forked from s434650/CatOrNot
792 lines
24 KiB
Python
792 lines
24 KiB
Python
# -*- coding: utf-8 -*-
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#
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# Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# https://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""RSA key generation code.
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Create new keys with the newkeys() function. It will give you a PublicKey and a
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PrivateKey object.
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Loading and saving keys requires the pyasn1 module. This module is imported as
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late as possible, such that other functionality will remain working in absence
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of pyasn1.
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.. note::
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Storing public and private keys via the `pickle` module is possible.
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However, it is insecure to load a key from an untrusted source.
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The pickle module is not secure against erroneous or maliciously
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constructed data. Never unpickle data received from an untrusted
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or unauthenticated source.
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"""
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import logging
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import warnings
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from rsa._compat import range
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import rsa.prime
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import rsa.pem
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import rsa.common
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import rsa.randnum
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import rsa.core
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log = logging.getLogger(__name__)
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DEFAULT_EXPONENT = 65537
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class AbstractKey(object):
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"""Abstract superclass for private and public keys."""
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__slots__ = ('n', 'e')
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def __init__(self, n, e):
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self.n = n
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self.e = e
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@classmethod
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def _load_pkcs1_pem(cls, keyfile):
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"""Loads a key in PKCS#1 PEM format, implement in a subclass.
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:param keyfile: contents of a PEM-encoded file that contains
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the public key.
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:type keyfile: bytes
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:return: the loaded key
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:rtype: AbstractKey
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"""
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@classmethod
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def _load_pkcs1_der(cls, keyfile):
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"""Loads a key in PKCS#1 PEM format, implement in a subclass.
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:param keyfile: contents of a DER-encoded file that contains
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the public key.
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:type keyfile: bytes
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:return: the loaded key
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:rtype: AbstractKey
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"""
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def _save_pkcs1_pem(self):
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"""Saves the key in PKCS#1 PEM format, implement in a subclass.
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:returns: the PEM-encoded key.
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:rtype: bytes
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"""
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def _save_pkcs1_der(self):
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"""Saves the key in PKCS#1 DER format, implement in a subclass.
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:returns: the DER-encoded key.
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:rtype: bytes
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"""
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@classmethod
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def load_pkcs1(cls, keyfile, format='PEM'):
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"""Loads a key in PKCS#1 DER or PEM format.
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:param keyfile: contents of a DER- or PEM-encoded file that contains
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the key.
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:type keyfile: bytes
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:param format: the format of the file to load; 'PEM' or 'DER'
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:type format: str
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:return: the loaded key
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:rtype: AbstractKey
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"""
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methods = {
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'PEM': cls._load_pkcs1_pem,
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'DER': cls._load_pkcs1_der,
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}
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method = cls._assert_format_exists(format, methods)
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return method(keyfile)
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@staticmethod
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def _assert_format_exists(file_format, methods):
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"""Checks whether the given file format exists in 'methods'.
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"""
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try:
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return methods[file_format]
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except KeyError:
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formats = ', '.join(sorted(methods.keys()))
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raise ValueError('Unsupported format: %r, try one of %s' % (file_format,
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formats))
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def save_pkcs1(self, format='PEM'):
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"""Saves the key in PKCS#1 DER or PEM format.
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:param format: the format to save; 'PEM' or 'DER'
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:type format: str
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:returns: the DER- or PEM-encoded key.
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:rtype: bytes
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"""
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methods = {
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'PEM': self._save_pkcs1_pem,
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'DER': self._save_pkcs1_der,
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}
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method = self._assert_format_exists(format, methods)
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return method()
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def blind(self, message, r):
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"""Performs blinding on the message using random number 'r'.
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:param message: the message, as integer, to blind.
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:type message: int
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:param r: the random number to blind with.
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:type r: int
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:return: the blinded message.
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:rtype: int
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The blinding is such that message = unblind(decrypt(blind(encrypt(message))).
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See https://en.wikipedia.org/wiki/Blinding_%28cryptography%29
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"""
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return (message * pow(r, self.e, self.n)) % self.n
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def unblind(self, blinded, r):
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"""Performs blinding on the message using random number 'r'.
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:param blinded: the blinded message, as integer, to unblind.
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:param r: the random number to unblind with.
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:return: the original message.
