Merge pull request #1371 from reaperhulk/advance-rsa-deprecation-cycle

Advance RSA deprecation cycle

7 files changed, 80 insertions, 1101 deletions

diff --git a/cryptography/hazmat/backends/interfaces.py b/cryptography/hazmat/backends/interfaces.py
index f471b948..00bcc443 100644
--- a/cryptography/hazmat/backends/interfaces.py
+++ b/cryptography/hazmat/backends/interfaces.py
@@ -112,39 +112,6 @@ class RSABackend(object):
         """
 
     @abc.abstractmethod
-    def create_rsa_signature_ctx(self, private_key, padding, algorithm):
-        """
-        Returns an object conforming to the AsymmetricSignatureContext
-        interface.
-        """
-
-    @abc.abstractmethod
-    def create_rsa_verification_ctx(self, public_key, signature, padding,
-                                    algorithm):
-        """
-        Returns an object conforming to the AsymmetricVerificationContext
-        interface.
-        """
-
-    @abc.abstractmethod
-    def mgf1_hash_supported(self, algorithm):
-        """
-        Return True if the hash algorithm is supported for MGF1 in PSS.
-        """
-
-    @abc.abstractmethod
-    def decrypt_rsa(self, private_key, ciphertext, padding):
-        """
-        Returns decrypted bytes.
-        """
-
-    @abc.abstractmethod
-    def encrypt_rsa(self, public_key, plaintext, padding):
-        """
-        Returns encrypted bytes.
-        """
-
-    @abc.abstractmethod
     def rsa_padding_supported(self, padding):
         """
         Returns True if the backend supports the given padding options.
diff --git a/cryptography/hazmat/backends/openssl/backend.py b/cryptography/hazmat/backends/openssl/backend.py
index 9a36674a..a0a7ac18 100644
--- a/cryptography/hazmat/backends/openssl/backend.py
+++ b/cryptography/hazmat/backends/openssl/backend.py
@@ -44,8 +44,7 @@ from cryptography.hazmat.backends.openssl.ec import (
 from cryptography.hazmat.backends.openssl.hashes import _HashContext
 from cryptography.hazmat.backends.openssl.hmac import _HMACContext
 from cryptography.hazmat.backends.openssl.rsa import (
-    _RSAPrivateKey, _RSAPublicKey, _RSASignatureContext,
-    _RSAVerificationContext
+    _RSAPrivateKey, _RSAPublicKey
 )
 from cryptography.hazmat.bindings.openssl.binding import Binding
 from cryptography.hazmat.primitives import hashes
@@ -551,69 +550,6 @@ class Backend(object):
             pem_password_cb
         )
 
-    def _rsa_cdata_from_private_key(self, private_key):
-        ctx = self._lib.RSA_new()
-        assert ctx != self._ffi.NULL
-        ctx = self._ffi.gc(ctx, self._lib.RSA_free)
-
-        ctx.p = self._int_to_bn(private_key.p)
-        ctx.q = self._int_to_bn(private_key.q)
-        ctx.d = self._int_to_bn(private_key.d)
-        ctx.e = self._int_to_bn(private_key.e)
-        ctx.n = self._int_to_bn(private_key.n)
-        ctx.dmp1 = self._int_to_bn(private_key.dmp1)
-        ctx.dmq1 = self._int_to_bn(private_key.dmq1)
-        ctx.iqmp = self._int_to_bn(private_key.iqmp)
-        res = self._lib.RSA_blinding_on(ctx, self._ffi.NULL)
-        assert res == 1
-
-        return ctx
-
-    def _rsa_cdata_from_public_key(self, public_key):
-        ctx = self._lib.RSA_new()
-        assert ctx != self._ffi.NULL
-        ctx = self._ffi.gc(ctx, self._lib.RSA_free)
-
-        ctx.e = self._int_to_bn(public_key.e)
-        ctx.n = self._int_to_bn(public_key.n)
-        res = self._lib.RSA_blinding_on(ctx, self._ffi.NULL)
-        assert res == 1
-
-        return ctx
-
-    def create_rsa_signature_ctx(self, private_key, padding, algorithm):
-        warnings.warn(
-            "create_rsa_signature_ctx is deprecated and will be removed in a "
-            "future version.",
-            utils.DeprecatedIn05,
-            stacklevel=2
-        )
-        rsa_cdata = self._rsa_cdata_from_private_key(private_key)
-        key = _RSAPrivateKey(self, rsa_cdata)
-        return _RSASignatureContext(self, key, padding, algorithm)
-
-    def create_rsa_verification_ctx(self, public_key, signature, padding,
-                                    algorithm):
-        warnings.warn(
-            "create_rsa_verification_ctx is deprecated and will be removed in "
-            "a future version.",
-            utils.DeprecatedIn05,
-            stacklevel=2
-        )
-        rsa_cdata = self._rsa_cdata_from_public_key(public_key)
-        key = _RSAPublicKey(self, rsa_cdata)
-        return _RSAVerificationContext(self, key, signature, padding,
-                                       algorithm)
-
-    def mgf1_hash_supported(self, algorithm):
-        warnings.warn(
-            "mgf1_hash_supported is deprecated and will be removed in "
-            "a future version.",
-            utils.DeprecatedIn05,
-            stacklevel=2
-        )
-        return self._mgf1_hash_supported(algorithm)
-
     def _mgf1_hash_supported(self, algorithm):
         if self._lib.Cryptography_HAS_MGF1_MD:
             return self.hash_supported(algorithm)
@@ -774,28 +710,6 @@ class Backend(object):
         else:
             return True
 
-    def decrypt_rsa(self, private_key, ciphertext, padding):
-        warnings.warn(
-            "decrypt_rsa is deprecated and will be removed in a future "
-            "version.",
-            utils.DeprecatedIn05,
-            stacklevel=2
-        )
-        rsa_cdata = self._rsa_cdata_from_private_key(private_key)
-        key = _RSAPrivateKey(self, rsa_cdata)
-        return key.decrypt(ciphertext, padding)
-
-    def encrypt_rsa(self, public_key, plaintext, padding):
-        warnings.warn(
-            "encrypt_rsa is deprecated and will be removed in a future "
-            "version.",
-            utils.DeprecatedIn05,
-            stacklevel=2
-        )
-        rsa_cdata = self._rsa_cdata_from_public_key(public_key)
-        key = _RSAPublicKey(self, rsa_cdata)
-        return key.encrypt(plaintext, padding)
-
     def cmac_algorithm_supported(self, algorithm):
         return (
             self._lib.Cryptography_HAS_CMAC == 1
diff --git a/cryptography/hazmat/primitives/asymmetric/rsa.py b/cryptography/hazmat/primitives/asymmetric/rsa.py
index 398b3763..c192811d 100644
--- a/cryptography/hazmat/primitives/asymmetric/rsa.py
+++ b/cryptography/hazmat/primitives/asymmetric/rsa.py
@@ -13,11 +13,8 @@
 
 from __future__ import absolute_import, division, print_function
 
-import warnings
-
 import six
 
-from cryptography import utils
 from cryptography.exceptions import UnsupportedAlgorithm, _Reasons
 from cryptography.hazmat.backends.interfaces import RSABackend
 
@@ -94,65 +91,6 @@ def _check_public_key_components(e, n):
         raise ValueError("e must be odd.")
 
