OpenSSL DH backend implementation [Second attempt] (#2914)

* Start of OpenSSL DH backend implementation

* Supporting DH in MultiBackend

* DHBackend has dh_parameters_supported method

* Removed DHParametersWithNumbers and DHPrivateKeyWithNumbers from documentation

* Removed ExchangeContext. exchange is a method of DHPrivateKeyWithSerialization

* PEP8 fixes

* Fixed TestDH.test_bad_tls_exchange

* Fixed generate_private_key reference in dh documentation

* test DH multibackend support

* testing DH coversion to serialized

* Validating that we receive serialized class in test_generate_dh

* Testing DH exchange symmetric key padding

* struct DH is now opaqued

* PEP8 fixes

* Testing load_dh_private_numbers throws ValueError when DH_check fails

* Using openssl_assert

* Passing keywords arguments in DH key exchange example

* test_dh::test_bad_tls_exchange now uses pre calculated parameters

* TestDH - Add test that the computed secret is equivalent to the definition by comparing with secret computed in pure python

* Add missing generator parameter to DHBackend interface docs.

* Include parameter type in DHBackend abc docs.

* Add docs for dh.generate_parameters function

* Remove the dh Numbers section, and move the DHNumbers class docs to where they are first used.

* Add note of big endian byte packing to DH exchange method.

* DH documentation updates.

Add single sentence overview with wikipedia link.
Add paragraph on assembling using Numbers objects.
Add link to backend interface docs.
First section was all indented, I think by mistake.

* Add exchange method to DHPrivateKey abstract base class.

* Small tweaks to DH documentation - remove Provider.

* Add endian to dictionary

* Use utils.int_from_bytes in test_tls_exchange_algorithm

* Removed duplicate line

* Change dh.rst exchange algorithm from doctest to code-block

The example in the Diffie-Hellman exhange algorithm is using
2048 bits key. Generating the parameters of 2048 takes long
time. This caused the automated tests to fail. In order to
pass the tests we change the example to code-block so it
will not run in the doc tests.

* Fix dh docs

* Document the generator in DHBackend relevant methods

* Fix dh tests

* use DHparams_dup

* Fix key type to unsigned char as expected by DH_compute_key

* Validate that DH generator is 2 or 5

* test dh exchange using botan vectors

* group all numbers classes

* Simplify _DHPrivateKey

* Rename test with serialized to numbers

* Move bad exchange params to external vector file

* update exchange versionadded to 1.7

* Make key_size bit accurate

* Change botan link

* Added CHANGELOG entry

6 files changed, 399 insertions, 15 deletions

diff --git a/src/cryptography/exceptions.py b/src/cryptography/exceptions.py
index ee43fed7..648cf9df 100644
--- a/src/cryptography/exceptions.py
+++ b/src/cryptography/exceptions.py
@@ -18,6 +18,7 @@ class _Reasons(Enum):
     UNSUPPORTED_SERIALIZATION = 7
     UNSUPPORTED_X509 = 8
     UNSUPPORTED_EXCHANGE_ALGORITHM = 9
+    UNSUPPORTED_DIFFIE_HELLMAN = 10
 
 
 class UnsupportedAlgorithm(Exception):
diff --git a/src/cryptography/hazmat/backends/interfaces.py b/src/cryptography/hazmat/backends/interfaces.py
index e15a7ca4..c5f2951c 100644
--- a/src/cryptography/hazmat/backends/interfaces.py
+++ b/src/cryptography/hazmat/backends/interfaces.py
@@ -322,9 +322,10 @@ class X509Backend(object):
 @six.add_metaclass(abc.ABCMeta)
 class DHBackend(object):
     @abc.abstractmethod
-    def generate_dh_parameters(self, key_size):
+    def generate_dh_parameters(self, generator, key_size):
         """
         Generate a DHParameters instance with a modulus of key_size bits.
+        Using the given generator. Often 2 or 5.
         """
 
