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PyBitmessage/rsa/key.py

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# -*- coding: utf-8 -*-
#
# Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
'''RSA key generation code.
Create new keys with the newkeys() function. It will give you a PublicKey and a
PrivateKey object.
Loading and saving keys requires the pyasn1 module. This module is imported as
late as possible, such that other functionality will remain working in absence
of pyasn1.
'''
import logging
from rsa._compat import b
import rsa.prime
import rsa.pem
import rsa.common
log = logging.getLogger(__name__)
class AbstractKey(object):
'''Abstract superclass for private and public keys.'''
@classmethod
def load_pkcs1(cls, keyfile, format='PEM'):
r'''Loads a key in PKCS#1 DER or PEM format.
:param keyfile: contents of a DER- or PEM-encoded file that contains
the public key.
:param format: the format of the file to load; 'PEM' or 'DER'
:return: a PublicKey object
'''
methods = {
'PEM': cls._load_pkcs1_pem,
'DER': cls._load_pkcs1_der,
}
if format not in methods:
formats = ', '.join(sorted(methods.keys()))
raise ValueError('Unsupported format: %r, try one of %s' % (format,
formats))
method = methods[format]
return method(keyfile)
def save_pkcs1(self, format='PEM'):
'''Saves the public key in PKCS#1 DER or PEM format.
:param format: the format to save; 'PEM' or 'DER'
:returns: the DER- or PEM-encoded public key.
'''
methods = {
'PEM': self._save_pkcs1_pem,
'DER': self._save_pkcs1_der,
}
if format not in methods:
formats = ', '.join(sorted(methods.keys()))
raise ValueError('Unsupported format: %r, try one of %s' % (format,
formats))
method = methods[format]
return method()
class PublicKey(AbstractKey):
'''Represents a public RSA key.
This key is also known as the 'encryption key'. It contains the 'n' and 'e'
values.
Supports attributes as well as dictionary-like access. Attribute accesss is
faster, though.
>>> PublicKey(5, 3)
PublicKey(5, 3)
>>> key = PublicKey(5, 3)
>>> key.n
5
>>> key['n']
5
>>> key.e
3
>>> key['e']
3
'''
__slots__ = ('n', 'e')
def __init__(self, n, e):
self.n = n
self.e = e
def __getitem__(self, key):
return getattr(self, key)
def __repr__(self):
return 'PublicKey(%i, %i)' % (self.n, self.e)
def __eq__(self, other):
if other is None:
return False
if not isinstance(other, PublicKey):
return False
return self.n == other.n and self.e == other.e
def __ne__(self, other):
return not (self == other)
@classmethod
def _load_pkcs1_der(cls, keyfile):
r'''Loads a key in PKCS#1 DER format.
@param keyfile: contents of a DER-encoded file that contains the public
key.
@return: a PublicKey object
First let's construct a DER encoded key:
>>> import base64
>>> b64der = 'MAwCBQCNGmYtAgMBAAE='
>>> der = base64.decodestring(b64der)
This loads the file:
>>> PublicKey._load_pkcs1_der(der)
PublicKey(2367317549, 65537)
'''
from pyasn1.codec.der import decoder
(priv, _) = decoder.decode(keyfile)
# ASN.1 contents of DER encoded public key:
#
# RSAPublicKey ::= SEQUENCE {
# modulus INTEGER, -- n
# publicExponent INTEGER, -- e
as_ints = tuple(int(x) for x in priv)
return cls(*as_ints)
def _save_pkcs1_der(self):
'''Saves the public key in PKCS#1 DER format.
@returns: the DER-encoded public key.
'''
from pyasn1.type import univ, namedtype
from pyasn1.codec.der import encoder
class AsnPubKey(univ.Sequence):
componentType = namedtype.NamedTypes(
namedtype.NamedType('modulus', univ.Integer()),
namedtype.NamedType('publicExponent', univ.Integer()),
)
# Create the ASN object
asn_key = AsnPubKey()
asn_key.setComponentByName('modulus', self.n)
asn_key.setComponentByName('publicExponent', self.e)
return encoder.encode(asn_key)
@classmethod
def _load_pkcs1_pem(cls, keyfile):
'''Loads a PKCS#1 PEM-encoded public key file.
The contents of the file before the "-----BEGIN RSA PUBLIC KEY-----" and
after the "-----END RSA PUBLIC KEY-----" lines is ignored.
@param keyfile: contents of a PEM-encoded file that contains the public
key.
@return: a PublicKey object
'''
der = rsa.pem.load_pem(keyfile, 'RSA PUBLIC KEY')
return cls._load_pkcs1_der(der)
def _save_pkcs1_pem(self):
'''Saves a PKCS#1 PEM-encoded public key file.
@return: contents of a PEM-encoded file that contains the public key.
