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diff --git a/tests/hazmat/primitives/test_rsa.py b/tests/hazmat/primitives/test_rsa.py
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+++ b/tests/hazmat/primitives/test_rsa.py
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+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+# implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+
+from __future__ import absolute_import, division, print_function
+
+import os
+
+import pytest
+
+from cryptography.hazmat.primitives.asymmetric import rsa
+
+from ...utils import load_pkcs1_vectors, load_vectors_from_file
+
+
+class TestRSA(object):
+    @pytest.mark.parametrize(
+        "pkcs1_example",
+        load_vectors_from_file(
+            os.path.join(
+                "asymmetric", "RSA", "pkcs-1v2-1d2-vec", "pss-vect.txt"),
+            load_pkcs1_vectors
+        )
+    )
+    def test_load_pss_vect_example_keys(self, pkcs1_example):
+        secret, public = pkcs1_example
+
+        skey = rsa.RSAPrivateKey(**secret)
+        pkey = rsa.RSAPublicKey(**public)
+        pkey2 = skey.public_key()
+
+        assert skey and pkey and pkey2
+
+        assert skey.modulus
+        assert skey.modulus == pkey.modulus
+        assert skey.modulus == skey.n
+        assert skey.public_exponent == pkey.public_exponent
+        assert skey.public_exponent == skey.e
+        assert skey.private_exponent == skey.d
+
+        assert pkey.modulus
+        assert pkey.modulus == pkey2.modulus
+        assert pkey.modulus == pkey.n
+        assert pkey.public_exponent == pkey2.public_exponent
+        assert pkey.public_exponent == pkey.e
+
+        assert skey.key_size
+        assert skey.key_size == pkey.key_size
+        assert skey.key_size == pkey2.key_size
+
+        assert skey.p * skey.q == skey.modulus
+
+    def test_invalid_private_key_argument_types(self):
+        with pytest.raises(TypeError):
+            rsa.RSAPrivateKey(None, None, None, None, None)
+
+    def test_invalid_public_key_argument_types(self):
+        with pytest.raises(TypeError):
+            rsa.RSAPublicKey(None, None)
+
+    def test_invalid_private_key_argument_values(self):
+        # Start with p=3, q=5, private_exponent=14, public_exponent=7,
+        # modulus=15. Then change one value at a time to test the bounds.
+
+        # Test a modulus < 3.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=5,
+                private_exponent=14,
+                public_exponent=7,
+                modulus=2
+            )
+
+        # Test a modulus != p * q.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=5,
+                private_exponent=14,
+                public_exponent=7,
+                modulus=16
+            )
+
+        # Test a p > modulus.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=16,
+                q=5,
+                private_exponent=14,
+                public_exponent=7,
+                modulus=15
+            )
+
+        # Test a q > modulus.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=16,
+                private_exponent=14,
+                public_exponent=7,
+                modulus=15
+            )
+
+        # Test a private_exponent > modulus
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=5,
+                private_exponent=16,
+                public_exponent=7,
+                modulus=15
+            )
+
+        # Test a public_exponent < 3
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=5,
+                private_exponent=14,
+                public_exponent=1,
+                modulus=15
+            )
+
+        # Test a public_exponent > modulus
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=5,
+                private_exponent=14,
+                public_exponent=17,
+                modulus=15
+            )
+
+        # Test a public_exponent that is not odd.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=5,
+                private_exponent=14,
+                public_exponent=6,
+                modulus=15
+            )
+
+    def test_invalid_public_key_argument_values(self):
+        # Start with public_exponent=7, modulus=15. Then change one value at a
+        # time to test the bounds.
+
+        # Test a modulus < 3.
+        with pytest.raises(ValueError):
+            rsa.RSAPublicKey(public_exponent=7, modulus=2)
+
+        # Test a public_exponent < 3
+        with pytest.raises(ValueError):
+            rsa.RSAPublicKey(public_exponent=1, modulus=15)
+
+        # Test a public_exponent > modulus
+        with pytest.raises(ValueError):
+            rsa.RSAPublicKey(public_exponent=17, modulus=15)
+
+        # Test a public_exponent that is not odd.
+        with pytest.raises(ValueError):
+            rsa.RSAPublicKey(public_exponent=6, modulus=15)