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The blinding is such that message = unblind(decrypt(blind(encrypt(message))).
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See https://en.wikipedia.org/wiki/Blinding_%28cryptography%29
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"""
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return (rsa.common.inverse(r, self.n) * blinded) % self.n
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class PublicKey(AbstractKey):
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"""Represents a public RSA key.
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This key is also known as the 'encryption key'. It contains the 'n' and 'e'
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values.
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Supports attributes as well as dictionary-like access. Attribute access is
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faster, though.
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>>> PublicKey(5, 3)
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PublicKey(5, 3)
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>>> key = PublicKey(5, 3)
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>>> key.n
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5
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>>> key['n']
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5
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>>> key.e
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3
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>>> key['e']
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3
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"""
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__slots__ = ('n', 'e')
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def __getitem__(self, key):
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return getattr(self, key)
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def __repr__(self):
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return 'PublicKey(%i, %i)' % (self.n, self.e)
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def __getstate__(self):
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"""Returns the key as tuple for pickling."""
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return self.n, self.e
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def __setstate__(self, state):
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"""Sets the key from tuple."""
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self.n, self.e = state
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def __eq__(self, other):
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if other is None:
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return False
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if not isinstance(other, PublicKey):
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return False
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return self.n == other.n and self.e == other.e
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def __ne__(self, other):
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return not (self == other)
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def __hash__(self):
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return hash((self.n, self.e))
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@classmethod
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def _load_pkcs1_der(cls, keyfile):
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"""Loads a key in PKCS#1 DER format.
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:param keyfile: contents of a DER-encoded file that contains the public
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key.
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:return: a PublicKey object
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First let's construct a DER encoded key:
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>>> import base64
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>>> b64der = 'MAwCBQCNGmYtAgMBAAE='
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>>> der = base64.standard_b64decode(b64der)
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This loads the file:
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>>> PublicKey._load_pkcs1_der(der)
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PublicKey(2367317549, 65537)
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"""
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from pyasn1.codec.der import decoder
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from rsa.asn1 import AsnPubKey
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(priv, _) = decoder.decode(keyfile, asn1Spec=AsnPubKey())
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return cls(n=int(priv['modulus']), e=int(priv['publicExponent']))
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def _save_pkcs1_der(self):
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"""Saves the public key in PKCS#1 DER format.
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:returns: the DER-encoded public key.
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:rtype: bytes
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"""
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from pyasn1.codec.der import encoder
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from rsa.asn1 import AsnPubKey
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# Create the ASN object
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asn_key = AsnPubKey()
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asn_key.setComponentByName('modulus', self.n)
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asn_key.setComponentByName('publicExponent', self.e)
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return encoder.encode(asn_key)
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@classmethod
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def _load_pkcs1_pem(cls, keyfile):
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"""Loads a PKCS#1 PEM-encoded public key file.
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The contents of the file before the "-----BEGIN RSA PUBLIC KEY-----" and
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after the "-----END RSA PUBLIC KEY-----" lines is ignored.
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:param keyfile: contents of a PEM-encoded file that contains the public
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key.
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:return: a PublicKey object
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"""
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der = rsa.pem.load_pem(keyfile, 'RSA PUBLIC KEY')
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return cls._load_pkcs1_der(der)
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def _save_pkcs1_pem(self):
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"""Saves a PKCS#1 PEM-encoded public key file.
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:return: contents of a PEM-encoded file that contains the public key.
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:rtype: bytes
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"""
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der = self._save_pkcs1_der()
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return rsa.pem.save_pem(der, 'RSA PUBLIC KEY')
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@classmethod
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def load_pkcs1_openssl_pem(cls, keyfile):
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"""Loads a PKCS#1.5 PEM-encoded public key file from OpenSSL.
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These files can be recognised in that they start with BEGIN PUBLIC KEY
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rather than BEGIN RSA PUBLIC KEY.
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The contents of the file before the "-----BEGIN PUBLIC KEY-----" and
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after the "-----END PUBLIC KEY-----" lines is ignored.
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:param keyfile: contents of a PEM-encoded file that contains the public
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key, from OpenSSL.
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:type keyfile: bytes
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:return: a PublicKey object
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"""
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der = rsa.pem.load_pem(keyfile, 'PUBLIC KEY')
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return cls.load_pkcs1_openssl_der(der)
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@classmethod
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def load_pkcs1_openssl_der(cls, keyfile):
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"""Loads a PKCS#1 DER-encoded public key file from OpenSSL.