'''
der = self._save_pkcs1_der()
return rsa.pem.save_pem(der, 'RSA PUBLIC KEY')
class PrivateKey(AbstractKey):
'''Represents a private RSA key.
This key is also known as the 'decryption key'. It contains the 'n', 'e',
'd', 'p', 'q' and other values.
Supports attributes as well as dictionary-like access. Attribute accesss is
faster, though.
>>> PrivateKey(3247, 65537, 833, 191, 17)
PrivateKey(3247, 65537, 833, 191, 17)
exp1, exp2 and coef don't have to be given, they will be calculated:
>>> pk = PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
>>> pk.exp1
55063
>>> pk.exp2
10095
>>> pk.coef
50797
If you give exp1, exp2 or coef, they will be used as-is:
>>> pk = PrivateKey(1, 2, 3, 4, 5, 6, 7, 8)
>>> pk.exp1
6
>>> pk.exp2
7
>>> pk.coef
8
'''
__slots__ = ('n', 'e', 'd', 'p', 'q', 'exp1', 'exp2', 'coef')
def __init__(self, n, e, d, p, q, exp1=None, exp2=None, coef=None):
self.n = n
self.e = e
self.d = d
self.p = p
self.q = q
# Calculate the other values if they aren't supplied
if exp1 is None:
self.exp1 = int(d % (p - 1))
else:
self.exp1 = exp1
if exp1 is None:
self.exp2 = int(d % (q - 1))
else:
self.exp2 = exp2
if coef is None:
self.coef = rsa.common.inverse(q, p)
else:
self.coef = coef
def __getitem__(self, key):
return getattr(self, key)
def __repr__(self):
return 'PrivateKey(%(n)i, %(e)i, %(d)i, %(p)i, %(q)i)' % self
def __eq__(self, other):
if other is None:
return False
if not isinstance(other, PrivateKey):
return False
return (self.n == other.n and
self.e == other.e and
self.d == other.d and
self.p == other.p and
self.q == other.q and
self.exp1 == other.exp1 and
self.exp2 == other.exp2 and
self.coef == other.coef)
def __ne__(self, other):
return not (self == other)
@classmethod
def _load_pkcs1_der(cls, keyfile):
r'''Loads a key in PKCS#1 DER format.
@param keyfile: contents of a DER-encoded file that contains the private
key.
@return: a PrivateKey object
First let's construct a DER encoded key:
>>> import base64
>>> b64der = 'MC4CAQACBQDeKYlRAgMBAAECBQDHn4npAgMA/icCAwDfxwIDANcXAgInbwIDAMZt'
>>> der = base64.decodestring(b64der)
This loads the file:
>>> PrivateKey._load_pkcs1_der(der)
PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
'''
from pyasn1.codec.der import decoder
(priv, _) = decoder.decode(keyfile)
# ASN.1 contents of DER encoded private key:
#
# RSAPrivateKey ::= SEQUENCE {
# version Version,
# modulus INTEGER, -- n
# publicExponent INTEGER, -- e
# privateExponent INTEGER, -- d
# prime1 INTEGER, -- p
# prime2 INTEGER, -- q
# exponent1 INTEGER, -- d mod (p-1)
# exponent2 INTEGER, -- d mod (q-1)
# coefficient INTEGER, -- (inverse of q) mod p
# otherPrimeInfos OtherPrimeInfos OPTIONAL
# }
if priv[0] != 0:
raise ValueError('Unable to read this file, version %s != 0' % priv[0])
as_ints = tuple(int(x) for x in priv[1:9])
return cls(*as_ints)
def _save_pkcs1_der(self):
'''Saves the private key in PKCS#1 DER format.
@returns: the DER-encoded private key.
'''
from pyasn1.type import univ, namedtype
from pyasn1.codec.der import encoder
class AsnPrivKey(univ.Sequence):
componentType = namedtype.NamedTypes(
namedtype.NamedType('version', univ.Integer()),
namedtype.NamedType('modulus', univ.Integer()),
namedtype.NamedType('publicExponent', univ.Integer()),
namedtype.NamedType('privateExponent', univ.Integer()),
namedtype.NamedType('prime1', univ.Integer()),
namedtype.NamedType('prime2', univ.Integer()),
namedtype.NamedType('exponent1', univ.Integer()),
namedtype.NamedType('exponent2', univ.Integer()),
namedtype.NamedType('coefficient', univ.Integer()),
)
# Create the ASN object
asn_key = AsnPrivKey()
asn_key.setComponentByName('version', 0)
asn_key.setComponentByName('modulus', self.n)
asn_key.setComponentByName('publicExponent', self.e)
asn_key.setComponentByName('privateExponent', self.d)
asn_key.setComponentByName('prime1', self.p)
asn_key.setComponentByName('prime2', self.q)
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.
@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.
'''
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')
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