     @abc.abstractmethod
@@ -335,33 +336,28 @@ class DHBackend(object):
         """
 
     @abc.abstractmethod
-    def generate_dh_private_key_and_parameters(self, key_size):
+    def generate_dh_private_key_and_parameters(self, generator, key_size):
         """
         Generate a DHPrivateKey instance using key size only.
+        Using the given generator. Often 2 or 5.
         """
 
     @abc.abstractmethod
     def load_dh_private_numbers(self, numbers):
         """
-        Returns a DHPrivateKey provider.
+        Load a DHPrivateKey from DHPrivateNumbers
         """
 
     @abc.abstractmethod
     def load_dh_public_numbers(self, numbers):
         """
-        Returns a DHPublicKey provider.
+        Load a DHPublicKey from DHPublicNumbers.
         """
 
     @abc.abstractmethod
     def load_dh_parameter_numbers(self, numbers):
         """
-        Returns a DHParameters provider.
-        """
-
-    @abc.abstractmethod
-    def dh_exchange_algorithm_supported(self, exchange_algorithm):
-        """
-        Returns whether the exchange algorithm is supported by this backend.
+        Load DHParameters from DHParameterNumbers.
         """
 
     @abc.abstractmethod
diff --git a/src/cryptography/hazmat/backends/multibackend.py b/src/cryptography/hazmat/backends/multibackend.py
index bcd9c520..097b4908 100644
--- a/src/cryptography/hazmat/backends/multibackend.py
+++ b/src/cryptography/hazmat/backends/multibackend.py
@@ -7,9 +7,10 @@ from __future__ import absolute_import, division, print_function
 from cryptography import utils
 from cryptography.exceptions import UnsupportedAlgorithm, _Reasons
 from cryptography.hazmat.backends.interfaces import (
-    CMACBackend, CipherBackend, DERSerializationBackend, DSABackend,
-    EllipticCurveBackend, HMACBackend, HashBackend, PBKDF2HMACBackend,
-    PEMSerializationBackend, RSABackend, ScryptBackend, X509Backend
+    CMACBackend, CipherBackend, DERSerializationBackend, DHBackend,
+    DSABackend, EllipticCurveBackend, HMACBackend, HashBackend,
+    PBKDF2HMACBackend, PEMSerializationBackend, RSABackend, ScryptBackend,
+    X509Backend
 )
 
 
@@ -24,6 +25,7 @@ from cryptography.hazmat.backends.interfaces import (
 @utils.register_interface(EllipticCurveBackend)
 @utils.register_interface(PEMSerializationBackend)
 @utils.register_interface(X509Backend)
+@utils.register_interface(DHBackend)
 @utils.register_interface(ScryptBackend)
 class MultiBackend(object):
     name = "multibackend"
@@ -424,6 +426,70 @@ class MultiBackend(object):
             _Reasons.UNSUPPORTED_X509
         )
 
