diff --git a/docs/hazmat/primitives/key-derivation-functions.rst b/docs/hazmat/primitives/key-derivation-functions.rst
index 78d4031..7def2a2 100644
--- a/docs/hazmat/primitives/key-derivation-functions.rst
+++ b/docs/hazmat/primitives/key-derivation-functions.rst
@@ -324,6 +324,192 @@
         ``key_material`` generates the same key as the ``expected_key``, and
         raises an exception if they do not match.
 
+.. currentmodule:: cryptography.hazmat.primitives.kdf.concatkdf
+
+.. class:: ConcatKDFHash(algorithm, length, otherinfo, backend)
+
+    .. versionadded:: 1.0
+
+    ConcatKDFHash (Concatenation Key Derivation Function) is defined by the
+    NIST Special Publication `NIST SP 800-56Ar2`_ document, to be used to
+    derive keys for use after a Key Exchange negotiation operation.
+
+    .. warning::
+
+        ConcatKDFHash should not be used for password storage.
+
+    .. doctest::
+
+        >>> import os
+        >>> from cryptography.hazmat.primitives import hashes
+        >>> from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHash
+        >>> from cryptography.hazmat.backends import default_backend
+        >>> backend = default_backend()
+        >>> salt = os.urandom(16)
+        >>> otherinfo = b"concatkdf-example"
+        >>> ckdf = ConcatKDFHash(
+        ...     algorithm=hashes.SHA256(),
+        ...     length=256,
+        ...     otherinfo=otherinfo,
+        ...     backend=backend
+        ... )
+        >>> key = ckdf.derive(b"input key")
+        >>> ckdf = ConcatKDFHash(
+        ...     algorithm=hashes.SHA256(),
+        ...     length=256,
+        ...     otherinfo=otherinfo,
+        ...     backend=backend
+        ... )
+        >>> ckdf.verify(b"input key", key)
+
+    :param algorithm: An instance of a
+        :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm`
+        provider
+
+    :param int length: The desired length of the derived key in bytes.
+        Maximum is ``hashlen * (2^32 -1)``.
+
+    :param bytes otherinfo: Application specific context information.
+        If ``None`` is explicitly passed an empty byte string will be used.
+
+    :param backend: A
+        :class:`~cryptography.hazmat.backends.interfaces.HashBackend`
+        provider.
+
+    :raises cryptography.exceptions.UnsupportedAlgorithm: This is raised
+        if the provided ``backend`` does not implement
+        :class:`~cryptography.hazmat.backends.interfaces.HashBackend`
+
+    :raises TypeError: This exception is raised if ``otherinfo`` is not
+        ``bytes``.
+
+    .. method:: derive(key_material)
+
+        :param bytes key_material: The input key material.
+        :return bytes: The derived key.
+        :raises TypeError: This exception is raised if ``key_material`` is
+                            not ``bytes``.
+
+        Derives a new key from the input key material by performing both the
+        extract and expand operations.
+
+    .. method:: verify(key_material, expected_key)
+
+        :param bytes key_material: The input key material. This is the same as
+                                   ``key_material`` in :meth:`derive`.
+        :param bytes expected_key: The expected result of deriving a new key,
+                                   this is the same as the return value of
+                                   :meth:`derive`.
+        :raises cryptography.exceptions.InvalidKey: This is raised when the
+                                                    derived key does not match
+                                                    the expected key.
+        :raises cryptography.exceptions.AlreadyFinalized: This is raised when
+                                                          :meth:`derive` or
+                                                          :meth:`verify` is
+                                                          called more than
+                                                          once.
+
+        This checks whether deriving a new key from the supplied
+        ``key_material`` generates the same key as the ``expected_key``, and
+        raises an exception if they do not match.
+
+
+.. class:: ConcatKDFHMAC(algorithm, length, salt, otherinfo, backend)
+
+    .. versionadded:: 1.0
+
+    Similar to ConcatKFDHash but uses an HMAC function instead.
+
+    .. warning::
+
+        ConcatKDFHMAC should not be used for password storage.