 
-class RSAPublicKey(object):
-    def __init__(self, public_exponent, modulus):
-        warnings.warn(
-            "The RSAPublicKey class is deprecated and will be removed in a "
-            "future version.",
-            utils.DeprecatedIn05,
-            stacklevel=2
-        )
-        if (
-            not isinstance(public_exponent, six.integer_types) or
-            not isinstance(modulus, six.integer_types)
-        ):
-            raise TypeError("RSAPublicKey arguments must be integers.")
-
-        _check_public_key_components(public_exponent, modulus)
-
-        self._public_exponent = public_exponent
-        self._modulus = modulus
-
-    def verifier(self, signature, padding, algorithm, backend):
-        if not isinstance(backend, RSABackend):
-            raise UnsupportedAlgorithm(
-                "Backend object does not implement RSABackend.",
-                _Reasons.BACKEND_MISSING_INTERFACE
-            )
-
-        return backend.create_rsa_verification_ctx(self, signature, padding,
-                                                   algorithm)
-
-    def encrypt(self, plaintext, padding, backend):
-        if not isinstance(backend, RSABackend):
-            raise UnsupportedAlgorithm(
-                "Backend object does not implement RSABackend.",
-                _Reasons.BACKEND_MISSING_INTERFACE
-            )
-
-        return backend.encrypt_rsa(self, plaintext, padding)
-
-    @property
-    def key_size(self):
-        return utils.bit_length(self.modulus)
-
-    @property
-    def public_exponent(self):
-        return self._public_exponent
-
-    @property
-    def modulus(self):
-        return self._modulus
-
-    @property
-    def e(self):
-        return self.public_exponent
-
-    @property
-    def n(self):
-        return self.modulus
-
-
 def _modinv(e, m):
     """
     Modular Multiplicative Inverse. Returns x such that: (x*e) mod m == 1
@@ -189,136 +127,6 @@ def rsa_crt_dmq1(private_exponent, q):
     return private_exponent % (q - 1)
 
 
-class RSAPrivateKey(object):
-    def __init__(self, p, q, private_exponent, dmp1, dmq1, iqmp,
-                 public_exponent, modulus):
-        warnings.warn(
-            "The RSAPrivateKey class is deprecated and will be removed in a "
-            "future version.",
-            utils.DeprecatedIn05,
-            stacklevel=2
-        )
-        if (
-            not isinstance(p, six.integer_types) or
-            not isinstance(q, six.integer_types) or
-            not isinstance(dmp1, six.integer_types) or
-            not isinstance(dmq1, six.integer_types) or
-            not isinstance(iqmp, six.integer_types) or
-            not isinstance(private_exponent, six.integer_types) or
-            not isinstance(public_exponent, six.integer_types) or
-            not isinstance(modulus, six.integer_types)
-        ):
-            raise TypeError("RSAPrivateKey arguments must be integers.")
-
-        _check_private_key_components(p, q, private_exponent, dmp1, dmq1, iqmp,
-                                      public_exponent, modulus)
-
-        self._p = p
-        self._q = q
-        self._dmp1 = dmp1
-        self._dmq1 = dmq1
-        self._iqmp = iqmp
-        self._private_exponent = private_exponent
-        self._public_exponent = public_exponent
-        self._modulus = modulus
-
-    @classmethod
-    def generate(cls, public_exponent, key_size, backend):
-        warnings.warn(
-            "generate is deprecated and will be removed in a future version.",
-            utils.DeprecatedIn05,
-            stacklevel=2
-        )
-        if not isinstance(backend, RSABackend):
-            raise UnsupportedAlgorithm(
-                "Backend object does not implement RSABackend.",
-                _Reasons.BACKEND_MISSING_INTERFACE
-            )
-
-        _verify_rsa_parameters(public_exponent, key_size)
-        key = backend.generate_rsa_private_key(public_exponent, key_size)
-        private_numbers = key.private_numbers()
-        return RSAPrivateKey(
-            p=private_numbers.p,
-            q=private_numbers.q,
-            dmp1=private_numbers.dmp1,
-            dmq1=private_numbers.dmq1,
-            iqmp=private_numbers.iqmp,
-            private_exponent=private_numbers.d,
-            public_exponent=private_numbers.public_numbers.e,
-            modulus=private_numbers.public_numbers.n
-        )
-
-    def signer(self, padding, algorithm, backend):
-        if not isinstance(backend, RSABackend):
-            raise UnsupportedAlgorithm(
-                "Backend object does not implement RSABackend.",
-                _Reasons.BACKEND_MISSING_INTERFACE
-            )
-
-        return backend.create_rsa_signature_ctx(self, padding, algorithm)
-
-    def decrypt(self, ciphertext, padding, backend):
-        if not isinstance(backend, RSABackend):
-            raise UnsupportedAlgorithm(
-                "Backend object does not implement RSABackend.",
-                _Reasons.BACKEND_MISSING_INTERFACE
-            )
-
-        return backend.decrypt_rsa(self, ciphertext, padding)
-
-    @property
-    def key_size(self):
-        return utils.bit_length(self.modulus)
-
-    def public_key(self):
-        return RSAPublicKey(self.public_exponent, self.modulus)
-
-    @property
-    def p(self):
-        return self._p
-
-    @property
-    def q(self):
-        return self._q
-
-    @property
-    def private_exponent(self):
-        return self._private_exponent
-
-    @property
-    def public_exponent(self):
-        return self._public_exponent
-
-    @property
-    def modulus(self):
-        return self._modulus
-
-    @property
-    def d(self):
-        return self.private_exponent
-
-    @property
-    def dmp1(self):
-        return self._dmp1
-
-    @property
-    def dmq1(self):
-        return self._dmq1
-
-    @property
-    def iqmp(self):
-        return self._iqmp
-
-    @property
-    def e(self):
-        return self.public_exponent
-
-    @property
-    def n(self):
-        return self.modulus
-
-
 class RSAPrivateNumbers(object):
     def __init__(self, p, q, d, dmp1, dmq1, iqmp,
                  public_numbers):
diff --git a/docs/hazmat/backends/interfaces.rst b/docs/hazmat/backends/interfaces.rst
index 77de4ac8..4f4c5680 100644
--- a/docs/hazmat/backends/interfaces.rst
+++ b/docs/hazmat/backends/interfaces.rst
@@ -240,63 +240,6 @@ A specific ``backend`` may provide one or more of these interfaces.
 
