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.. hazmat::

Diffie-Hellman key exchange
===========================

.. currentmodule:: cryptography.hazmat.primitives.asymmetric.dh

`Diffie-Hellman key exchange`_ (D–H) is a method that allows two parties
to jointly agree on a shared secret using an insecure channel.

Exchange Algorithm
~~~~~~~~~~~~~~~~~~

For most applications the ``shared_key`` should be passed to a key
derivation function.

.. code-block:: pycon

>>> from cryptography.hazmat.backends import default_backend
    >>> from cryptography.hazmat.primitives.asymmetric import dh
    >>> parameters = dh.generate_parameters(generator=2, key_size=2048,
    ...                                     backend=default_backend())
    >>> private_key = parameters.generate_private_key()
    >>> peer_public_key = parameters.generate_private_key().public_key()
    >>> shared_key = private_key.exchange(peer_public_key)

DHE (or EDH), the ephemeral form of this exchange, is **strongly
preferred** over simple DH and provides `forward secrecy`_ when used.
You must generate a new private key using :func:`~DHParameters.generate_private_key` for
each :meth:`~DHPrivateKeyWithSerialization.exchange` when performing an DHE key
exchange.

To assemble a :class:`~DHParameters` and a :class:`~DHPublicKey` from
primitive integers, you must first create the
:class:`~DHParameterNumbers` and :class:`~DHPublicNumbers` objects. For
example if **p**, **g**, and **y** are :class:`int` objects received from a
peer::

pn = dh.DHParameterNumbers(p, g)
    parameters = pn.parameters(default_backend())
    peer_public_numbers = dh.DHPublicNumbers(y, pn)
    peer_public_key = peer_public_numbers.public_key(default_backend())

See also the :class:`~cryptography.hazmat.backends.interfaces.DHBackend`
API for additional functionality.

Group parameters
~~~~~~~~~~~~~~~~

.. function:: generate_parameters(generator, key_size, backend)

.. versionadded:: 0.9

Generate a new DH parameter group for use with ``backend``.

:param generator: The :class:`int` to use as a generator. Must be
        2 or 5.

:param key_size: The bit length of the prime modulus to generate.

:param backend: A
        :class:`~cryptography.hazmat.backends.interfaces.DHBackend`
        instance.

:returns: DH parameters as a new instance of
        :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHParameters`.

:raises ValueError: If ``key_size`` is not at least 512.

.. class:: DHParameters

.. versionadded:: 0.9

.. method:: generate_private_key()

.. versionadded:: 0.9

Generate a DH private key. This method can be used to generate many
        new private keys from a single set of parameters.

:return: An instance of
            :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHPrivateKey`.

.. class:: DHParametersWithSerialization

.. versionadded:: 0.9

Inherits from :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHParameters`.

.. method:: parameter_numbers()

Return the numbers that make up this set of parameters.

:return: A :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHParameterNumbers`.

Key interfaces
~~~~~~~~~~~~~~

.. class:: DHPrivateKey

.. versionadded:: 0.9

.. attribute:: key_size

The bit length of the prime modulus.

.. method:: public_key()

Return the public key associated with this private key.

:return: A :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHPublicKey`.

.. method:: parameters()

Return the parameters associated with this private key.

:return: A :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHParameters`.

.. class:: DHPrivateKeyWithSerialization

.. versionadded:: 0.9

Inherits from :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHPrivateKey`.

.. method:: private_numbers()

Return the numbers that make up this private key.

:return: A :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHPrivateNumbers`.

.. method:: exchange(peer_public_key)

.. versionadded:: 1.7

:param DHPublicKeyWithSerialization peer_public_key: The public key for the
            peer.

:return bytes: The agreed key. The bytes are ordered in 'big' endian.

.. class:: DHPublicKey

.. versionadded:: 0.9

.. attribute:: key_size

The bit length of the prime modulus.

.. method:: parameters()

Return the parameters associated with this private key.

:return: A :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHParameters`.

.. class:: DHPublicKeyWithSerialization

.. versionadded:: 0.9

Inherits from :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHPublicKey`.

.. method:: public_numbers()

Return the numbers that make up this public key.

:return: A :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHPublicNumbers`.

Numbers
~~~~~~~

.. class:: DHParameterNumbers(p, g)

.. versionadded:: 0.8

The collection of integers that define a Diffie-Hellman group.

.. attribute:: p

:type: int

The prime modulus value.

.. attribute:: g

:type: int

The generator value. Must be 2 or 5.

.. class:: DHPrivateNumbers(x, public_numbers)

.. versionadded:: 0.8

The collection of integers that make up a Diffie-Hellman private key.

.. attribute:: public_numbers

:type: :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHPublicNumbers`

The :class:`DHPublicNumbers` which makes up the DH public
        key associated with this DH private key.

.. attribute:: x

:type: int

The private value.

.. class:: DHPublicNumbers(y, parameter_numbers)

.. versionadded:: 0.8

The collection of integers that make up a Diffie-Hellman public key.

.. attribute:: parameter_numbers

:type: :class:`~cryptography.hazmat.primitives.asymmetric.dh.DHParameterNumbers`

The parameters for this DH group.

.. attribute:: y

:type: int

The public value.

.. _`Diffie-Hellman key exchange`: https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange
.. _`forward secrecy`: https://en.wikipedia.org/wiki/Forward_secrecy