+
+    .. doctest::
+
+        >>> import os
+        >>> from cryptography.hazmat.primitives import hashes
+        >>> from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHMAC
+        >>> from cryptography.hazmat.backends import default_backend
+        >>> backend = default_backend()
+        >>> salt = os.urandom(16)
+        >>> otherinfo = b"concatkdf-example"
+        >>> ckdf = ConcatKDFHMAC(
+        ...     algorithm=hashes.SHA256(),
+        ...     length=256,
+        ...     salt=salt,
+        ...     otherinfo=otherinfo,
+        ...     backend=backend
+        ... )
+        >>> key = ckdf.derive(b"input key")
+        >>> ckdf = ConcatKDFHMAC(
+        ...     algorithm=hashes.SHA256(),
+        ...     length=256,
+        ...     salt=salt,
+        ...     otherinfo=otherinfo,
+        ...     backend=backend
+        ... )
+        >>> ckdf.verify(b"input key", key)
+
+    :param algorithm: An instance of a
+        :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm`
+        provider
+
+    :param int length: The desired length of the derived key in bytes. Maximum
+        is ``hashlen * (2^32 -1)``.
+
+    :param bytes salt: A salt. Randomizes the KDF's output. Optional, but
+        highly recommended. Ideally as many bits of entropy as the security
+        level of the hash: often that means cryptographically random and as
+        long as the hash output. Does not have to be secret, but may cause
+        stronger security guarantees if secret; If ``None`` is explicitly
+        passed a default salt of ``algorithm.block_size`` null bytes will be
+        used.
+
+    :param bytes otherinfo: Application specific context information.
+        If ``None`` is explicitly passed an empty byte string will be used.
+
+    :param backend: A
+        :class:`~cryptography.hazmat.backends.interfaces.HMACBackend`
+        provider.
+
+    :raises cryptography.exceptions.UnsupportedAlgorithm: This is raised if the
+        provided ``backend`` does not implement
+        :class:`~cryptography.hazmat.backends.interfaces.HMACBackend`
+
+    :raises TypeError: This exception is raised if ``salt`` or ``otherinfo``
+        is not ``bytes``.
+
+    .. method:: derive(key_material)
+
+        :param bytes key_material: The input key material.
+        :return bytes: The derived key.
+        :raises TypeError: This exception is raised if ``key_material`` is not
+                           ``bytes``.
+
+        Derives a new key from the input key material by performing both the
+        extract and expand operations.
+
+    .. method:: verify(key_material, expected_key)
+
+        :param bytes key_material: The input key material. This is the same as
+                                   ``key_material`` in :meth:`derive`.
+        :param bytes expected_key: The expected result of deriving a new key,
+                                   this is the same as the return value of
+                                   :meth:`derive`.
+        :raises cryptography.exceptions.InvalidKey: This is raised when the
+                                                    derived key does not match
+                                                    the expected key.
+        :raises cryptography.exceptions.AlreadyFinalized: This is raised when
+                                                          :meth:`derive` or
+                                                          :meth:`verify` is
+                                                          called more than
+                                                          once.
+
+        This checks whether deriving a new key from the supplied
+        ``key_material`` generates the same key as the ``expected_key``, and
+        raises an exception if they do not match.
+
+
 Interface
 ~~~~~~~~~
 
@@ -372,6 +558,7 @@
 
 
 .. _`NIST SP 800-132`: http://csrc.nist.gov/publications/nistpubs/800-132/nist-sp800-132.pdf
+.. _`NIST SP 800-56Ar2`: http://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Ar2.pdf
 .. _`Password Storage Cheat Sheet`: https://www.owasp.org/index.php/Password_Storage_Cheat_Sheet
 .. _`PBKDF2`: https://en.wikipedia.org/wiki/PBKDF2
 .. _`scrypt`: https://en.wikipedia.org/wiki/Scrypt
diff --git a/src/cryptography/hazmat/primitives/kdf/concatkdf.py b/src/cryptography/hazmat/primitives/kdf/concatkdf.py
new file mode 100644
index 0000000..c6399e4
--- /dev/null
+++ b/src/cryptography/hazmat/primitives/kdf/concatkdf.py
@@ -0,0 +1,125 @@
+# 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
+
+import struct
+
+from cryptography import utils
+from cryptography.exceptions import (
+    AlreadyFinalized, InvalidKey, UnsupportedAlgorithm, _Reasons
+)
+from cryptography.hazmat.backends.interfaces import HMACBackend
+from cryptography.hazmat.backends.interfaces import HashBackend
+from cryptography.hazmat.primitives import constant_time, hashes, hmac
+from cryptography.hazmat.primitives.kdf import KeyDerivationFunction
+
+
+def _int_to_u32be(n):
+    return struct.pack('>I', n)
+
+
+def _common_args_checks(algorithm, length, otherinfo):
+    max_length = algorithm.digest_size * (2 ** 32 - 1)
+    if length > max_length:
+        raise ValueError(
+            "Can not derive keys larger than {0} bits.".format(
+                max_length
+            ))
+    if not (otherinfo is None or isinstance(otherinfo, bytes)):
+        raise TypeError("otherinfo must be bytes.")