         :raises ValueError: If the public_exponent is not valid.
 
-    .. method:: create_rsa_signature_ctx(private_key, padding, algorithm)
-
-        .. deprecated:: 0.5
-
-        :param private_key: An instance of an
-            :class:`~cryptography.hazmat.primitives.interfaces.RSAPrivateKey`
-            provider.
-
-        :param padding: An instance of an
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :param algorithm: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.HashAlgorithm`
-            provider.
-
-        :returns:
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricSignatureContext`
-
-    .. method:: create_rsa_verification_ctx(public_key, signature, padding, algorithm)
-
-        .. deprecated:: 0.5
-
-        :param public_key: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.RSAPublicKey`
-            provider.
-
-        :param bytes signature: The signature to verify.
-
-        :param padding: An instance of an
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :param algorithm: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.HashAlgorithm`
-            provider.
-
-        :returns:
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricVerificationContext`
-
-    .. method:: mgf1_hash_supported(algorithm)
-
-        ..deprecated:: 0.5
-
-        Check if the specified ``algorithm`` is supported for use with
-        :class:`~cryptography.hazmat.primitives.asymmetric.padding.MGF1`
-        inside :class:`~cryptography.hazmat.primitives.asymmetric.padding.PSS`
-        padding. This method is deprecated in favor of
-        ``rsa_padding_supported``.
-
-        :param algorithm: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.HashAlgorithm`
-            provider.
-
-        :returns: ``True`` if the specified ``algorithm`` is supported by this
-            backend, otherwise ``False``.
-
     .. method:: rsa_padding_supported(padding)
 
         Check if the specified ``padding`` is supported by the backend.
@@ -317,49 +260,6 @@ A specific ``backend`` may provide one or more of these interfaces.
 
         :param int key_size: The bit length of the generated modulus.
 
-    .. method:: decrypt_rsa(private_key, ciphertext, padding)
-
-        .. deprecated:: 0.5
-
-        :param private_key: An instance of an
-            :class:`~cryptography.hazmat.primitives.interfaces.RSAPrivateKey`
-            provider.
-
-        :param bytes ciphertext: The ciphertext to decrypt.
-
-        :param padding: An instance of an
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :return bytes: The decrypted data.
-
-        :raises cryptography.exceptions.UnsupportedAlgorithm: If an unsupported
-            MGF, hash function, or padding is chosen.
-
-        :raises ValueError: When decryption fails or key size does not match
-            ciphertext length.
-
-    .. method:: encrypt_rsa(public_key, plaintext, padding)
-
-        .. deprecated:: 0.5
-
-        :param public_key: An instance of an
-            :class:`~cryptography.hazmat.primitives.interfaces.RSAPublicKey`
-            provider.
-
-        :param bytes plaintext: The plaintext to encrypt.
-
-        :param padding: An instance of an
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :return bytes: The encrypted data.
-
-        :raises cryptography.exceptions.UnsupportedAlgorithm: If an unsupported
-            MGF, hash function, or padding is chosen.
-
-        :raises ValueError: When plaintext is too long for the key size.
-
     .. method:: load_rsa_private_numbers(numbers):
 
         :param numbers: An instance of
diff --git a/docs/hazmat/primitives/asymmetric/rsa.rst b/docs/hazmat/primitives/asymmetric/rsa.rst
index a9637523..a5cebb1d 100644
--- a/docs/hazmat/primitives/asymmetric/rsa.rst
+++ b/docs/hazmat/primitives/asymmetric/rsa.rst
@@ -265,243 +265,6 @@ this without having to do the math themselves.
     Generates the ``dmq1`` parameter from the RSA private exponent and prime
     ``q``.
 
-Deprecated Concrete Classes
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-These classes were deprecated in version 0.5 in favor of backend specific
-providers of the
-:class:`~cryptography.hazmat.primitives.interfaces.RSAPrivateKey` and
-:class:`~cryptography.hazmat.primitives.interfaces.RSAPublicKey` interfaces.
-
-.. class:: RSAPrivateKey(p, q, private_exponent, dmp1, dmq1, iqmp, public_exponent, modulus)
-
-    .. versionadded:: 0.2
-
-    .. deprecated:: 0.5
-
-    An RSA private key is required for decryption and signing of messages.
-
-    You should use :func:`generate_private_key` to generate new keys.
-
-    .. warning::
-        This method only checks a limited set of properties of its arguments.
-        Using an RSA private key that you do not trust or with incorrect
-        parameters may lead to insecure operation, crashes, and other undefined
-        behavior. We recommend that you only ever load private keys that were
-        generated with software you trust.
-
-
-    :raises TypeError: This is raised when the arguments are not all integers.
-
-    :raises ValueError: This is raised when the values of ``p``, ``q``,
-                        ``private_exponent``, ``public_exponent``, or
-                        ``modulus`` do not match the bounds specified in
-                        :rfc:`3447`.
-
-    .. classmethod:: generate(public_exponent, key_size, backend)
-
-        Generate a new ``RSAPrivateKey`` instance using ``backend``.
-
-        :param int public_exponent: The public exponent of the new key.
-            Usually one of the small Fermat primes 3, 5, 17, 257, 65537. If in
-            doubt you should `use 65537`_.
-        :param int key_size: The length of the modulus in bits. For keys
-            generated in 2014 it is strongly recommended to be
-            `at least 2048`_ (See page 41). It must not be less than 512.
-            Some backends may have additional limitations.
-        :param backend: A
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend`
-            provider.
-        :return: A new instance of ``RSAPrivateKey``.
-
-        :raises cryptography.exceptions.UnsupportedAlgorithm: This is raised if
-            the provided ``backend`` does not implement
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend`
-
-
-    .. method:: signer(padding, algorithm, backend)
-
-        .. versionadded:: 0.3
-
-        Sign data which can be verified later by others using the public key.
-
-        :param padding: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider. Valid values are
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.PSS` and
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.PKCS1v15`
-            (``PSS`` is recommended for all new applications).
-
-        :param algorithm: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.HashAlgorithm`
-            provider.
-
-        :param backend: A
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend`
-            provider.
-
-        :returns:
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricSignatureContext`
-
-        :raises cryptography.exceptions.UnsupportedAlgorithm: This is raised if
-            the provided ``backend`` does not implement
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend` or if
-            the backend does not support the chosen hash or padding algorithm.
-            If the padding is
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.PSS`
-            with the
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.MGF1`
-            mask generation function it may also refer to the ``MGF1`` hash
-            algorithm.
-
-        :raises TypeError: This is raised when the padding is not an
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :raises ValueError: This is raised when the chosen hash algorithm is
-            too large for the key size.
-
-    .. method:: decrypt(ciphertext, padding, backend)
-
-        .. versionadded:: 0.4
-
-        Decrypt data that was encrypted with the public key.
-
-        :param bytes ciphertext: The ciphertext to decrypt.
-
-        :param padding: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :param backend: A
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend`
-            provider.
-
-        :return bytes: Decrypted data.
-
-        :raises cryptography.exceptions.UnsupportedAlgorithm: This is raised if
-            the provided ``backend`` does not implement
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend` or if
-            the backend does not support the chosen hash or padding algorithm.
-            If the padding is
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.OAEP`
-            with the
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.MGF1`
-            mask generation function it may also refer to the ``MGF1`` hash
-            algorithm.
-
-        :raises TypeError: This is raised when the padding is not an
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :raises ValueError: This is raised when decryption fails or the data
-            is too large for the key size. If the padding is
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.OAEP`
-            it may also be raised for invalid label values.
-
-
-.. class:: RSAPublicKey(public_exponent, modulus)
-
-    .. versionadded:: 0.2
-
-    .. deprecated:: 0.5
-
-    An RSA public key is required for encryption and verification of messages.
-
-    Normally you do not need to directly construct public keys because you'll
-    be loading them from a file, generating them automatically or receiving
-    them from a 3rd party.
-
-    :raises TypeError: This is raised when the arguments are not all integers.
-
-    :raises ValueError: This is raised when the values of ``public_exponent``
-                        or ``modulus`` do not match the bounds specified in
-                        :rfc:`3447`.
-
-    .. method:: verifier(signature, padding, algorithm, backend)
-
-        .. versionadded:: 0.3
-
-        Verify data was signed by the private key associated with this public
-        key.
-
-        :param bytes signature: The signature to verify.
-
-        :param padding: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider. Valid values are
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.PSS` and
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.PKCS1v15`
-            (``PSS`` is recommended for all new applications).
-
-        :param algorithm: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.HashAlgorithm`
-            provider.
-
-        :param backend: A
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend`
-            provider.
-
-        :returns:
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricVerificationContext`
-
-        :raises cryptography.exceptions.UnsupportedAlgorithm: This is raised if
-            the provided ``backend`` does not implement
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend` or if
-            the backend does not support the chosen hash or padding algorithm.
-            If the padding is
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.PSS`
-            with the
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.MGF1`
-            mask generation function it may also refer to the ``MGF1`` hash
-            algorithm.
-
-        :raises TypeError: This is raised when the padding is not an
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :raises ValueError: This is raised when the chosen hash algorithm is
-            too large for the key size.
-
-    .. method:: encrypt(plaintext, padding, backend)
-
-        .. versionadded:: 0.4
-
-        Encrypt data using the public key. The resulting ciphertext can only
-        be decrypted with the private key.
-
-        :param bytes plaintext: The plaintext to encrypt.
-
-        :param padding: An instance of a
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :param backend: A
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend`
-            provider.
-
-        :return bytes: Encrypted data.
-
-        :raises cryptography.exceptions.UnsupportedAlgorithm: This is raised if
-            the provided ``backend`` does not implement
-            :class:`~cryptography.hazmat.backends.interfaces.RSABackend` or if
-            the backend does not support the chosen hash or padding algorithm.
-            If the padding is
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.OAEP`
-            with the
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.MGF1`
-            mask generation function it may also refer to the ``MGF1`` hash
-            algorithm.
-
-        :raises TypeError: This is raised when the padding is not an
-            :class:`~cryptography.hazmat.primitives.interfaces.AsymmetricPadding`
-            provider.
-
-        :raises ValueError: This is raised if the data is too large for the
-            key size. If the padding is
-            :class:`~cryptography.hazmat.primitives.asymmetric.padding.OAEP`
-            it may also be raised for invalid label values.
-
 
 .. _`RSA`: https://en.wikipedia.org/wiki/RSA_(cryptosystem)
 .. _`public-key`: https://en.wikipedia.org/wiki/Public-key_cryptography
diff --git a/tests/hazmat/backends/test_openssl.py b/tests/hazmat/backends/test_openssl.py
index b00543fe..b3a17884 100644
--- a/tests/hazmat/backends/test_openssl.py
+++ b/tests/hazmat/backends/test_openssl.py
@@ -325,7 +325,7 @@ class TestOpenSSLRSA(object):
         reason="Requires an older OpenSSL. Must be < 1.0.1"
     )
     def test_non_sha1_pss_mgf1_hash_algorithm_on_old_openssl(self):
-        private_key = rsa.RSAPrivateKey.generate(
+        private_key = rsa.generate_private_key(
             public_exponent=65537,
             key_size=512,
             backend=backend
@@ -338,8 +338,7 @@ class TestOpenSSLRSA(object):
                     ),
                     salt_length=padding.PSS.MAX_LENGTH
                 ),
-                hashes.SHA1(),
-                backend
+                hashes.SHA1()
             )
         public_key = private_key.public_key()
         with raises_unsupported_algorithm(_Reasons.UNSUPPORTED_HASH):
@@ -351,16 +350,9 @@ class TestOpenSSLRSA(object):
                     ),
                     salt_length=padding.PSS.MAX_LENGTH
                 ),
-                hashes.SHA1(),
-                backend
+                hashes.SHA1()
             )
 
-    def test_unsupported_mgf1_hash_algorithm(self):
-        assert pytest.deprecated_call(
-            backend.mgf1_hash_supported,
-            DummyHash()
-        ) is False
-
     def test_rsa_padding_unsupported_pss_mgf1_hash(self):
         assert backend.rsa_padding_supported(
             padding.PSS(mgf=padding.MGF1(DummyHash()), salt_length=0)
@@ -400,7 +392,7 @@ class TestOpenSSLRSA(object):
         ) is False
 
     def test_unsupported_mgf1_hash_algorithm_decrypt(self):
-        private_key = rsa.RSAPrivateKey.generate(
+        private_key = rsa.generate_private_key(
             public_exponent=65537,
             key_size=512,
             backend=backend
@@ -412,12 +404,11 @@ class TestOpenSSLRSA(object):
                     mgf=padding.MGF1(algorithm=hashes.SHA256()),
                     algorithm=hashes.SHA1(),
                     label=None
-                ),
-                backend
+                )
             )
 
     def test_unsupported_oaep_hash_algorithm_decrypt(self):
-        private_key = rsa.RSAPrivateKey.generate(
+        private_key = rsa.generate_private_key(
             public_exponent=65537,
             key_size=512,
             backend=backend
@@ -429,12 +420,11 @@ class TestOpenSSLRSA(object):
                     mgf=padding.MGF1(algorithm=hashes.SHA1()),
                     algorithm=hashes.SHA256(),
                     label=None
-                ),
-                backend
+                )
             )
 
     def test_unsupported_oaep_label_decrypt(self):
-        private_key = rsa.RSAPrivateKey.generate(
+        private_key = rsa.generate_private_key(
             public_exponent=65537,
             key_size=512,
             backend=backend
@@ -446,8 +436,7 @@ class TestOpenSSLRSA(object):
                     mgf=padding.MGF1(algorithm=hashes.SHA1()),
                     algorithm=hashes.SHA1(),
                     label=b"label"
-                ),
-                backend
+                )
             )
 
 
@@ -513,44 +502,6 @@ class TestOpenSSLEllipticCurve(object):
             _sn_to_elliptic_curve(backend, b"fake")
 
 
-class TestDeprecatedRSABackendMethods(object):
-    def test_create_rsa_signature_ctx(self):
-        private_key = rsa.RSAPrivateKey.generate(65537, 512, backend)
-        pytest.deprecated_call(
-            backend.create_rsa_signature_ctx,
-            private_key,
-            padding.PKCS1v15(),
-            hashes.SHA1()
-        )
-
-    def test_create_rsa_verification_ctx(self):
-        private_key = rsa.RSAPrivateKey.generate(65537, 512, backend)
-        public_key = private_key.public_key()
-        pytest.deprecated_call(
-            backend.create_rsa_verification_ctx,
-            public_key,
-            b"\x00" * 64,
-            padding.PKCS1v15(),
-            hashes.SHA1()
-        )
-
-    def test_encrypt_decrypt_rsa(self):
-        private_key = rsa.RSAPrivateKey.generate(65537, 512, backend)
-        public_key = private_key.public_key()
-        ct = pytest.deprecated_call(
-            backend.encrypt_rsa,
-            public_key,
-            b"\x00" * 32,
-            padding.PKCS1v15()
-        )
-        pytest.deprecated_call(
-            backend.decrypt_rsa,
-            private_key,
-            ct,
-            padding.PKCS1v15()
-        )
-
-
 class TestDeprecatedDSABackendMethods(object):
     def test_create_dsa_signature_ctx(self):
         params = dsa.DSAParameters.generate(1024, backend)
diff --git a/tests/hazmat/primitives/test_rsa.py b/tests/hazmat/primitives/test_rsa.py
index 88b30d61..d1583e25 100644
--- a/tests/hazmat/primitives/test_rsa.py
+++ b/tests/hazmat/primitives/test_rsa.py
@@ -103,16 +103,6 @@ class TestRSA(object):
             pkey = skey.public_key()
             assert isinstance(pkey.public_numbers(), rsa.RSAPublicNumbers)
 
-    def test_generate_rsa_key_class_method(self, backend):
-        skey = pytest.deprecated_call(
-            rsa.RSAPrivateKey.generate,
-            65537,
-            512,
-            backend
-        )
-        assert skey.key_size == 512
-        assert skey.public_exponent == 65537
-
     def test_generate_bad_public_exponent(self, backend):
         with pytest.raises(ValueError):
             rsa.generate_private_key(public_exponent=1,
@@ -172,239 +162,6 @@ class TestRSA(object):
         assert public_num.n == public_num2.n
         assert public_num.e == public_num2.e
 
-    def test_invalid_private_key_argument_types(self):
-        with pytest.raises(TypeError):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                None,
-                None,
-                None,
-                None,
-                None,
-                None,
-                None,
-                None
-            )
-
-    def test_invalid_public_key_argument_types(self):
-        with pytest.raises(TypeError):
-            pytest.deprecated_call(rsa.RSAPublicKey, None, None)
-
-    def test_invalid_private_key_argument_values(self):
-        # 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):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                p=3,
-                q=11,
-                private_exponent=3,
-                dmp1=1,
-                dmq1=3,
-                iqmp=2,
-                public_exponent=7,
-                modulus=2
-            )
-
-        # Test a modulus != p * q.
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                p=3,
-                q=11,
-                private_exponent=3,
-                dmp1=1,
-                dmq1=3,
-                iqmp=2,
-                public_exponent=7,
-                modulus=35
-            )
-
-        # Test a p > modulus.
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                p=37,
-                q=11,
-                private_exponent=3,
-                dmp1=1,
-                dmq1=3,
-                iqmp=2,
-                public_exponent=7,
-                modulus=33
-            )
-
-        # Test a q > modulus.
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                p=3,
-                q=37,
-                private_exponent=3,
-                dmp1=1,
-                dmq1=3,
-                iqmp=2,
-                public_exponent=7,
-                modulus=33
-            )
-
-        # Test a dmp1 > modulus.
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                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):
-            pytest.deprecated_call(
-                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):
-            pytest.deprecated_call(
-                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):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                p=3,
-                q=11,
-                private_exponent=37,
-                dmp1=1,
-                dmq1=3,
-                iqmp=2,
-                public_exponent=7,
-                modulus=33
-            )
-
-        # Test a public_exponent < 3
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                p=3,
-                q=11,
-                private_exponent=3,
-                dmp1=1,
-                dmq1=3,
-                iqmp=2,
-                public_exponent=1,
-                modulus=33
-            )
-
-        # Test a public_exponent > modulus
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                p=3,
-                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):
-            pytest.deprecated_call(
-                rsa.RSAPrivateKey,
-                p=3,
-                q=11,
-                private_exponent=3,
-                dmp1=1,
-                dmq1=3,
-                iqmp=2,
-                public_exponent=6,
-                modulus=33
-            )
-
-        # Test a dmp1 that is not odd.
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                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):
-            pytest.deprecated_call(
-                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):
-        # Start with public_exponent=7, modulus=15. Then change one value at a
-        # time to test the bounds.
-
-        # Test a modulus < 3.
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPublicKey, public_exponent=7, modulus=2
-            )
-
-        # Test a public_exponent < 3
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPublicKey, public_exponent=1, modulus=15
-            )
-
-        # Test a public_exponent > modulus
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPublicKey, public_exponent=17, modulus=15
-            )
-
-        # Test a public_exponent that is not odd.
-        with pytest.raises(ValueError):
-            pytest.deprecated_call(
-                rsa.RSAPublicKey, public_exponent=6, modulus=15
-            )
-
 
 def test_rsa_generate_invalid_backend():
     pretend_backend = object()
@@ -412,11 +169,6 @@ def test_rsa_generate_invalid_backend():
     with raises_unsupported_algorithm(_Reasons.BACKEND_MISSING_INTERFACE):
         rsa.generate_private_key(65537, 2048, pretend_backend)
 
-    with raises_unsupported_algorithm(_Reasons.BACKEND_MISSING_INTERFACE):
-        pytest.deprecated_call(
-            rsa.RSAPrivateKey.generate, 65537, 2048, pretend_backend
-        )
-
 
 @pytest.mark.rsa
 class TestRSASignature(object):
@@ -436,18 +188,19 @@ class TestRSASignature(object):
     )
     def test_pkcs1v15_signing(self, pkcs1_example, backend):
         private, public, example = pkcs1_example
-        private_key = pytest.deprecated_call(
-            rsa.RSAPrivateKey,
+        private_key = rsa.RSAPrivateNumbers(
             p=private["p"],
             q=private["q"],
-            private_exponent=private["private_exponent"],
+            d=private["private_exponent"],
             dmp1=private["dmp1"],
             dmq1=private["dmq1"],
             iqmp=private["iqmp"],
-            public_exponent=private["public_exponent"],
-            modulus=private["modulus"]
-        )
-        signer = private_key.signer(padding.PKCS1v15(), hashes.SHA1(), backend)
+            public_numbers=rsa.RSAPublicNumbers(
+                e=private["public_exponent"],
+                n=private["modulus"]
+            )
+        ).private_key(backend)
+        signer = private_key.signer(padding.PKCS1v15(), hashes.SHA1())
         signer.update(binascii.unhexlify(example["message"]))
         signature = signer.finalize()
         assert binascii.hexlify(signature) == example["signature"]
@@ -471,28 +224,28 @@ class TestRSASignature(object):
     )
     def test_pss_signing(self, pkcs1_example, backend):
         private, public, example = pkcs1_example
-        private_key = pytest.deprecated_call(
-            rsa.RSAPrivateKey,
+        private_key = rsa.RSAPrivateNumbers(
             p=private["p"],
             q=private["q"],
-            private_exponent=private["private_exponent"],
+            d=private["private_exponent"],
             dmp1=private["dmp1"],
             dmq1=private["dmq1"],
             iqmp=private["iqmp"],
-            public_exponent=private["public_exponent"],
-            modulus=private["modulus"]
-        )
-        public_key = rsa.RSAPublicKey(
-            public_exponent=public["public_exponent"],
-            modulus=public["modulus"]
-        )
+            public_numbers=rsa.RSAPublicNumbers(
+                e=private["public_exponent"],
+                n=private["modulus"]
+            )
+        ).private_key(backend)
+        public_key = rsa.RSAPublicNumbers(
+            e=public["public_exponent"],
+            n=public["modulus"]
+        ).public_key(backend)
         signer = private_key.signer(
             padding.PSS(
                 mgf=padding.MGF1(algorithm=hashes.SHA1()),
                 salt_length=padding.PSS.MAX_LENGTH
             ),
-            hashes.SHA1(),
-            backend
+            hashes.SHA1()
         )
         signer.update(binascii.unhexlify(example["message"]))
         signature = signer.finalize()
@@ -507,7 +260,6 @@ class TestRSASignature(object):
                 salt_length=padding.PSS.MAX_LENGTH
             ),
             hashes.SHA1(),
-            backend
         )
         verifier.update(binascii.unhexlify(example["message"]))
         verifier.verify()
@@ -635,24 +387,6 @@ class TestRSASignature(object):
         with pytest.raises(TypeError):
             private_key.signer("notpadding", hashes.SHA1())
 
-    def test_rsa_signer_invalid_backend(self, backend):
-        pretend_backend = object()
-        private_key = pytest.deprecated_call(
-            rsa.RSAPrivateKey,
-            p=RSA_KEY_512.p,
-            q=RSA_KEY_512.q,
-            private_exponent=RSA_KEY_512.d,
-            dmp1=RSA_KEY_512.dmp1,
-            dmq1=RSA_KEY_512.dmq1,
-            iqmp=RSA_KEY_512.iqmp,
-            public_exponent=RSA_KEY_512.public_numbers.e,
-            modulus=RSA_KEY_512.public_numbers.n
-        )
-
-        with raises_unsupported_algorithm(_Reasons.BACKEND_MISSING_INTERFACE):
-            private_key.signer(
-                padding.PKCS1v15(), hashes.SHA256, pretend_backend)
-
     @pytest.mark.supported(
         only_if=lambda backend: backend.rsa_padding_supported(
             padding.PSS(mgf=padding.MGF1(hashes.SHA1()), salt_length=0)
@@ -720,15 +454,14 @@ class TestRSAVerification(object):
     )
     def test_pkcs1v15_verification(self, pkcs1_example, backend):
         private, public, example = pkcs1_example
-        public_key = rsa.RSAPublicKey(
-            public_exponent=public["public_exponent"],
-            modulus=public["modulus"]
-        )
+        public_key = rsa.RSAPublicNumbers(
+            e=public["public_exponent"],
+            n=public["modulus"]
+        ).public_key(backend)
         verifier = public_key.verifier(
             binascii.unhexlify(example["signature"]),
             padding.PKCS1v15(),
-            hashes.SHA1(),
-            backend
+            hashes.SHA1()
         )
         verifier.update(binascii.unhexlify(example["message"]))
         verifier.verify()
@@ -795,18 +528,17 @@ class TestRSAVerification(object):
     )
     def test_pss_verification(self, pkcs1_example, backend):
         private, public, example = pkcs1_example
-        public_key = rsa.RSAPublicKey(
-            public_exponent=public["public_exponent"],
-            modulus=public["modulus"]
-        )
+        public_key = rsa.RSAPublicNumbers(
+            e=public["public_exponent"],
+            n=public["modulus"]
+        ).public_key(backend)
         verifier = public_key.verifier(
             binascii.unhexlify(example["signature"]),
             padding.PSS(
                 mgf=padding.MGF1(algorithm=hashes.SHA1()),
                 salt_length=20
             ),
-            hashes.SHA1(),
-            backend
+            hashes.SHA1()
         )
         verifier.update(binascii.unhexlify(example["message"]))
         verifier.verify()
@@ -821,14 +553,14 @@ class TestRSAVerification(object):
         skip_message="Does not support PSS."
     )
     def test_invalid_pss_signature_wrong_data(self, backend):
-        public_key = rsa.RSAPublicKey(
-            modulus=int(
+        public_key = rsa.RSAPublicNumbers(
+            n=int(
                 b"dffc2137d5e810cde9e4b4612f5796447218bab913b3fa98bdf7982e4fa6"
                 b"ec4d6653ef2b29fb1642b095befcbea6decc178fb4bed243d3c3592c6854"
                 b"6af2d3f3", 16
             ),
-            public_exponent=65537
-        )
+            e=65537
+        ).public_key(backend)
         signature = binascii.unhexlify(
             b"0e68c3649df91c5bc3665f96e157efa75b71934aaa514d91e94ca8418d100f45"
             b"6f05288e58525f99666bab052adcffdf7186eb40f583bd38d98c97d3d524808b"
@@ -839,8 +571,7 @@ class TestRSAVerification(object):
                 mgf=padding.MGF1(algorithm=hashes.SHA1()),
                 salt_length=padding.PSS.MAX_LENGTH
             ),
-            hashes.SHA1(),
-            backend
+            hashes.SHA1()
         )
         verifier.update(b"incorrect data")
         with pytest.raises(InvalidSignature):
@@ -860,24 +591,23 @@ class TestRSAVerification(object):
             b"3a1880165014ba6eb53cc1449d13e5132ebcc0cfd9ade6d7a2494a0503bd0826"
             b"f8a46c431e0d7be0ca3e453f8b2b009e2733764da7927cc6dbe7a021437a242e"
         )
-        public_key = rsa.RSAPublicKey(
-            modulus=int(
+        public_key = rsa.RSAPublicNumbers(
+            n=int(
                 b"381201f4905d67dfeb3dec131a0fbea773489227ec7a1448c3109189ac68"
                 b"5a95441be90866a14c4d2e139cd16db540ec6c7abab13ffff91443fd46a8"
                 b"960cbb7658ded26a5c95c86f6e40384e1c1239c63e541ba221191c4dd303"
                 b"231b42e33c6dbddf5ec9a746f09bf0c25d0f8d27f93ee0ae5c0d723348f4"
                 b"030d3581e13522e1", 16
             ),
-            public_exponent=65537
-        )
+            e=65537
+        ).public_key(backend)
         verifier = public_key.verifier(
             signature,
             padding.PSS(
                 mgf=padding.MGF1(algorithm=hashes.SHA1()),
                 salt_length=padding.PSS.MAX_LENGTH
             ),
-            hashes.SHA1(),
-            backend
+            hashes.SHA1()
         )
         verifier.update(b"sign me")
         with pytest.raises(InvalidSignature):
@@ -897,24 +627,23 @@ class TestRSAVerification(object):
             b"cb43bde4f7ab89eb4a79c6e8dd67e0d1af60715da64429d90c716a490b799c29"
             b"194cf8046509c6ed851052367a74e2e92d9b38947ed74332acb115a03fcc0222"
         )
-        public_key = rsa.RSAPublicKey(
-            modulus=int(
+        public_key = rsa.RSAPublicNumbers(
+            n=int(
                 b"381201f4905d67dfeb3dec131a0fbea773489227ec7a1448c3109189ac68"
                 b"5a95441be90866a14c4d2e139cd16db540ec6c7abab13ffff91443fd46a8"
                 b"960cbb7658ded26a5c95c86f6e40384e1c1239c63e541ba221191c4dd303"
                 b"231b42e33c6dbddf5ec9a746f09bf0c25d0f8d27f93ee0ae5c0d723348f4"
                 b"030d3581e13522", 16
             ),
-            public_exponent=65537
-        )
+            e=65537
+        ).public_key(backend)
         verifier = public_key.verifier(
             signature,
             padding.PSS(
                 mgf=padding.MGF1(algorithm=hashes.SHA1()),
                 salt_length=padding.PSS.MAX_LENGTH
             ),
-            hashes.SHA1(),
-            backend
+            hashes.SHA1()
         )
         verifier.update(b"sign me")
         with pytest.raises(InvalidSignature):
@@ -957,20 +686,6 @@ class TestRSAVerification(object):
         with pytest.raises(TypeError):
             public_key.verifier(b"sig", "notpadding", hashes.SHA1())
 
