diff --git a/src/montgomery.rs b/src/montgomery.rs
index de0f8b7..867496c 100644
--- a/src/montgomery.rs
+++ b/src/montgomery.rs
@@ -94,6 +94,13 @@ impl PartialEq for MontgomeryPoint {
 
 impl Eq for MontgomeryPoint {}
 
+impl Identity for MontgomeryPoint {
+    /// Return the group identity element, which has order 4.
+    fn identity() -> MontgomeryPoint {
+        MontgomeryPoint([0u8; 32])
+    }
+}
+
 impl Zeroize for MontgomeryPoint {
     fn zeroize(&mut self) {
         self.0.zeroize();
@@ -351,6 +358,14 @@ mod test {
 
     use rand_core::OsRng;
 
+    #[test]
+    fn identity_in_different_coordinates() {
+        let id_projective = ProjectivePoint::identity();
+        let id_montgomery = id_projective.to_affine();
+
+        assert!(id_montgomery == MontgomeryPoint::identity());
+    }
+
     #[test]
     #[cfg(feature = "serde")]
     fn serde_bincode_basepoint_roundtrip() {