+
+
+def _concatkdf_derive(key_material, length, auxfn, otherinfo):
+    if not isinstance(key_material, bytes):
+        raise TypeError("key_material must be bytes.")
+
+    output = [b""]
+    outlen = 0
+    counter = 1
+
+    while (length > outlen):
+        h = auxfn()
+        h.update(_int_to_u32be(counter))
+        h.update(key_material)
+        h.update(otherinfo)
+        output.append(h.finalize())
+        outlen += len(output[-1])
+        counter += 1
+
+    return b"".join(output)[:length]
+
+
+@utils.register_interface(KeyDerivationFunction)
+class ConcatKDFHash(object):
+    def __init__(self, algorithm, length, otherinfo, backend):
+
+        _common_args_checks(algorithm, length, otherinfo)
+        self._algorithm = algorithm
+        self._length = length
+        self._otherinfo = otherinfo
+        if self._otherinfo is None:
+            self._otherinfo = b""
+
+        if not isinstance(backend, HashBackend):
+            raise UnsupportedAlgorithm(
+                "Backend object does not implement HashBackend.",
+                _Reasons.BACKEND_MISSING_INTERFACE
+            )
+        self._backend = backend
+        self._used = False
+
+    def _hash(self):
+        return hashes.Hash(self._algorithm, self._backend)
+
+    def derive(self, key_material):
+        if self._used:
+            raise AlreadyFinalized
+        self._used = True
+        return _concatkdf_derive(key_material, self._length,
+                                 self._hash, self._otherinfo)
+
+    def verify(self, key_material, expected_key):
+        if not constant_time.bytes_eq(self.derive(key_material), expected_key):
+            raise InvalidKey
+
+
+@utils.register_interface(KeyDerivationFunction)
+class ConcatKDFHMAC(object):
+    def __init__(self, algorithm, length, salt, otherinfo, backend):
+
+        _common_args_checks(algorithm, length, otherinfo)
+        self._algorithm = algorithm
+        self._length = length
+        self._otherinfo = otherinfo
+        if self._otherinfo is None:
+            self._otherinfo = b""
+
+        if not (salt is None or isinstance(salt, bytes)):
+            raise TypeError("salt must be bytes.")
+        if salt is None:
+            salt = b"\x00" * algorithm.block_size
+        self._salt = salt
+
+        if not isinstance(backend, HMACBackend):
+            raise UnsupportedAlgorithm(
+                "Backend object does not implement HMACBackend.",
+                _Reasons.BACKEND_MISSING_INTERFACE
+            )
+        self._backend = backend
+        self._used = False
+
+    def _hmac(self):
+        return hmac.HMAC(self._salt, self._algorithm, self._backend)
+
+    def derive(self, key_material):
+        if self._used:
+            raise AlreadyFinalized
+        self._used = True
+        return _concatkdf_derive(key_material, self._length,
+                                 self._hmac, self._otherinfo)
+
+    def verify(self, key_material, expected_key):
+        if not constant_time.bytes_eq(self.derive(key_material), expected_key):
+            raise InvalidKey
diff --git a/tests/hazmat/primitives/test_concatkdf.py b/tests/hazmat/primitives/test_concatkdf.py
new file mode 100644
index 0000000..27e5460
--- /dev/null
+++ b/tests/hazmat/primitives/test_concatkdf.py
@@ -0,0 +1,251 @@
+# 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
+
+import binascii
+
+import pytest
+
+from cryptography.exceptions import (
+    AlreadyFinalized, InvalidKey, _Reasons
+)
+from cryptography.hazmat.backends.interfaces import HMACBackend
+from cryptography.hazmat.backends.interfaces import HashBackend
+from cryptography.hazmat.primitives import hashes
+from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHMAC
+from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHash
+
+from ...utils import raises_unsupported_algorithm
+
+
+@pytest.mark.requires_backend_interface(interface=HashBackend)
+class TestConcatKDFHash(object):
+    def test_length_limit(self, backend):
+        big_length = hashes.SHA256().digest_size * (2 ** 32 - 1) + 1
+
+        with pytest.raises(ValueError):
+            ConcatKDFHash(hashes.SHA256(), big_length, None, backend)
+
+    def test_already_finalized(self, backend):
+        ckdf = ConcatKDFHash(hashes.SHA256(), 16, None, backend)
+
+        ckdf.derive(b"\x01" * 16)
+
+        with pytest.raises(AlreadyFinalized):
+            ckdf.derive(b"\x02" * 16)
+
+    def test_derive(self, backend):
+        prk = binascii.unhexlify(
+            b"52169af5c485dcc2321eb8d26d5efa21fb9b93c98e38412ee2484cf14f0d0d23"
+        )
+
+        okm = binascii.unhexlify(b"1c3bc9e7c4547c5191c0d478cccaed55")
+
+        oinfo = binascii.unhexlify(
+            b"a1b2c3d4e53728157e634612c12d6d5223e204aeea4341565369647bd184bcd2"
+            b"46f72971f292badaa2fe4124612cba"
+        )
+
+        ckdf = ConcatKDFHash(hashes.SHA256(), 16, oinfo, backend)
+
+        assert ckdf.derive(prk) == okm
+
+    def test_verify(self, backend):
+        prk = binascii.unhexlify(
+            b"52169af5c485dcc2321eb8d26d5efa21fb9b93c98e38412ee2484cf14f0d0d23"
+        )
+
+        okm = binascii.unhexlify(b"1c3bc9e7c4547c5191c0d478cccaed55")
+
+        oinfo = binascii.unhexlify(
+            b"a1b2c3d4e53728157e634612c12d6d5223e204aeea4341565369647bd184bcd2"
+            b"46f72971f292badaa2fe4124612cba"
+        )
+
+        ckdf = ConcatKDFHash(hashes.SHA256(), 16, oinfo, backend)
+
+        assert ckdf.verify(prk, okm) is None
+
+    def test_invalid_verify(self, backend):
+        prk = binascii.unhexlify(
+            b"52169af5c485dcc2321eb8d26d5efa21fb9b93c98e38412ee2484cf14f0d0d23"
+        )
+
+        oinfo = binascii.unhexlify(
+            b"a1b2c3d4e53728157e634612c12d6d5223e204aeea4341565369647bd184bcd2"
+            b"46f72971f292badaa2fe4124612cba"
+        )
+
+        ckdf = ConcatKDFHash(hashes.SHA256(), 16, oinfo, backend)
+
+        with pytest.raises(InvalidKey):
+            ckdf.verify(prk, b"wrong key")
+
+    def test_unicode_typeerror(self, backend):
+        with pytest.raises(TypeError):
+            ConcatKDFHash(
+                hashes.SHA256(),
+                16,
+                otherinfo=u"foo",
+                backend=backend
+            )
+
+        with pytest.raises(TypeError):
+            ckdf = ConcatKDFHash(
+                hashes.SHA256(),
+                16,
+                otherinfo=None,
+                backend=backend
+            )
+
+            ckdf.derive(u"foo")
+
+        with pytest.raises(TypeError):
+            ckdf = ConcatKDFHash(
+                hashes.SHA256(),
+                16,
+                otherinfo=None,
+                backend=backend
+            )
+
+            ckdf.verify(u"foo", b"bar")
+
+        with pytest.raises(TypeError):
+            ckdf = ConcatKDFHash(
+                hashes.SHA256(),
+                16,
+                otherinfo=None,
+                backend=backend
+            )
+
+            ckdf.verify(b"foo", u"bar")
+
+
+@pytest.mark.requires_backend_interface(interface=HMACBackend)
+class TestConcatKDFHMAC(object):
+    def test_length_limit(self, backend):
+        big_length = hashes.SHA256().digest_size * (2 ** 32 - 1) + 1
+
+        with pytest.raises(ValueError):
+            ConcatKDFHMAC(hashes.SHA256(), big_length, None, None, backend)
+
+    def test_already_finalized(self, backend):
+        ckdf = ConcatKDFHMAC(hashes.SHA256(), 16, None, None, backend)
+
+        ckdf.derive(b"\x01" * 16)
+
+        with pytest.raises(AlreadyFinalized):
+            ckdf.derive(b"\x02" * 16)
+
+    def test_derive(self, backend):
+        prk = binascii.unhexlify(
+            b"013951627c1dea63ea2d7702dd24e963eef5faac6b4af7e4"
+            b"b831cde499dff1ce45f6179f741c728aa733583b02409208"
+            b"8f0af7fce1d045edbc5790931e8d5ca79c73"
+        )
+
+        okm = binascii.unhexlify(b"64ce901db10d558661f10b6836a122a7"
+                                 b"605323ce2f39bf27eaaac8b34cf89f2f")
+
+        oinfo = binascii.unhexlify(
+            b"a1b2c3d4e55e600be5f367e0e8a465f4bf2704db00c9325c"
+            b"9fbd216d12b49160b2ae5157650f43415653696421e68e"
+        )
+
+        ckdf = ConcatKDFHMAC(hashes.SHA512(), 32, None, oinfo, backend)
+
+        assert ckdf.derive(prk) == okm
+
+    def test_verify(self, backend):
+        prk = binascii.unhexlify(
+            b"013951627c1dea63ea2d7702dd24e963eef5faac6b4af7e4"
+            b"b831cde499dff1ce45f6179f741c728aa733583b02409208"
+            b"8f0af7fce1d045edbc5790931e8d5ca79c73"
+        )
+
+        okm = binascii.unhexlify(b"64ce901db10d558661f10b6836a122a7"
+                                 b"605323ce2f39bf27eaaac8b34cf89f2f")
+
+        oinfo = binascii.unhexlify(
+            b"a1b2c3d4e55e600be5f367e0e8a465f4bf2704db00c9325c"
+            b"9fbd216d12b49160b2ae5157650f43415653696421e68e"
+        )
+
+        ckdf = ConcatKDFHMAC(hashes.SHA512(), 32, None, oinfo, backend)
+
+        assert ckdf.verify(prk, okm) is None
+
+    def test_invalid_verify(self, backend):
+        prk = binascii.unhexlify(
+            b"013951627c1dea63ea2d7702dd24e963eef5faac6b4af7e4"
+            b"b831cde499dff1ce45f6179f741c728aa733583b02409208"
+            b"8f0af7fce1d045edbc5790931e8d5ca79c73"
+        )
+
+        oinfo = binascii.unhexlify(
+            b"a1b2c3d4e55e600be5f367e0e8a465f4bf2704db00c9325c"
+            b"9fbd216d12b49160b2ae5157650f43415653696421e68e"
+        )
+
+        ckdf = ConcatKDFHMAC(hashes.SHA512(), 32, None, oinfo, backend)
+
+        with pytest.raises(InvalidKey):
+            ckdf.verify(prk, b"wrong key")
+
+    def test_unicode_typeerror(self, backend):
+        with pytest.raises(TypeError):
+            ConcatKDFHMAC(
+                hashes.SHA256(),
+                16, salt=u"foo",
+                otherinfo=None,
+                backend=backend
+            )
+
+        with pytest.raises(TypeError):
+            ConcatKDFHMAC(
+                hashes.SHA256(),
+                16, salt=None,
+                otherinfo=u"foo",
+                backend=backend
+            )
+
+        with pytest.raises(TypeError):
+            ckdf = ConcatKDFHMAC(
+                hashes.SHA256(),
+                16, salt=None,
+                otherinfo=None,
+                backend=backend
+            )
+
+            ckdf.derive(u"foo")
+
+        with pytest.raises(TypeError):
+            ckdf = ConcatKDFHMAC(
+                hashes.SHA256(),
+                16, salt=None,
+                otherinfo=None,
+                backend=backend
+            )
+
+            ckdf.verify(u"foo", b"bar")
+
+        with pytest.raises(TypeError):
+            ckdf = ConcatKDFHMAC(
+                hashes.SHA256(),
+                16, salt=None,
+                otherinfo=None,
+                backend=backend
+            )
+
+            ckdf.verify(b"foo", u"bar")
+
+
+def test_invalid_backend():
+    pretend_backend = object()
+
+    with raises_unsupported_algorithm(_Reasons.BACKEND_MISSING_INTERFACE):
+        ConcatKDFHash(hashes.SHA256(), 16, None, pretend_backend)
+    with raises_unsupported_algorithm(_Reasons.BACKEND_MISSING_INTERFACE):
+        ConcatKDFHMAC(hashes.SHA256(), 16, None, None, pretend_backend)