+    def generate_dh_parameters(self, generator, key_size):
+        for b in self._filtered_backends(DHBackend):
+            return b.generate_dh_parameters(generator, key_size)
+
+        raise UnsupportedAlgorithm(
+            "This backend does not support Diffie-Hellman",
+            _Reasons.UNSUPPORTED_DIFFIE_HELLMAN
+        )
+
+    def load_dh_parameter_numbers(self, numbers):
+        for b in self._filtered_backends(DHBackend):
+            return b.load_dh_parameter_numbers(numbers)
+
+        raise UnsupportedAlgorithm(
+            "This backend does not support Diffie-Hellman",
+            _Reasons.UNSUPPORTED_DIFFIE_HELLMAN
+        )
+
+    def generate_dh_private_key(self, parameters):
+        for b in self._filtered_backends(DHBackend):
+            return b.generate_dh_private_key(parameters)
+
+        raise UnsupportedAlgorithm(
+            "This backend does not support Diffie-Hellman",
+            _Reasons.UNSUPPORTED_DIFFIE_HELLMAN
+        )
+
+    def load_dh_private_numbers(self, numbers):
+        for b in self._filtered_backends(DHBackend):
+            return b.load_dh_private_numbers(numbers)
+
+        raise UnsupportedAlgorithm(
+            "This backend does not support Diffie-Hellman",
+            _Reasons.UNSUPPORTED_DIFFIE_HELLMAN
+        )
+
+    def load_dh_public_numbers(self, numbers):
+        for b in self._filtered_backends(DHBackend):
+            return b.load_dh_public_numbers(numbers)
+
+        raise UnsupportedAlgorithm(
+            "This backend does not support Diffie-Hellman",
+            _Reasons.UNSUPPORTED_DIFFIE_HELLMAN
+        )
+
+    def generate_dh_private_key_and_parameters(self, generator, key_size):
+        for b in self._filtered_backends(DHBackend):
+            return b.generate_dh_private_key_and_parameters(generator,
+                                                            key_size)
+
+        raise UnsupportedAlgorithm(
+            "This backend does not support Diffie-Hellman",
+            _Reasons.UNSUPPORTED_DIFFIE_HELLMAN
+        )
+
+    def dh_parameters_supported(self, p, g):
+        for b in self._filtered_backends(DHBackend):
+            return b.dh_parameters_supported(p, g)
+
+        raise UnsupportedAlgorithm(
+            "This backend does not support Diffie-Hellman",
+            _Reasons.UNSUPPORTED_DIFFIE_HELLMAN
+        )
+
     def x509_name_bytes(self, name):
         for b in self._filtered_backends(X509Backend):
             return b.x509_name_bytes(name)
diff --git a/src/cryptography/hazmat/backends/openssl/backend.py b/src/cryptography/hazmat/backends/openssl/backend.py
index 4a341fc2..9df113b6 100644
--- a/src/cryptography/hazmat/backends/openssl/backend.py
+++ b/src/cryptography/hazmat/backends/openssl/backend.py
@@ -16,7 +16,7 @@ import six
 from cryptography import utils, x509
 from cryptography.exceptions import UnsupportedAlgorithm, _Reasons
 from cryptography.hazmat.backends.interfaces import (
-    CMACBackend, CipherBackend, DERSerializationBackend, DSABackend,
+    CMACBackend, CipherBackend, DERSerializationBackend, DHBackend, DSABackend,
     EllipticCurveBackend, HMACBackend, HashBackend, PBKDF2HMACBackend,
     PEMSerializationBackend, RSABackend, ScryptBackend, X509Backend
 )
@@ -24,6 +24,9 @@ from cryptography.hazmat.backends.openssl.ciphers import (
     _AESCTRCipherContext, _CipherContext
 )
 from cryptography.hazmat.backends.openssl.cmac import _CMACContext
+from cryptography.hazmat.backends.openssl.dh import (
+    _DHParameters, _DHPrivateKey, _DHPublicKey
+)
 from cryptography.hazmat.backends.openssl.dsa import (
     _DSAParameters, _DSAPrivateKey, _DSAPublicKey
 )
@@ -107,6 +110,7 @@ def _pem_password_cb(buf, size, writing, userdata_handle):
 @utils.register_interface(CipherBackend)
 @utils.register_interface(CMACBackend)
 @utils.register_interface(DERSerializationBackend)
+@utils.register_interface(DHBackend)
 @utils.register_interface(DSABackend)
 @utils.register_interface(EllipticCurveBackend)
 @utils.register_interface(HashBackend)
@@ -329,6 +333,7 @@ class Backend(object):
 
     def _bn_to_int(self, bn):
         assert bn != self._ffi.NULL
+
         if six.PY3:
             # Python 3 has constant time from_bytes, so use that.
             bn_num_bytes = self._lib.BN_num_bytes(bn)
@@ -1734,6 +1739,117 @@ class Backend(object):
                 serialization._ssh_write_string(public_numbers.encode_point())
             )
 
+    def generate_dh_parameters(self, generator, key_size):
+        if key_size < 512:
+            raise ValueError("DH key_size must be at least 512 bits")
+
+        if generator not in (2, 5):
+            raise ValueError("DH generator must be 2 or 5")
+
+        dh_param_cdata = self._lib.DH_new()
+        self.openssl_assert(dh_param_cdata != self._ffi.NULL)
+        dh_param_cdata = self._ffi.gc(dh_param_cdata, self._lib.DH_free)
+
+        res = self._lib.DH_generate_parameters_ex(
+            dh_param_cdata,
+            key_size,
+            generator,
+            self._ffi.NULL
+        )
+        self.openssl_assert(res == 1)
+
+        return _DHParameters(self, dh_param_cdata)
+
+    def generate_dh_private_key(self, parameters):
+        dh_key_cdata = self._lib.DHparams_dup(parameters._dh_cdata)
+        self.openssl_assert(dh_key_cdata != self._ffi.NULL)
+        dh_key_cdata = self._ffi.gc(dh_key_cdata, self._lib.DH_free)
+
+        res = self._lib.DH_generate_key(dh_key_cdata)
+        self.openssl_assert(res == 1)
+
+        return _DHPrivateKey(self, dh_key_cdata)
+
+    def generate_dh_private_key_and_parameters(self, generator, key_size):
+        return self.generate_dh_private_key(
+            self.generate_dh_parameters(generator, key_size))
+
+    def load_dh_private_numbers(self, numbers):
+        parameter_numbers = numbers.public_numbers.parameter_numbers
+
+        dh_cdata = self._lib.DH_new()
+        self.openssl_assert(dh_cdata != self._ffi.NULL)
+        dh_cdata = self._ffi.gc(dh_cdata, self._lib.DH_free)
+
+        p = self._int_to_bn(parameter_numbers.p)
+        g = self._int_to_bn(parameter_numbers.g)
+        pub_key = self._int_to_bn(numbers.public_numbers.y)
+        priv_key = self._int_to_bn(numbers.x)
+
+        res = self._lib.DH_set0_pqg(dh_cdata, p, self._ffi.NULL, g)
+        self.openssl_assert(res == 1)
+
+        res = self._lib.DH_set0_key(dh_cdata, pub_key, priv_key)
+        self.openssl_assert(res == 1)
+
+        codes = self._ffi.new("int[]", 1)
+        res = self._lib.DH_check(dh_cdata, codes)
+        self.openssl_assert(res == 1)
+
+        if codes[0] != 0:
+            raise ValueError("DH private numbers did not pass safety checks.")
+
+        return _DHPrivateKey(self, dh_cdata)
+
+    def load_dh_public_numbers(self, numbers):
+        dh_cdata = self._lib.DH_new()
+        self.openssl_assert(dh_cdata != self._ffi.NULL)
+        dh_cdata = self._ffi.gc(dh_cdata, self._lib.DH_free)
+
+        parameter_numbers = numbers.parameter_numbers
+
+        p = self._int_to_bn(parameter_numbers.p)
+        g = self._int_to_bn(parameter_numbers.g)
+        pub_key = self._int_to_bn(numbers.y)
+
+        res = self._lib.DH_set0_pqg(dh_cdata, p, self._ffi.NULL, g)
+        self.openssl_assert(res == 1)
+
+        res = self._lib.DH_set0_key(dh_cdata, pub_key, self._ffi.NULL)
+        self.openssl_assert(res == 1)
+
+        return _DHPublicKey(self, dh_cdata)
+
+    def load_dh_parameter_numbers(self, numbers):
+        dh_cdata = self._lib.DH_new()
+        self.openssl_assert(dh_cdata != self._ffi.NULL)
+        dh_cdata = self._ffi.gc(dh_cdata, self._lib.DH_free)
+
+        p = self._int_to_bn(numbers.p)
+        g = self._int_to_bn(numbers.g)
+
+        res = self._lib.DH_set0_pqg(dh_cdata, p, self._ffi.NULL, g)
+        self.openssl_assert(res == 1)
+
+        return _DHParameters(self, dh_cdata)
+
+    def dh_parameters_supported(self, p, g):
+        dh_cdata = self._lib.DH_new()
+        self.openssl_assert(dh_cdata != self._ffi.NULL)
+        dh_cdata = self._ffi.gc(dh_cdata, self._lib.DH_free)
+
+        p = self._int_to_bn(p)
+        g = self._int_to_bn(g)
+
+        res = self._lib.DH_set0_pqg(dh_cdata, p, self._ffi.NULL, g)
+        self.openssl_assert(res == 1)
+
+        codes = self._ffi.new("int[]", 1)
+        res = self._lib.DH_check(dh_cdata, codes)
+        self.openssl_assert(res == 1)
+
+        return codes[0] == 0
+
     def x509_name_bytes(self, name):
         x509_name = _encode_name_gc(self, name)
         pp = self._ffi.new("unsigned char **")
diff --git a/src/cryptography/hazmat/backends/openssl/dh.py b/src/cryptography/hazmat/backends/openssl/dh.py
new file mode 100644
index 00000000..666429f2
--- /dev/null
+++ b/src/cryptography/hazmat/backends/openssl/dh.py
@@ -0,0 +1,182 @@
+# This file is dual licensed under the terms of the Apache License, Version
+# 2.0, and the BSD License. See the LICENSE file in the root of this repository
+# for complete details.
+
+from __future__ import absolute_import, division, print_function
+
+from cryptography import utils
+from cryptography.hazmat.primitives.asymmetric import dh
+
+
+def _dh_cdata_to_parameters(dh_cdata, backend):
+    lib = backend._lib
+    ffi = backend._ffi
+
+    param_cdata = lib.DHparams_dup(dh_cdata)
+    backend.openssl_assert(param_cdata != ffi.NULL)
+    param_cdata = ffi.gc(param_cdata, lib.DH_free)
+
+    return _DHParameters(backend, param_cdata)
+
+
+@utils.register_interface(dh.DHParametersWithSerialization)
+class _DHParameters(object):
+    def __init__(self, backend, dh_cdata):
+        self._backend = backend
+        self._dh_cdata = dh_cdata
+
+    def parameter_numbers(self):
+        p = self._backend._ffi.new("BIGNUM **")
+        g = self._backend._ffi.new("BIGNUM **")
+        self._backend._lib.DH_get0_pqg(self._dh_cdata,
+                                       p, self._backend._ffi.NULL, g)
+        self._backend.openssl_assert(p[0] != self._backend._ffi.NULL)
+        self._backend.openssl_assert(g[0] != self._backend._ffi.NULL)
+        return dh.DHParameterNumbers(
+            p=self._backend._bn_to_int(p[0]),
+            g=self._backend._bn_to_int(g[0])
+        )
+
+    def generate_private_key(self):
+        return self._backend.generate_dh_private_key(self)
+
+
+def _handle_dh_compute_key_error(errors, backend):
+    lib = backend._lib
+
+    backend.openssl_assert(errors[0][1:] == (
+        lib.ERR_LIB_DH,
+        lib.DH_F_COMPUTE_KEY,
+        lib.DH_R_INVALID_PUBKEY
+    ))
+
+    raise ValueError("Public key value is invalid for this exchange.")
+
+
+def _get_dh_num_bits(backend, dh_cdata):
+    p = backend._ffi.new("BIGNUM **")
+    backend._lib.DH_get0_pqg(dh_cdata, p,
+                             backend._ffi.NULL,
+                             backend._ffi.NULL)
+    backend.openssl_assert(p[0] != backend._ffi.NULL)
+    return backend._lib.BN_num_bits(p[0])
+
+
+@utils.register_interface(dh.DHPrivateKeyWithSerialization)
+class _DHPrivateKey(object):
+    def __init__(self, backend, dh_cdata):
+        self._backend = backend
+        self._dh_cdata = dh_cdata
+        self._key_size_bytes = self._backend._lib.DH_size(dh_cdata)
+
+    @property
+    def key_size(self):
+        return _get_dh_num_bits(self._backend, self._dh_cdata)
+
+    def private_numbers(self):
+        p = self._backend._ffi.new("BIGNUM **")
+        g = self._backend._ffi.new("BIGNUM **")
+        self._backend._lib.DH_get0_pqg(self._dh_cdata,
+                                       p, self._backend._ffi.NULL, g)
+        self._backend.openssl_assert(p[0] != self._backend._ffi.NULL)
+        self._backend.openssl_assert(g[0] != self._backend._ffi.NULL)
+        pub_key = self._backend._ffi.new("BIGNUM **")
+        priv_key = self._backend._ffi.new("BIGNUM **")
+        self._backend._lib.DH_get0_key(self._dh_cdata, pub_key, priv_key)
+        self._backend.openssl_assert(pub_key[0] != self._backend._ffi.NULL)
+        self._backend.openssl_assert(priv_key[0] != self._backend._ffi.NULL)
+        return dh.DHPrivateNumbers(
+            public_numbers=dh.DHPublicNumbers(
+                parameter_numbers=dh.DHParameterNumbers(
+                    p=self._backend._bn_to_int(p[0]),
+                    g=self._backend._bn_to_int(g[0])
+                ),
+                y=self._backend._bn_to_int(pub_key[0])
+            ),
+            x=self._backend._bn_to_int(priv_key[0])
+        )
+
+    def exchange(self, peer_public_key):
+
+        buf = self._backend._ffi.new("unsigned char[]", self._key_size_bytes)
+        pub_key = self._backend._ffi.new("BIGNUM **")
+        self._backend._lib.DH_get0_key(peer_public_key._dh_cdata, pub_key,
+                                       self._backend._ffi.NULL)
+        self._backend.openssl_assert(pub_key[0] != self._backend._ffi.NULL)
+        res = self._backend._lib.DH_compute_key(
+            buf,
+            pub_key[0],
+            self._dh_cdata
+        )
+
+        if res == -1:
+            errors = self._backend._consume_errors()
+            return _handle_dh_compute_key_error(errors, self._backend)
+        else:
+            self._backend.openssl_assert(res >= 1)
+
+            key = self._backend._ffi.buffer(buf)[:res]
+            pad = self._key_size_bytes - len(key)
+
+            if pad > 0:
+                key = (b"\x00" * pad) + key
+
+            return key
+
+    def public_key(self):
+        dh_cdata = self._backend._lib.DHparams_dup(self._dh_cdata)
+        self._backend.openssl_assert(dh_cdata != self._backend._ffi.NULL)
+        dh_cdata = self._backend._ffi.gc(
+            dh_cdata, self._backend._lib.DH_free
+        )
+
+        pub_key = self._backend._ffi.new("BIGNUM **")
+        self._backend._lib.DH_get0_key(self._dh_cdata,
+                                       pub_key, self._backend._ffi.NULL)
+        self._backend.openssl_assert(pub_key[0] != self._backend._ffi.NULL)
+        pub_key_dup = self._backend._lib.BN_dup(pub_key[0])
+        self._backend.openssl_assert(pub_key_dup != self._backend._ffi.NULL)
+
+        res = self._backend._lib.DH_set0_key(dh_cdata,
+                                             pub_key_dup,
+                                             self._backend._ffi.NULL)
+        self._backend.openssl_assert(res == 1)
+
+        return _DHPublicKey(self._backend, dh_cdata)
+
+    def parameters(self):
+        return _dh_cdata_to_parameters(self._dh_cdata, self._backend)
+
+
+@utils.register_interface(dh.DHPublicKeyWithSerialization)
+class _DHPublicKey(object):
+    def __init__(self, backend, dh_cdata):
+        self._backend = backend
+        self._dh_cdata = dh_cdata
+        self._key_size_bits = _get_dh_num_bits(self._backend, self._dh_cdata)
+
+    @property
+    def key_size(self):
+        return self._key_size_bits
+
+    def public_numbers(self):
+        p = self._backend._ffi.new("BIGNUM **")
+        g = self._backend._ffi.new("BIGNUM **")
+        self._backend._lib.DH_get0_pqg(self._dh_cdata,
+                                       p, self._backend._ffi.NULL, g)
+        self._backend.openssl_assert(p[0] != self._backend._ffi.NULL)
+        self._backend.openssl_assert(g[0] != self._backend._ffi.NULL)
+        pub_key = self._backend._ffi.new("BIGNUM **")
+        self._backend._lib.DH_get0_key(self._dh_cdata,
+                                       pub_key, self._backend._ffi.NULL)
+        self._backend.openssl_assert(pub_key[0] != self._backend._ffi.NULL)
+        return dh.DHPublicNumbers(
+            parameter_numbers=dh.DHParameterNumbers(
+                p=self._backend._bn_to_int(p[0]),
+                g=self._backend._bn_to_int(g[0])
+            ),
+            y=self._backend._bn_to_int(pub_key[0])
+        )
+
+    def parameters(self):
+        return _dh_cdata_to_parameters(self._dh_cdata, self._backend)
diff --git a/src/cryptography/hazmat/primitives/asymmetric/dh.py b/src/cryptography/hazmat/primitives/asymmetric/dh.py
index 12d53eed..ec044ddd 100644
--- a/src/cryptography/hazmat/primitives/asymmetric/dh.py
+++ b/src/cryptography/hazmat/primitives/asymmetric/dh.py
@@ -11,6 +11,10 @@ import six
 from cryptography import utils
 