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:param keyfile: contents of a DER-encoded file that contains the public
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key, from OpenSSL.
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:return: a PublicKey object
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:rtype: bytes
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"""
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from rsa.asn1 import OpenSSLPubKey
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from pyasn1.codec.der import decoder
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from pyasn1.type import univ
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(keyinfo, _) = decoder.decode(keyfile, asn1Spec=OpenSSLPubKey())
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if keyinfo['header']['oid'] != univ.ObjectIdentifier('1.2.840.113549.1.1.1'):
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raise TypeError("This is not a DER-encoded OpenSSL-compatible public key")
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return cls._load_pkcs1_der(keyinfo['key'][1:])
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class PrivateKey(AbstractKey):
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"""Represents a private RSA key.
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This key is also known as the 'decryption key'. It contains the 'n', 'e',
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'd', 'p', 'q' and other values.
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Supports attributes as well as dictionary-like access. Attribute access is
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faster, though.
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>>> PrivateKey(3247, 65537, 833, 191, 17)
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PrivateKey(3247, 65537, 833, 191, 17)
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exp1, exp2 and coef will be calculated:
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>>> pk = PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
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>>> pk.exp1
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55063
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>>> pk.exp2
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10095
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>>> pk.coef
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50797
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"""
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__slots__ = ('n', 'e', 'd', 'p', 'q', 'exp1', 'exp2', 'coef')
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def __init__(self, n, e, d, p, q):
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AbstractKey.__init__(self, n, e)
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self.d = d
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self.p = p
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self.q = q
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# Calculate exponents and coefficient.
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self.exp1 = int(d % (p - 1))
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self.exp2 = int(d % (q - 1))
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self.coef = rsa.common.inverse(q, p)
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def __getitem__(self, key):
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return getattr(self, key)
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def __repr__(self):
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return 'PrivateKey(%(n)i, %(e)i, %(d)i, %(p)i, %(q)i)' % self
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def __getstate__(self):
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"""Returns the key as tuple for pickling."""
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return self.n, self.e, self.d, self.p, self.q, self.exp1, self.exp2, self.coef
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def __setstate__(self, state):
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"""Sets the key from tuple."""
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self.n, self.e, self.d, self.p, self.q, self.exp1, self.exp2, self.coef = state
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def __eq__(self, other):
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if other is None:
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return False
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if not isinstance(other, PrivateKey):
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return False
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return (self.n == other.n and
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self.e == other.e and
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self.d == other.d and
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self.p == other.p and
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self.q == other.q and
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self.exp1 == other.exp1 and
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self.exp2 == other.exp2 and
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self.coef == other.coef)
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def __ne__(self, other):
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return not (self == other)
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def __hash__(self):
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return hash((self.n, self.e, self.d, self.p, self.q, self.exp1, self.exp2, self.coef))
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def blinded_decrypt(self, encrypted):
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"""Decrypts the message using blinding to prevent side-channel attacks.
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:param encrypted: the encrypted message
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:type encrypted: int
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:returns: the decrypted message
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:rtype: int
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"""
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blind_r = rsa.randnum.randint(self.n - 1)
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blinded = self.blind(encrypted, blind_r) # blind before decrypting
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decrypted = rsa.core.decrypt_int(blinded, self.d, self.n)
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return self.unblind(decrypted, blind_r)
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def blinded_encrypt(self, message):
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"""Encrypts the message using blinding to prevent side-channel attacks.
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:param message: the message to encrypt
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:type message: int
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:returns: the encrypted message
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:rtype: int
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"""
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blind_r = rsa.randnum.randint(self.n - 1)
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blinded = self.blind(message, blind_r) # blind before encrypting
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encrypted = rsa.core.encrypt_int(blinded, self.d, self.n)
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return self.unblind(encrypted, blind_r)
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@classmethod
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def _load_pkcs1_der(cls, keyfile):
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"""Loads a key in PKCS#1 DER format.
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:param keyfile: contents of a DER-encoded file that contains the private
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key.
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:type keyfile: bytes
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:return: a PrivateKey object
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First let's construct a DER encoded key:
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>>> import base64
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>>> b64der = 'MC4CAQACBQDeKYlRAgMBAAECBQDHn4npAgMA/icCAwDfxwIDANcXAgInbwIDAMZt'
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>>> der = base64.standard_b64decode(b64der)
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This loads the file:
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>>> PrivateKey._load_pkcs1_der(der)
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PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
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"""
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from pyasn1.codec.der import decoder
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(priv, _) = decoder.decode(keyfile)
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# ASN.1 contents of DER encoded private key:
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#
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# RSAPrivateKey ::= SEQUENCE {
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# version Version,
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# modulus INTEGER, -- n
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# publicExponent INTEGER, -- e
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# privateExponent INTEGER, -- d
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# prime1 INTEGER, -- p
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# prime2 INTEGER, -- q
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# exponent1 INTEGER, -- d mod (p-1)
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# exponent2 INTEGER, -- d mod (q-1)
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# coefficient INTEGER, -- (inverse of q) mod p
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# otherPrimeInfos OtherPrimeInfos OPTIONAL
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# }
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if priv[0] != 0:
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raise ValueError('Unable to read this file, version %s != 0' % priv[0])
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as_ints = map(int, priv[1:6])
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key = cls(*as_ints)
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exp1, exp2, coef = map(int, priv[6:9])
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if (key.exp1, key.exp2, key.coef) != (exp1, exp2, coef):
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warnings.warn(
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'You have provided a malformed keyfile. Either the exponents '
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'or the coefficient are incorrect. Using the correct values '
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'instead.',
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UserWarning,
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)
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return key
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def _save_pkcs1_der(self):
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"""Saves the private key in PKCS#1 DER format.
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:returns: the DER-encoded private key.
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:rtype: bytes
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"""
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from pyasn1.type import univ, namedtype
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from pyasn1.codec.der import encoder
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class AsnPrivKey(univ.Sequence):
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componentType = namedtype.NamedTypes(
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namedtype.NamedType('version', univ.Integer()),
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namedtype.NamedType('modulus', univ.Integer()),
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namedtype.NamedType('publicExponent', univ.Integer()),
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namedtype.NamedType('privateExponent', univ.Integer()),
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namedtype.NamedType('prime1', univ.Integer()),
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namedtype.NamedType('prime2', univ.Integer()),
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namedtype.NamedType('exponent1', univ.Integer()),
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namedtype.NamedType('exponent2', univ.Integer()),
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namedtype.NamedType('coefficient', univ.Integer()),
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)
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# Create the ASN object
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asn_key = AsnPrivKey()
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asn_key.setComponentByName('version', 0)
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asn_key.setComponentByName('modulus', self.n)
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asn_key.setComponentByName('publicExponent', self.e)
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asn_key.setComponentByName('privateExponent', self.d)
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asn_key.setComponentByName('prime1', self.p)
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asn_key.setComponentByName('prime2', self.q)
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asn_key.setComponentByName('exponent1', self.exp1)
|
|
asn_key.setComponentByName('exponent2', self.exp2)
|
|
asn_key.setComponentByName('coefficient', self.coef)
|
|
|
|
return encoder.encode(asn_key)
|
|
|
|
@classmethod
|
|
def _load_pkcs1_pem(cls, keyfile):
|
|
"""Loads a PKCS#1 PEM-encoded private key file.
|
|
|
|
The contents of the file before the "-----BEGIN RSA PRIVATE KEY-----" and
|
|
after the "-----END RSA PRIVATE KEY-----" lines is ignored.
|
|
|
|
:param keyfile: contents of a PEM-encoded file that contains the private
|
|
key.
|
|
:type keyfile: bytes
|
|
:return: a PrivateKey object
|
|
"""
|
|
|
|
der = rsa.pem.load_pem(keyfile, b'RSA PRIVATE KEY')
|
|
return cls._load_pkcs1_der(der)
|
|
|
|
def _save_pkcs1_pem(self):
|
|
"""Saves a PKCS#1 PEM-encoded private key file.
|
|
|
|
:return: contents of a PEM-encoded file that contains the private key.
|
|
:rtype: bytes
|
|
"""
|
|
|
|
der = self._save_pkcs1_der()
|
|
return rsa.pem.save_pem(der, b'RSA PRIVATE KEY')
|
|
|
|
|
|
def find_p_q(nbits, getprime_func=rsa.prime.getprime, accurate=True):
|
|
"""Returns a tuple of two different primes of nbits bits each.
