diff --git a/noise/backends/default/diffie_hellmans.py b/noise/backends/default/diffie_hellmans.py
index 5ddbc65..008cca0 100644
--- a/noise/backends/default/diffie_hellmans.py
+++ b/noise/backends/default/diffie_hellmans.py
@@ -1,4 +1,5 @@
 from cryptography.hazmat.primitives.asymmetric import x25519, x448
+from cryptography.hazmat.primitives import serialization
 
 from noise.backends.default.keypairs import KeyPair25519, KeyPair448
 from noise.exceptions import NoiseValueError
@@ -17,7 +18,9 @@ class ED25519(DH):
     def generate_keypair(self) -> 'KeyPair':
         private_key = x25519.X25519PrivateKey.generate()
         public_key = private_key.public_key()
-        return KeyPair25519(private_key, public_key, public_key.public_bytes())
+        return KeyPair25519(private_key, public_key,
+                            public_key.public_bytes(serialization.Encoding.Raw,
+                                                    serialization.PublicFormat.Raw))
 
     def dh(self, private_key, public_key) -> bytes:
         if not isinstance(private_key, x25519.X25519PrivateKey) or not isinstance(public_key, x25519.X25519PublicKey):
@@ -37,7 +40,9 @@ class ED448(DH):
     def generate_keypair(self) -> 'KeyPair':
         private_key = x448.X448PrivateKey.generate()
         public_key = private_key.public_key()
-        return KeyPair448(private_key, public_key, public_key.public_bytes())
+        return KeyPair448(private_key, public_key,
+                          public_key.public_bytes(serialization.Encoding.Raw,
+                                                  serialization.PublicFormat.Raw))
 
     def dh(self, private_key, public_key) -> bytes:
         if not isinstance(private_key, x448.X448PrivateKey) or not isinstance(public_key, x448.X448PublicKey):
diff --git a/tests/test_connection.py b/tests/test_connection.py
new file mode 100644
index 0000000..3995b53
--- /dev/null
+++ b/tests/test_connection.py
@@ -0,0 +1,34 @@
+from noise.connection import NoiseConnection
+
+class TestConnection(object):
+    def do_test_connection(self, name):
+        key = b"\x00" * 32
+        left = NoiseConnection.from_name(name)
+        left.set_psks(key)
+        left.set_as_initiator()
+        left.start_handshake()
+
+        right = NoiseConnection.from_name(name)
+        right.set_psks(key)
+        right.set_as_responder()
+        right.start_handshake()
+
+        h = left.write_message()
+        _ = right.read_message(h)
+        h2 = right.write_message()
+        left.read_message(h2)
+
+        assert left.handshake_finished
+        assert right.handshake_finished
+
+        enc = left.encrypt(b"hello")
+        dec = right.decrypt(enc)
+        assert dec == b"hello"
+
+    def test_25519(self):
+        name = b"Noise_NNpsk0_25519_ChaChaPoly_BLAKE2s"
+        self.do_test_connection(name)
+
+    def test_448(self):
+        name = b"Noise_NNpsk0_448_ChaChaPoly_BLAKE2s"
+        self.do_test_connection(name)