,
 {
     fn from(value: NonIdentity<P>) -> Self {
-        PublicKey::from(&value)
+        Self::from(&value)
     }
 }
 
@@ -287,6 +292,24 @@ where
     }
 }
 
+impl<C> From<PublicKey<C>> for NonIdentity<AffinePoint<C>>
+where
+    C: CurveArithmetic,
+{
+    fn from(value: PublicKey<C>) -> Self {
+        Self::from(&value)
+    }
+}
+
+impl<C> From<&PublicKey<C>> for NonIdentity<AffinePoint<C>>
+where
+    C: CurveArithmetic,
+{
+    fn from(value: &PublicKey<C>) -> Self {
+        PublicKey::to_non_identity(value)
+    }
+}
+
 #[cfg(feature = "sec1")]
 impl<C> PartialOrd for PublicKey<C>
 where