2 files changed, 11 insertions, 3 deletions

diff --git a/pyecsca/ec/curve.py b/pyecsca/ec/curve.py
index 2e08abb..18d7e65 100644
--- a/pyecsca/ec/curve.py
+++ b/pyecsca/ec/curve.py
@@ -257,7 +257,11 @@ class EllipticCurve:
         :param point: The point to test.
         :return: Whether it is the neutral point.
         """
-        return self.neutral == point
+        # Neutral is either InfinityPoint or Point in either affine or some other coord system.
+        if isinstance(point.coordinate_model, AffineCoordinateModel):
+            return self.neutral_is_affine and self.affine_neutral == point
+        else:
+            return self.neutral.equals_homog(point)
 
     def is_on_curve(self, point: Point) -> bool:
         """
diff --git a/pyecsca/ec/point.py b/pyecsca/ec/point.py
index 1833f46..5a486bc 100644
--- a/pyecsca/ec/point.py
+++ b/pyecsca/ec/point.py
@@ -169,7 +169,9 @@ class Point:
         if not isinstance(other, Point) or isinstance(other, InfinityPoint):
             return False
         if self.coordinate_model.curve_model != other.coordinate_model.curve_model:
-            return False
+            raise ValueError("Can only compare points with the same curve model.")
+        if self.coordinate_model != other.coordinate_model:
+            raise ValueError("Can only compare points with the same coordinate model.")
         if "z" in self.coordinate_model.formulas:
             formula = self.coordinate_model.formulas["z"]
             self_mapped = formula(self.field, self)
@@ -188,7 +190,9 @@ class Point:
         if not isinstance(other, Point) or isinstance(other, InfinityPoint):
             return False
         if self.coordinate_model.curve_model != other.coordinate_model.curve_model:
-            return False
+            raise ValueError("Can only compare points with the same curve model.")
+        if self.coordinate_model != other.coordinate_model:
+            raise ValueError("Can only compare points with the same coordinate model.")
         weights = sorted(self.coordinate_model.homogweights.items(), key=itemgetter(1))
         lambdas: Set[Mod] = set()
         for var, weight in weights: