diff --git a/tests/test_primitives/conftest.py b/tests/test_primitives/conftest.py
index 713fb58..4de3e9f 100644
--- a/tests/test_primitives/conftest.py
+++ b/tests/test_primitives/conftest.py
@@ -48,7 +48,7 @@ def mock_openssl(mocker, random_ec_point1: Point, random_ec_curvebn1: CurveBN, r
             check_point_ctypes(ec_point, other_point)
             assert 'BN_CTX' in str(context)
             assert 'EC_GROUP' in str(group)
-            assert random_ec_point1.group == group
+            assert random_ec_point1.curve.ec_group == group
             assert not bool(actual_backend['EC_POINT_cmp'](group, random_ec_point1.ec_point, ec_point, context))
             result = actual_backend['EC_POINT_cmp'](group, random_ec_point1.ec_point, other_point, context)
             assert not bool(result)
diff --git a/tests/test_primitives/test_point/test_point_arithmetic.py b/tests/test_primitives/test_point/test_point_arithmetic.py
index 62646ae..8c1bee2 100644
--- a/tests/test_primitives/test_point/test_point_arithmetic.py
+++ b/tests/test_primitives/test_point/test_point_arithmetic.py
@@ -30,8 +30,7 @@ def test_point_curve_multiplication_regression():
     # Make sure we have instantiated a new, unequal point in the same curve and group
     assert isinstance(product_with_star_operator, Point), "Point.__mul__ did not return a point instance"
     assert k256_point != product_with_star_operator
-    assert k256_point.curve_nid == product_with_star_operator.curve_nid
-    assert k256_point.group == product_with_star_operator.group
+    assert k256_point.curve == product_with_star_operator.curve
 
     product_bytes = b'\x03\xc9\xda\xa2\x88\xe2\xa0+\xb1N\xb6\xe6\x1c\xa5(\xe6\xe0p\xf6\xf4\xa9\xfc\xb1\xfaUV\xd3\xb3\x0e4\x94\xbe\x12'
     product_point = Point.from_bytes(product_bytes)
diff --git a/tests/test_primitives/test_point/test_point_serializers.py b/tests/test_primitives/test_point/test_point_serializers.py
index fa80d43..1e67360 100644
--- a/tests/test_primitives/test_point/test_point_serializers.py
+++ b/tests/test_primitives/test_point/test_point_serializers.py
@@ -36,15 +36,9 @@ def test_generate_random_points():
 
 @pytest.mark.parametrize("curve, nid, point_bytes", generate_test_points_bytes())
 def test_bytes_serializers(point_bytes, nid, curve):
-
-    point_with_nid = Point.from_bytes(point_bytes, curve=nid)         # from nid
-    assert isinstance(point_with_nid, Point)
-
-    point_with_curve = Point.from_bytes(point_bytes, curve=curve)     # from curve
+    point_with_curve = Point.from_bytes(point_bytes, curve=curve) # from curve
     assert isinstance(point_with_curve, Point)
 
-    assert point_with_nid == point_with_curve
-
     the_same_point_bytes = point_with_curve.to_bytes()
     assert point_bytes == the_same_point_bytes
 
@@ -67,9 +61,7 @@ def test_bytes_serializers(point_bytes, nid, curve):
 
 @pytest.mark.parametrize("curve, nid, point_affine", generate_test_points_affine())
 def test_affine(point_affine, nid, curve):
-    point = Point.from_affine(point_affine, curve=nid)              # from nid
-    the_same_point = Point.from_affine(point_affine, curve=curve)   # from curve instance
-    assert point == the_same_point
+    point = Point.from_affine(point_affine, curve=curve)  # from curve
     assert isinstance(point, Point)
     point_affine2 = point.to_affine()
     assert point_affine == point_affine2
diff --git a/tests/test_simple_api.py b/tests/test_simple_api.py
index c6ff3e0..348044e 100644
--- a/tests/test_simple_api.py
+++ b/tests/test_simple_api.py
@@ -4,22 +4,23 @@ from cryptography.hazmat.primitives.asymmetric import ec
 
 from umbral import pre
 from umbral.fragments import KFrag, CapsuleFrag
+from umbral.curve import SECP384R1, SECP256R1
 from umbral.config import default_curve
 from umbral.params import UmbralParameters
 from umbral.signing import Signer
 from umbral.keys import UmbralPrivateKey, UmbralPublicKey
 from .conftest import parameters, wrong_parameters
 
+
 secp_curves = [
-    ec.SECP384R1,
-    ec.SECP192R1
+    SECP384R1(),
+    SECP256R1()
 ]
 
 
 @pytest.mark.parametrize("N, M", parameters)
 def test_simple_api(N, M, curve=default_curve()):
     """Manually injects umbralparameters for multi-curve testing."""
-
     params = UmbralParameters(curve=curve)
 
     delegating_privkey = UmbralPrivateKey.gen_key(params=params)
diff --git a/umbral/curvebn.py b/umbral/curvebn.py
index 8d3c6a0..7fcec25 100644
--- a/umbral/curvebn.py
+++ b/umbral/curvebn.py
@@ -241,7 +241,7 @@ class CurveBN(object):
         """
         if type(other) == int:
             other = openssl._int_to_bn(other)
-            other = CurveBN(other, None, None, None)
+            other = CurveBN(other, self.curve)
 
         rem = openssl._get_new_BN()
         with backend._tmp_bn_ctx() as bn_ctx:
diff --git a/umbral/point.py b/umbral/point.py
index bd1faef..293d48c 100644
--- a/umbral/point.py
+++ b/umbral/point.py
@@ -67,9 +67,9 @@ class Point(object):
 
         group = openssl._get_ec_group_by_curve_nid(curve.curve_nid)
         ec_point = openssl._get_EC_POINT_via_affine(affine_x, affine_y,
-                                                    ec_group=self.curve.ec_group)
+                                                    ec_group=curve.ec_group)
 
-        return cls(ec_point, curve_nid, group)
+        return cls(ec_point, curve)
 
     def to_affine(self):
         """