-    def test_rsa_verifier_invalid_backend(self, backend):
-        pretend_backend = object()
-        private_key = pytest.deprecated_call(
-            rsa.RSAPrivateKey.generate,
-            65537,
-            2048,
-            backend
-        )
-        public_key = private_key.public_key()
-
-        with raises_unsupported_algorithm(_Reasons.BACKEND_MISSING_INTERFACE):
-            public_key.verifier(
-                b"foo", padding.PKCS1v15(), hashes.SHA256(), pretend_backend)
-
     @pytest.mark.supported(
         only_if=lambda backend: backend.rsa_padding_supported(
             padding.PSS(mgf=padding.MGF1(hashes.SHA1()), salt_length=0)
@@ -1034,14 +749,14 @@ class TestRSAVerification(object):
             b"8b9a3ae9fb3b64158f3476dd8d8a1f1425444e98940e0926378baa9944d219d8"
             b"534c050ef6b19b1bdc6eb4da422e89161106a6f5b5cc16135b11eb6439b646bd"
         )
-        public_key = rsa.RSAPublicKey(
-            modulus=int(
+        public_key = rsa.RSAPublicNumbers(
+            n=int(
                 b"d309e4612809437548b747d7f9eb9cd3340f54fe42bb3f84a36933b0839c"
                 b"11b0c8b7f67e11f7252370161e31159c49c784d4bc41c42a78ce0f0b40a3"
                 b"ca8ffb91", 16
             ),
-            public_exponent=65537
-        )
+            e=65537
+        ).public_key(backend)
         verifier = public_key.verifier(
             signature,
             padding.PSS(
@@ -1050,8 +765,7 @@ class TestRSAVerification(object):
                 ),
                 salt_length=1000000
             ),
-            hashes.SHA1(),
-            backend
+            hashes.SHA1()
         )
         verifier.update(b"sign me")
         with pytest.raises(InvalidSignature):
@@ -1354,23 +1068,21 @@ class TestRSADecryption(object):
     )
     def test_decrypt_pkcs1v15_vectors(self, vector, backend):
         private, public, example = vector
-        skey = rsa.RSAPrivateKey(
+        skey = rsa.RSAPrivateNumbers(
             p=private["p"],
             q=private["q"],
-            private_exponent=private["private_exponent"],
+            d=private["private_exponent"],
             dmp1=private["dmp1"],
             dmq1=private["dmq1"],
             iqmp=private["iqmp"],
-            public_exponent=private["public_exponent"],
-            modulus=private["modulus"]
-        )
+            public_numbers=rsa.RSAPublicNumbers(
+                e=private["public_exponent"],
+                n=private["modulus"]
+            )
+        ).private_key(backend)
         ciphertext = binascii.unhexlify(example["encryption"])
         assert len(ciphertext) == math.ceil(skey.key_size / 8.0)
-        message = skey.decrypt(
-            ciphertext,
-            padding.PKCS1v15(),
-            backend
-        )
+        message = skey.decrypt(ciphertext, padding.PKCS1v15())
         assert message == binascii.unhexlify(example["message"])
 
     def test_unsupported_padding(self, backend):
@@ -1424,19 +1136,6 @@ class TestRSADecryption(object):
                 padding.PKCS1v15()
             )
 
-    def test_rsa_decrypt_invalid_backend(self, backend):
-        pretend_backend = object()
-        private_key = pytest.deprecated_call(
-            rsa.RSAPrivateKey.generate, 65537, 2048, backend
-        )
-
-        with raises_unsupported_algorithm(_Reasons.BACKEND_MISSING_INTERFACE):
-            private_key.decrypt(
-                b"irrelevant",
-                padding.PKCS1v15(),
-                pretend_backend
-            )
-
     @pytest.mark.supported(
         only_if=lambda backend: backend.rsa_padding_supported(
             padding.OAEP(
@@ -1457,25 +1156,25 @@ class TestRSADecryption(object):
     )
     def test_decrypt_oaep_vectors(self, vector, backend):
         private, public, example = vector
-        skey = pytest.deprecated_call(
-            rsa.RSAPrivateKey,
+        skey = rsa.RSAPrivateNumbers(
             p=private["p"],
             q=private["q"],
-            private_exponent=private["private_exponent"],
+            d=private["private_exponent"],
             dmp1=private["dmp1"],
             dmq1=private["dmq1"],
             iqmp=private["iqmp"],
-            public_exponent=private["public_exponent"],
-            modulus=private["modulus"]
-        )
+            public_numbers=rsa.RSAPublicNumbers(
+                e=private["public_exponent"],
+                n=private["modulus"]
+            )
+        ).private_key(backend)
         message = skey.decrypt(
             binascii.unhexlify(example["encryption"]),
             padding.OAEP(
                 mgf=padding.MGF1(algorithm=hashes.SHA1()),
                 algorithm=hashes.SHA1(),
                 label=None
-            ),
-            backend
+            )
         )
         assert message == binascii.unhexlify(example["message"])
 
@@ -1520,22 +1219,13 @@ class TestRSAEncryption(object):
         )
     )
     def test_rsa_encrypt_oaep(self, key_data, pad, backend):
-        private_key = rsa.RSAPrivateKey(
-            p=key_data.p,
-            q=key_data.q,
-            private_exponent=key_data.d,
-            dmp1=key_data.dmp1,
-            dmq1=key_data.dmq1,
-            iqmp=key_data.iqmp,
-            public_exponent=key_data.public_numbers.e,
-            modulus=key_data.public_numbers.n
-        )
+        private_key = key_data.private_key(backend)
         pt = b"encrypt me!"
         public_key = private_key.public_key()
-        ct = public_key.encrypt(pt, pad, backend)
+        ct = public_key.encrypt(pt, pad)
         assert ct != pt
         assert len(ct) == math.ceil(public_key.key_size / 8.0)
-        recovered_pt = private_key.decrypt(ct, pad, backend)
+        recovered_pt = private_key.decrypt(ct, pad)
         assert recovered_pt == pt
 
     @pytest.mark.supported(
@@ -1596,20 +1286,6 @@ class TestRSAEncryption(object):
                 pad
             )
 
-    def test_rsa_encrypt_invalid_backend(self, backend):
-        pretend_backend = object()
-        private_key = pytest.deprecated_call(
-            rsa.RSAPrivateKey.generate, 65537, 512, backend
-        )
-        public_key = private_key.public_key()
-
-        with raises_unsupported_algorithm(_Reasons.BACKEND_MISSING_INTERFACE):
-            public_key.encrypt(
-                b"irrelevant",
-                padding.PKCS1v15(),
-                pretend_backend
-            )
-
     def test_unsupported_padding(self, backend):
         private_key = RSA_KEY_512.private_key(backend)
         public_key = private_key.public_key()
@@ -1775,7 +1451,7 @@ class TestRSANumbers(object):
 
         # Test a public_exponent that is not odd.
         with pytest.raises(ValueError):
-            rsa.RSAPublicNumbers(e=16, n=15).public_key(backend)
+            rsa.RSAPublicNumbers(e=14, n=15).public_key(backend)
 
     def test_invalid_private_numbers_argument_values(self, backend):
         # Start with p=3, q=11, private_exponent=3, public_exponent=7,