|
|
|
|
The resulting p * q has exacty 2 * nbits bits, and the returned p and q
|
|
will not be equal.
|
|
|
|
:param nbits: the number of bits in each of p and q.
|
|
:param getprime_func: the getprime function, defaults to
|
|
:py:func:`rsa.prime.getprime`.
|
|
|
|
*Introduced in Python-RSA 3.1*
|
|
|
|
:param accurate: whether to enable accurate mode or not.
|
|
:returns: (p, q), where p > q
|
|
|
|
>>> (p, q) = find_p_q(128)
|
|
>>> from rsa import common
|
|
>>> common.bit_size(p * q)
|
|
256
|
|
|
|
When not in accurate mode, the number of bits can be slightly less
|
|
|
|
>>> (p, q) = find_p_q(128, accurate=False)
|
|
>>> from rsa import common
|
|
>>> common.bit_size(p * q) <= 256
|
|
True
|
|
>>> common.bit_size(p * q) > 240
|
|
True
|
|
|
|
"""
|
|
|
|
total_bits = nbits * 2
|
|
|
|
# Make sure that p and q aren't too close or the factoring programs can
|
|
# factor n.
|
|
shift = nbits // 16
|
|
pbits = nbits + shift
|
|
qbits = nbits - shift
|
|
|
|
# Choose the two initial primes
|
|
log.debug('find_p_q(%i): Finding p', nbits)
|
|
p = getprime_func(pbits)
|
|
log.debug('find_p_q(%i): Finding q', nbits)
|
|
q = getprime_func(qbits)
|
|
|
|
def is_acceptable(p, q):
|
|
"""Returns True iff p and q are acceptable:
|
|
|
|
- p and q differ
|
|
- (p * q) has the right nr of bits (when accurate=True)
|
|
"""
|
|
|
|
if p == q:
|
|
return False
|
|
|
|
if not accurate:
|
|
return True
|
|
|
|
# Make sure we have just the right amount of bits
|
|
found_size = rsa.common.bit_size(p * q)
|
|
return total_bits == found_size
|
|
|
|
# Keep choosing other primes until they match our requirements.
|
|
change_p = False
|
|
while not is_acceptable(p, q):
|
|
# Change p on one iteration and q on the other
|
|
if change_p:
|
|
p = getprime_func(pbits)
|
|
else:
|
|
q = getprime_func(qbits)
|
|
|
|
change_p = not change_p
|
|
|
|
# We want p > q as described on
|
|
# http://www.di-mgt.com.au/rsa_alg.html#crt
|
|
return max(p, q), min(p, q)
|
|
|
|
|
|
def calculate_keys_custom_exponent(p, q, exponent):
|
|
"""Calculates an encryption and a decryption key given p, q and an exponent,
|
|
and returns them as a tuple (e, d)
|
|
|
|
:param p: the first large prime
|
|
:param q: the second large prime
|
|
:param exponent: the exponent for the key; only change this if you know
|
|
what you're doing, as the exponent influences how difficult your
|
|
private key can be cracked. A very common choice for e is 65537.
|
|
:type exponent: int
|
|
|
|
"""
|
|
|
|
phi_n = (p - 1) * (q - 1)
|
|
|
|
try:
|
|
d = rsa.common.inverse(exponent, phi_n)
|
|
except rsa.common.NotRelativePrimeError as ex:
|
|
raise rsa.common.NotRelativePrimeError(
|
|
exponent, phi_n, ex.d,
|
|
msg="e (%d) and phi_n (%d) are not relatively prime (divider=%i)" %
|
|
(exponent, phi_n, ex.d))
|
|
|
|
if (exponent * d) % phi_n != 1:
|
|
raise ValueError("e (%d) and d (%d) are not mult. inv. modulo "
|
|
"phi_n (%d)" % (exponent, d, phi_n))
|
|
|
|
return exponent, d
|
|
|
|
|
|
def calculate_keys(p, q):
|
|
"""Calculates an encryption and a decryption key given p and q, and
|
|
returns them as a tuple (e, d)
|
|
|
|
:param p: the first large prime
|
|
:param q: the second large prime
|
|
|
|
:return: tuple (e, d) with the encryption and decryption exponents.
|
|
"""
|
|
|
|
return calculate_keys_custom_exponent(p, q, DEFAULT_EXPONENT)
|
|
|
|
|
|
def gen_keys(nbits, getprime_func, accurate=True, exponent=DEFAULT_EXPONENT):
|
|
"""Generate RSA keys of nbits bits. Returns (p, q, e, d).
|
|
|
|
Note: this can take a long time, depending on the key size.
|
|
|
|
:param nbits: the total number of bits in ``p`` and ``q``. Both ``p`` and
|
|
``q`` will use ``nbits/2`` bits.
|
|
:param getprime_func: either :py:func:`rsa.prime.getprime` or a function
|
|
with similar signature.
|
|
:param exponent: the exponent for the key; only change this if you know
|
|
what you're doing, as the exponent influences how difficult your
|
|
private key can be cracked. A very common choice for e is 65537.
|
|
:type exponent: int
|
|
"""
|
|
|
|
# Regenerate p and q values, until calculate_keys doesn't raise a
|
|
# ValueError.
|
|
while True:
|
|
(p, q) = find_p_q(nbits // 2, getprime_func, accurate)
|
|
try:
|
|
(e, d) = calculate_keys_custom_exponent(p, q, exponent=exponent)
|
|
break
|
|
except ValueError:
|
|
pass
|
|
|
|
return p, q, e, d
|
|
|
|
|
|
def newkeys(nbits, accurate=True, poolsize=1, exponent=DEFAULT_EXPONENT):
|
|
"""Generates public and private keys, and returns them as (pub, priv).
|
|
|
|
The public key is also known as the 'encryption key', and is a
|
|
:py:class:`rsa.PublicKey` object. The private key is also known as the
|
|
'decryption key' and is a :py:class:`rsa.PrivateKey` object.
|
|
|
|
:param nbits: the number of bits required to store ``n = p*q``.
|
|
:param accurate: when True, ``n`` will have exactly the number of bits you
|
|
asked for. However, this makes key generation much slower. When False,
|
|
`n`` may have slightly less bits.
|
|
:param poolsize: the number of processes to use to generate the prime
|
|
numbers. If set to a number > 1, a parallel algorithm will be used.
|
|
This requires Python 2.6 or newer.
|
|
:param exponent: the exponent for the key; only change this if you know
|
|
what you're doing, as the exponent influences how difficult your
|
|
private key can be cracked. A very common choice for e is 65537.
|
|
:type exponent: int
|
|
|
|
:returns: a tuple (:py:class:`rsa.PublicKey`, :py:class:`rsa.PrivateKey`)
|
|
|
|
The ``poolsize`` parameter was added in *Python-RSA 3.1* and requires
|
|
Python 2.6 or newer.
|
|
|
|
"""
|
|
|
|
if nbits < 16:
|
|
raise ValueError('Key too small')
|
|
|
|
if poolsize < 1:
|
|
raise ValueError('Pool size (%i) should be >= 1' % poolsize)
|
|
|
|
# Determine which getprime function to use
|
|
if poolsize > 1:
|
|
from rsa import parallel
|
|
import functools
|
|
|
|
getprime_func = functools.partial(parallel.getprime, poolsize=poolsize)
|
|
else:
|
|
getprime_func = rsa.prime.getprime
|
|
|
|
# Generate the key components
|
|
(p, q, e, d) = gen_keys(nbits, getprime_func, accurate=accurate, exponent=exponent)
|
|
|
|
# Create the key objects
|
|
n = p * q
|
|
|
|
return (
|
|
PublicKey(n, e),
|
|
PrivateKey(n, e, d, p, q)
|
|
)
|
|
|
|
|
|
__all__ = ['PublicKey', 'PrivateKey', 'newkeys']
|
|
|
|
if __name__ == '__main__':
|
|
import doctest
|
|
|
|
try:
|
|
for count in range(100):
|
|
(failures, tests) = doctest.testmod()
|
|
if failures:
|
|
break
|
|
|
|
if (count % 10 == 0 and count) or count == 1:
|
|
print('%i times' % count)
|
|
except KeyboardInterrupt:
|
|
print('Aborted')
|
|
else:
|
|
print('Doctests done')
|