diff --git a/tests/hazmat/primitives/test_rsa.py b/tests/hazmat/primitives/test_rsa.py
index 0e930e4..9dc1a9e 100644
--- a/tests/hazmat/primitives/test_rsa.py
+++ b/tests/hazmat/primitives/test_rsa.py
@@ -24,6 +24,20 @@
 from ...utils import load_pkcs1_vectors, load_vectors_from_file
 
 
+def _egcd(a, b):
+    if a == 0:
+        return (b, 0, 1)
+    else:
+        g, y, x = _egcd(b % a, a)
+        return (g, x - (b // a) * y, y)
+
+
+def _modinv(a, m):
+    g, x, y = _egcd(a, m)
+    assert g == 1
+    return x % m
+
+
 def _check_rsa_private_key(skey):
     assert skey
     assert skey.modulus
@@ -31,6 +45,9 @@
     assert skey.private_exponent
     assert skey.p * skey.q == skey.modulus
     assert skey.key_size
+    assert skey._dmp1 == skey.d % (skey.p - 1)
+    assert skey._dmq1 == skey.d % (skey.q - 1)
+    assert skey._iqmp == _modinv(skey.q, skey.p)
 
     pkey = skey.public_key()
     assert pkey
@@ -115,22 +132,26 @@
 
     def test_invalid_private_key_argument_types(self):
         with pytest.raises(TypeError):
-            rsa.RSAPrivateKey(None, None, None, None, None)
+            rsa.RSAPrivateKey(None, None, None, 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.
+        # Start with p=3, q=11, private_exponent=3, public_exponent=7,
+        # modulus=33, dmp1=1, dmq1=3, iqmp=2. 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,
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=3,
+                iqmp=2,
                 public_exponent=7,
                 modulus=2
             )
@@ -139,70 +160,156 @@
         with pytest.raises(ValueError):
             rsa.RSAPrivateKey(
                 p=3,
-                q=5,
-                private_exponent=14,
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=3,
+                iqmp=2,
                 public_exponent=7,
-                modulus=16
+                modulus=35
             )
 
         # Test a p > modulus.
         with pytest.raises(ValueError):
             rsa.RSAPrivateKey(
-                p=16,
-                q=5,
-                private_exponent=14,
+                p=37,
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=3,
+                iqmp=2,
                 public_exponent=7,
-                modulus=15
+                modulus=33
             )
 
         # Test a q > modulus.
         with pytest.raises(ValueError):
             rsa.RSAPrivateKey(
                 p=3,
-                q=16,
-                private_exponent=14,
+                q=37,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=3,
+                iqmp=2,
                 public_exponent=7,
-                modulus=15
+                modulus=33
+            )
+
+        # Test a dmp1 > modulus.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=11,
+                private_exponent=3,
+                dmp1=35,
+                dmq1=3,
+                iqmp=2,
+                public_exponent=7,
+                modulus=33
+            )
+
+        # Test a dmq1 > modulus.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=35,
+                iqmp=2,
+                public_exponent=7,
+                modulus=33
+            )
+
+        # Test an iqmp > modulus.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=3,
+                iqmp=35,
+                public_exponent=7,
+                modulus=33
             )
 
         # Test a private_exponent > modulus
         with pytest.raises(ValueError):
             rsa.RSAPrivateKey(
                 p=3,
-                q=5,
-                private_exponent=16,
+                q=11,
+                private_exponent=37,
+                dmp1=1,
+                dmq1=3,
+                iqmp=2,
                 public_exponent=7,
-                modulus=15
+                modulus=33
             )
 
         # Test a public_exponent < 3
         with pytest.raises(ValueError):
             rsa.RSAPrivateKey(
                 p=3,
-                q=5,
-                private_exponent=14,
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=3,
+                iqmp=2,
                 public_exponent=1,
-                modulus=15
+                modulus=33
             )
 
         # Test a public_exponent > modulus
         with pytest.raises(ValueError):
             rsa.RSAPrivateKey(
                 p=3,
-                q=5,
-                private_exponent=14,
-                public_exponent=17,
-                modulus=15
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=3,
+                iqmp=2,
+                public_exponent=65537,
+                modulus=33
             )
 
