diff --git a/Cargo.lock b/Cargo.lock
index 39f29d385..5d9a348f1 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -403,8 +403,7 @@ checksum = "48c757948c5ede0e46177b7add2e67155f70e33c07fea8284df6576da70b3719"
 [[package]]
 name = "elliptic-curve"
 version = "0.14.0-rc.5"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "541598dba361b5ba0321caad955ba99ae82a604f4047c4f2743724996abf62f4"
+source = "git+https://github.com/RustCrypto/traits#f24c2ae0b6ab6e897fab9645274d5c1d815e671e"
 dependencies = [
  "base16ct",
  "base64ct",
diff --git a/Cargo.toml b/Cargo.toml
index 2d57d49d4..071db2023 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -22,3 +22,6 @@ opt-level = 2
 [patch.crates-io]
 primefield = { path = "primefield" }
 primeorder = { path = "primeorder" }
+
+# https://github.com/RustCrypto/traits/pull/1896
+elliptic-curve = { git = "https://github.com/RustCrypto/traits" }
diff --git a/k256/src/arithmetic/projective.rs b/k256/src/arithmetic/projective.rs
index 0e1cad2d9..04d8b059b 100644
--- a/k256/src/arithmetic/projective.rs
+++ b/k256/src/arithmetic/projective.rs
@@ -257,10 +257,10 @@ impl From<AffinePoint> for ProjectivePoint {
 }
 
 impl<const N: usize> BatchNormalize<[ProjectivePoint; N]> for ProjectivePoint {
-    type Output = [Self::AffineRepr; N];
+    type Output = [<Self as Curve>::AffineRepr; N];
 
     #[inline]
-    fn batch_normalize(points: &[Self; N]) -> [Self::AffineRepr; N] {
+    fn batch_normalize(points: &[Self; N]) -> [<Self as Curve>::AffineRepr; N] {
         let zs = [FieldElement::ONE; N];
         let mut affine_points = [AffinePoint::IDENTITY; N];
         batch_normalize_generic(points, zs, &mut affine_points);
@@ -270,10 +270,10 @@ impl<const N: usize> BatchNormalize<[ProjectivePoint; N]> for ProjectivePoint {
 
 #[cfg(feature = "alloc")]
 impl BatchNormalize<[ProjectivePoint]> for ProjectivePoint {
-    type Output = Vec<Self::AffineRepr>;
+    type Output = Vec<<Self as Curve>::AffineRepr>;
 
     #[inline]
-    fn batch_normalize(points: &[Self]) -> Vec<Self::AffineRepr> {
+    fn batch_normalize(points: &[Self]) -> Vec<<Self as Curve>::AffineRepr> {
         let zs = vec![FieldElement::ONE; points.len()];
         let mut affine_points = vec![AffinePoint::IDENTITY; points.len()];
         batch_normalize_generic(points, zs, &mut affine_points);
diff --git a/p256/tests/projective.rs b/p256/tests/projective.rs
index e57808cbd..0044a3e8f 100644
--- a/p256/tests/projective.rs
+++ b/p256/tests/projective.rs
@@ -3,14 +3,18 @@
 #![cfg(all(feature = "arithmetic", feature = "test-vectors"))]
 
 use elliptic_curve::{
+    BatchNormalize,
     group::{GroupEncoding, ff::PrimeField},
+    ops::ReduceNonZero,
+    point::NonIdentity,
     sec1::{self, ToEncodedPoint},
 };
 use p256::{
-    AffinePoint, ProjectivePoint, Scalar,
+    AffinePoint, NonZeroScalar, ProjectivePoint, Scalar,
     test_vectors::group::{ADD_TEST_VECTORS, MUL_TEST_VECTORS},
 };
 use primeorder::{Double, test_projective_arithmetic};
+use proptest::{prelude::any, prop_compose, proptest};
 
 test_projective_arithmetic!(
     AffinePoint,
@@ -25,3 +29,41 @@ fn projective_identity_to_bytes() {
     // This is technically an invalid SEC1 encoding, but is preferable to panicking.
     assert_eq!([0; 33], ProjectivePoint::IDENTITY.to_bytes().as_slice());
 }
+
+prop_compose! {
+    fn non_identity()(bytes in any::<[u8; 32]>()) -> NonIdentity<ProjectivePoint> {
+        NonIdentity::mul_by_generator(&NonZeroScalar::reduce_nonzero_bytes(&bytes.into()))
+    }
+}
+
+// TODO: move to `primeorder::test_projective_arithmetic`.
+proptest! {
+    #[test]
+    fn batch_normalize(
+        a in non_identity(),
+        b in non_identity(),
+    ) {
+        let points: [NonIdentity<ProjectivePoint>; 2] = [a, b];
+
+        let affine_points = NonIdentity::batch_normalize(&points);
+
+        for (point, affine_point) in points.into_iter().zip(affine_points) {
+            assert_eq!(affine_point, point.to_affine());
+        }
+    }
+
+    #[test]
+    #[cfg(feature = "alloc")]
+    fn batch_normalize_alloc(
+        a in non_identity(),
+        b in non_identity(),
+    ) {
+        let points = vec![a, b];
+
+        let affine_points = NonIdentity::batch_normalize(points.as_slice());
+
+        for (point, affine_point) in points.into_iter().zip(affine_points) {
+            assert_eq!(affine_point, point.to_affine());
+        }
+    }
+}
diff --git a/primeorder/src/projective.rs b/primeorder/src/projective.rs
index b4419a0c6..46d179477 100644
--- a/primeorder/src/projective.rs
+++ b/primeorder/src/projective.rs
@@ -13,7 +13,7 @@ use elliptic_curve::{
     array::ArraySize,
     bigint::ArrayEncoding,
     group::{
-        self, Group, GroupEncoding,
+        Curve, Group, GroupEncoding,
         prime::{PrimeCurve, PrimeGroup},
     },
     ops::{BatchInvert, LinearCombination},
@@ -308,7 +308,7 @@ where
     }
 }
 
-impl<C> group::Curve for ProjectivePoint<C>
+impl<C> Curve for ProjectivePoint<C>
 where
     Self: Double,
     C: PrimeCurveParams,
@@ -333,10 +333,10 @@ where
     Self: Double,
     C: PrimeCurveParams,
 {
-    type Output = [Self::AffineRepr; N];
+    type Output = [<Self as Curve>::AffineRepr; N];
 
     #[inline]
-    fn batch_normalize(points: &[Self; N]) -> [Self::AffineRepr; N] {
+    fn batch_normalize(points: &[Self; N]) -> [<Self as Curve>::AffineRepr; N] {
         let zs = [C::FieldElement::ONE; N];
         let mut affine_points = [C::AffinePoint::IDENTITY; N];
         batch_normalize_generic(points, zs, &mut affine_points);
@@ -350,10 +350,10 @@ where
     Self: Double,
     C: PrimeCurveParams,
 {
-    type Output = Vec<Self::AffineRepr>;
+    type Output = Vec<<Self as Curve>::AffineRepr>;
 
     #[inline]
-    fn batch_normalize(points: &[Self]) -> Vec<Self::AffineRepr> {
+    fn batch_normalize(points: &[Self]) -> Vec<<Self as Curve>::AffineRepr> {
         let mut zs = vec![C::FieldElement::ONE; points.len()];
         let mut affine_points = vec![AffinePoint::IDENTITY; points.len()];
         batch_normalize_generic(points, zs.as_mut_slice(), &mut affine_points);