 
+def generate_parameters(generator, key_size, backend):
+    return backend.generate_dh_parameters(generator, key_size)
+
+
 class DHPrivateNumbers(object):
     def __init__(self, x, public_numbers):
         if not isinstance(x, six.integer_types):
@@ -35,6 +39,9 @@ class DHPrivateNumbers(object):
     def __ne__(self, other):
         return not self == other
 
+    def private_key(self, backend):
+        return backend.load_dh_private_numbers(self)
+
     public_numbers = utils.read_only_property("_public_numbers")
     x = utils.read_only_property("_x")
 
@@ -63,6 +70,9 @@ class DHPublicNumbers(object):
     def __ne__(self, other):
         return not self == other
 
+    def public_key(self, backend):
+        return backend.load_dh_public_numbers(self)
+
     y = utils.read_only_property("_y")
     parameter_numbers = utils.read_only_property("_parameter_numbers")
 
@@ -75,6 +85,9 @@ class DHParameterNumbers(object):
         ):
             raise TypeError("p and g must be integers")
 
+        if g not in (2, 5):
+            raise ValueError("DH generator must be 2 or 5")
+
         self._p = p
         self._g = g
 
@@ -90,6 +103,9 @@ class DHParameterNumbers(object):
     def __ne__(self, other):
         return not self == other
 
+    def parameters(self, backend):
+        return backend.load_dh_parameter_numbers(self)
+
     p = utils.read_only_property("_p")
     g = utils.read_only_property("_g")
 
@@ -141,6 +157,13 @@ class DHPrivateKeyWithSerialization(DHPrivateKey):
         Returns a DHPrivateNumbers.
         """
 
+    @abc.abstractmethod
+    def exchange(self, peer_public_key):
+        """
+        Given peer's DHPublicKey, carry out the key exchange and
+        return shared key as bytes.
+        """
+
 
 @six.add_metaclass(abc.ABCMeta)
 class DHPublicKey(object):