         # Test a public_exponent that is not odd.
         with pytest.raises(ValueError):
             rsa.RSAPrivateKey(
                 p=3,
-                q=5,
-                private_exponent=14,
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=3,
+                iqmp=2,
                 public_exponent=6,
-                modulus=15
+                modulus=33
+            )
+
+        # Test a dmp1 that is not odd.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=11,
+                private_exponent=3,
+                dmp1=2,
+                dmq1=3,
+                iqmp=2,
+                public_exponent=7,
+                modulus=33
+            )
+
+        # Test a dmq1 that is not odd.
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(
+                p=3,
+                q=11,
+                private_exponent=3,
+                dmp1=1,
+                dmq1=4,
+                iqmp=2,
+                public_exponent=7,
+                modulus=33
             )
 
     def test_invalid_public_key_argument_values(self):
diff --git a/tests/test_utils.py b/tests/test_utils.py
index a0571ad..0e1d77b 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -768,7 +768,19 @@
                 'q': int(
                     '847e732376fc7900f898ea82eb2b0fc418565fdae62f7d9ec4ce2217b'
                     '97990dd272db157f99f63c0dcbb9fbacdbd4c4dadb6df67756358ca41'
-                    '74825b48f49706d', 16)
+                    '74825b48f49706d', 16),
+                'dmp1': int(
+                    '05c2a83c124b3621a2aa57ea2c3efe035eff4560f33ddebb7adab81fc'
+                    'e69a0c8c2edc16520dda83d59a23be867963ac65f2cc710bbcfb96ee1'
+                    '03deb771d105fd85', 16),
+                'dmq1': int(
+                    '04cae8aa0d9faa165c87b682ec140b8ed3b50b24594b7a3b2c220b366'
+                    '9bb819f984f55310a1ae7823651d4a02e99447972595139363434e5e3'
+                    '0a7e7d241551e1b9', 16),
+                'iqmp': int(
+                    '07d3e47bf686600b11ac283ce88dbb3f6051e8efd04680e44c171ef53'
+                    '1b80b2b7c39fc766320e2cf15d8d99820e96ff30dc69691839c4b40d7'
+                    'b06e45307dc91f3f', 16)
             },
 
             {
@@ -809,7 +821,22 @@
                     'ed4d71d0a6e24b93c2e5f6b4bbe05f5fb0afa042d204fe3378d365c2f'
                     '288b6a8dad7efe45d153eef40cacc7b81ff934002d108994b94a5e472'
                     '8cd9c963375ae49965bda55cbf0efed8d6553b4027f2d86208a6e6b48'
-                    '9c176128092d629e49d3d', 16)
+                    '9c176128092d629e49d3d', 16),
+                'dmp1': int(
+                    '2bb68bddfb0c4f56c8558bffaf892d8043037841e7fa81cfa61a38c5e'
+                    '39b901c8ee71122a5da2227bd6cdeeb481452c12ad3d61d5e4f776a0a'
+                    'b556591befe3e59e5a7fddb8345e1f2f35b9f4cee57c32414c086aec9'
+                    '93e9353e480d9eec6289f', 16),
+                'dmq1': int(
+                    '4ff897709fad079746494578e70fd8546130eeab5627c49b080f05ee4'
+                    'ad9f3e4b7cba9d6a5dff113a41c3409336833f190816d8a6bc42e9bec'
+                    '56b7567d0f3c9c696db619b245d901dd856db7c8092e77e9a1cccd56e'
+                    'e4dba42c5fdb61aec2669', 16),
+                'iqmp': int(
+                    '77b9d1137b50404a982729316efafc7dfe66d34e5a182600d5f30a0a8'
+                    '512051c560d081d4d0a1835ec3d25a60f4e4d6aa948b2bf3dbb5b124c'
+                    'bbc3489255a3a948372f6978496745f943e1db4f18382ceaa505dfc65'
+                    '757bb3f857a58dce52156', 16)
             },
 
             {
diff --git a/tests/utils.py b/tests/utils.py
index 408b05f..2bbecd7 100644
--- a/tests/utils.py
+++ b/tests/utils.py
@@ -262,6 +262,12 @@
             attr = "p"
         elif line.startswith("# Prime 2:"):
             attr = "q"
+        elif line.startswith("# Prime exponent 1:"):
+            attr = "dmp1"
+        elif line.startswith("# Prime exponent 2:"):
+            attr = "dmq1"
+        elif line.startswith("# Coefficient:"):
+            attr = "iqmp"
         elif line.startswith("#"):
             attr = None
         else: