582 lines
17 KiB
Python
582 lines
17 KiB
Python
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# -*- 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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# http://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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'''
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import logging
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from rsa._compat import b
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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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log = logging.getLogger(__name__)
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class AbstractKey(object):
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'''Abstract superclass for private and public keys.'''
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@classmethod
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def load_pkcs1(cls, keyfile, format='PEM'):
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r'''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 public key.
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:param format: the format of the file to load; 'PEM' or 'DER'
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:return: a PublicKey object
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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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if format not in methods:
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formats = ', '.join(sorted(methods.keys()))
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raise ValueError('Unsupported format: %r, try one of %s' % (format,
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formats))
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method = methods[format]
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return method(keyfile)
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def save_pkcs1(self, format='PEM'):
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'''Saves the public 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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:returns: the DER- or PEM-encoded public key.
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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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if format not in methods:
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formats = ', '.join(sorted(methods.keys()))
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raise ValueError('Unsupported format: %r, try one of %s' % (format,
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formats))
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method = methods[format]
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return method()
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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 accesss 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 __init__(self, n, e):
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self.n = n
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self.e = 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 __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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@classmethod
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def _load_pkcs1_der(cls, keyfile):
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r'''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.decodestring(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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(priv, _) = decoder.decode(keyfile)
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# ASN.1 contents of DER encoded public key:
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#
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# RSAPublicKey ::= SEQUENCE {
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# modulus INTEGER, -- n
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# publicExponent INTEGER, -- e
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as_ints = tuple(int(x) for x in priv)
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return cls(*as_ints)
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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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'''
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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 AsnPubKey(univ.Sequence):
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componentType = namedtype.NamedTypes(
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namedtype.NamedType('modulus', univ.Integer()),
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namedtype.NamedType('publicExponent', univ.Integer()),
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)
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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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'''
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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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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 accesss 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 don't have to be given, they 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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If you give exp1, exp2 or coef, they will be used as-is:
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>>> pk = PrivateKey(1, 2, 3, 4, 5, 6, 7, 8)
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>>> pk.exp1
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6
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>>> pk.exp2
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7
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>>> pk.coef
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8
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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, exp1=None, exp2=None, coef=None):
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self.n = n
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self.e = 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 the other values if they aren't supplied
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if exp1 is None:
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self.exp1 = int(d % (p - 1))
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else:
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self.exp1 = exp1
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if exp1 is None:
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self.exp2 = int(d % (q - 1))
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else:
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self.exp2 = exp2
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if coef is None:
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self.coef = rsa.common.inverse(q, p)
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else:
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self.coef = coef
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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 __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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@classmethod
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def _load_pkcs1_der(cls, keyfile):
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r'''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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@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.decodestring(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 = tuple(int(x) for x in priv[1:9])
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return cls(*as_ints)
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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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'''
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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)
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asn_key.setComponentByName('exponent2', self.exp2)
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asn_key.setComponentByName('coefficient', self.coef)
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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 private key file.
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The contents of the file before the "-----BEGIN RSA PRIVATE KEY-----" and
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after the "-----END RSA PRIVATE KEY-----" lines is ignored.
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@param keyfile: contents of a PEM-encoded file that contains the private
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key.
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@return: a PrivateKey object
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'''
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|
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.
|
||
|
|
'''
|
||
|
|
|
||
|
|
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(p, q, nbits):
|
||
|
|
'''Calculates an encryption and a decryption key given p and q, and
|
||
|
|
returns them as a tuple (e, d)
|
||
|
|
|
||
|
|
'''
|
||
|
|
|
||
|
|
phi_n = (p - 1) * (q - 1)
|
||
|
|
|
||
|
|
# A very common choice for e is 65537
|
||
|
|
e = 65537
|
||
|
|
|
||
|
|
try:
|
||
|
|
d = rsa.common.inverse(e, phi_n)
|
||
|
|
except ValueError:
|
||
|
|
raise ValueError("e (%d) and phi_n (%d) are not relatively prime" %
|
||
|
|
(e, phi_n))
|
||
|
|
|
||
|
|
if (e * d) % phi_n != 1:
|
||
|
|
raise ValueError("e (%d) and d (%d) are not mult. inv. modulo "
|
||
|
|
"phi_n (%d)" % (e, d, phi_n))
|
||
|
|
|
||
|
|
return (e, d)
|
||
|
|
|
||
|
|
def gen_keys(nbits, getprime_func, accurate=True):
|
||
|
|
'''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.
|
||
|
|
'''
|
||
|
|
|
||
|
|
(p, q) = find_p_q(nbits // 2, getprime_func, accurate)
|
||
|
|
(e, d) = calculate_keys(p, q, nbits // 2)
|
||
|
|
|
||
|
|
return (p, q, e, d)
|
||
|
|
|
||
|
|
def newkeys(nbits, accurate=True, poolsize=1):
|
||
|
|
'''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.
|
||
|
|
|
||
|
|
: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)
|
||
|
|
|
||
|
|
# 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 and count % 10 == 0) or count == 1:
|
||
|
|
print('%i times' % count)
|
||
|
|
except KeyboardInterrupt:
|
||
|
|
print('Aborted')
|
||
|
|
else:
|
||
|
|
print('Doctests done')
|