Apr 07, 2014
之前那会上班的时候，正好要用到RSA加密解密，
然后我出于偷懒的目的，所以我就百度了一个RSA的模块。
虽然python在大数运算上灰常容易，但是那个PKCS#1 v1.5想想就觉得麻烦~
所以直接用了人家的RSA模块。
介个是地址:https://pypi.python.org/pypi/rsa/
这个RSA模块真的是灰常强大啊，好厉害啊
These are some average timings from my desktop machine (Linux 2.6, 2.93 GHz quad-core Intel Core i7, 16 GB RAM) using 64-bit CPython 2.7. Since key generation is a random process, times may differ even on similar hardware. On all tests, we used the default accurate=True.
Keysize (bits)|single process|eight processes
128|0.01 sec.|0.01 sec.
256|0.03 sec.|0.02 sec.
384|0.09 sec.|0.04 sec.
512|0.11 sec.|0.07 sec.
1024|0.79 sec.|0.30 sec.
2048|6.55 sec.|1.60 sec.
3072|23.4 sec.|7.14 sec.
4096 |72.0 sec.|24.4 sec.
但是捏，由于我只做加密解密，用不到密钥的生成，所以为了加密解密带上一个包的RSA模块又觉得说不过去。
于是，在偷懒中，我对这个RSA的3.1.4版本进行了简单的精简，去除了密钥生成，只保留了加密解密部分代码，并且，将一个py包精简为一个py文件。由于很懒，所以精简的很随意，如果路过的大大们需要这样一个简单的RSALite包，就拿去吧~Tips:精简后，仍是基于PKCS#1 v1.5。
如果我的不成熟的代码能够帮到您，请[[戳我]][1]获得它
#! /usr/bin/env python
# -*- coding: utf-8 -*-
#
# rsalite by ino@o3or.com
#===========================================================================
# 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.
#===========================================================================
"""
RSALite module
Module for calculating large primes, and RSA encryption, decryption.
not includes generating public and private keys.
"""
from __future__ import absolute_import
import sys
import binascii
import hashlib
import os
from struct import pack
__author__ = "Sybren Stuvel, Barry Mead and Yesudeep Mangalapilly | lite by ino"
__date__ = "2014-03-28"
__version__ = '3.1.4lite'
# ===========================================================================
#"""Python compatibility wrappers."""
try:
MAX_INT = sys.maxsize
except AttributeError:
MAX_INT = sys.maxint
MAX_INT64 = (1 << 63) - 1
MAX_INT32 = (1 << 31) - 1
MAX_INT16 = (1 << 15) - 1
# Determine the word size of the processor.
if MAX_INT == MAX_INT64:
# 64-bit processor.
MACHINE_WORD_SIZE = 64
elif MAX_INT == MAX_INT32:
# 32-bit processor.
MACHINE_WORD_SIZE = 32
else:
# Else we just assume 64-bit processor keeping up with modern times.
MACHINE_WORD_SIZE = 64
try:
# < Python3
unicode_type = unicode
have_python3 = False
except NameError:
# Python3.
unicode_type = str
have_python3 = True
# Fake byte literals.
if str is unicode_type:
def byte_literal(s):
return s.encode('latin1')
else:
def byte_literal(s):
return s
# ``long`` is no more. Do type detection using this instead.
try:
integer_types = (int, long)
except NameError:
integer_types = (int,)
b = byte_literal
# To avoid calling b() multiple times in tight loops.
ZERO_BYTE = b('\x00')
EMPTY_BYTE = b('')
def is_integer(obj):
"""
Determines whether the given value is an integer.
:param obj:
The value to test.
:returns:
``True`` if ``value`` is an integer; ``False`` otherwise.
"""
return isinstance(obj, integer_types)
def get_word_alignment(num, force_arch=64,
_machine_word_size=MACHINE_WORD_SIZE):
"""
Returns alignment details for the given number based on the platform
Python is running on.
:param num:
Unsigned integral number.
:param force_arch:
If you don't want to use 64-bit unsigned chunks, set this to
anything other than 64. 32-bit chunks will be preferred then.
Default 64 will be used when on a 64-bit machine.
:param _machine_word_size:
(Internal) The machine word size used for alignment.
:returns:
4-tuple::
(word_bits, word_bytes,
max_uint, packing_format_type)
"""
max_uint64 = 0xffffffffffffffff
max_uint32 = 0xffffffff
max_uint16 = 0xffff
max_uint8 = 0xff
if force_arch == 64 and _machine_word_size >= 64 and num > max_uint32:
# 64-bit unsigned integer.
return 64, 8, max_uint64, "Q"
elif num > max_uint16:
# 32-bit unsigned integer
return 32, 4, max_uint32, "L"
elif num > max_uint8:
# 16-bit unsigned integer.
return 16, 2, max_uint16, "H"
else:
# 8-bit unsigned integer.
return 8, 1, max_uint8, "B"
# ===========================================================================
# '''Common functionality shared by several modules.'''
def bit_size(num):
'''
Number of bits needed to represent a integer excluding any prefix
0 bits.
As per definition from http://wiki.python.org/moin/BitManipulation and
to match the behavior of the Python 3 API.
Usage::
>>> bit_size(1023)
10
>>> bit_size(1024)
11
>>> bit_size(1025)
11
:param num:
Integer value. If num is 0, returns 0. Only the absolute value of the
number is considered. Therefore, signed integers will be abs(num)
before the number's bit length is determined.
:returns:
Returns the number of bits in the integer.
'''
if num == 0:
return 0
if num < 0:
num = -num
# Make sure this is an int and not a float.
num & 1
hex_num = "%x" % num
return ((len(hex_num) - 1) * 4) + {
'0':0, '1':1, '2':2, '3':2,
'4':3, '5':3, '6':3, '7':3,
'8':4, '9':4, 'a':4, 'b':4,
'c':4, 'd':4, 'e':4, 'f':4,
}[hex_num[0]]
def byte_size(number):
'''
Returns the number of bytes required to hold a specific long number.
The number of bytes is rounded up.
Usage::
>>> byte_size(1 << 1023)
128
>>> byte_size((1 << 1024) - 1)
128
>>> byte_size(1 << 1024)
129
:param number:
An unsigned integer
:returns:
The number of bytes required to hold a specific long number.
'''
quanta, mod = divmod(bit_size(number), 8)
if mod or number == 0:
quanta += 1
return quanta
#return int(math.ceil(bit_size(number) / 8.0))
# ===========================================================================
#'''Core mathematical operations.
#This is the actual core RSA implementation, which is only defined
#mathematically on integers.
#'''
def assert_int(var, name):
if is_integer(var):
return
raise TypeError('%s should be an integer, not %s' % (name, var.__class__))
def encrypt_int(message, ekey, n):
'''Encrypts a message using encryption key 'ekey', working modulo n'''
assert_int(message, 'message')
assert_int(ekey, 'ekey')
assert_int(n, 'n')
if message < 0:
raise ValueError('Only non-negative numbers are supported')
if message > n:
raise OverflowError("The message %i is too long for n=%i" % (message, n))
return pow(message, ekey, n)
def decrypt_int(cyphertext, dkey, n):
'''Decrypts a cypher text using the decryption key 'dkey', working
modulo n'''
assert_int(cyphertext, 'cyphertext')
assert_int(dkey, 'dkey')
assert_int(n, 'n')
message = pow(cyphertext, dkey, n)
return message
# ===========================================================================
#'''Data transformation functions.
#From bytes to a number, number to bytes, etc.
#'''
try:
# We'll use psyco if available on 32-bit architectures to speed up code.
# Using psyco (if available) cuts down the execution time on Python 2.5
# at least by half.
import psyco
psyco.full()
except ImportError:
pass
def bytes2int(raw_bytes):
r'''Converts a list of bytes or an 8-bit string to an integer.
When using unicode strings, encode it to some encoding like UTF8 first.
>>> (((128 * 256) + 64) * 256) + 15
8405007
>>> bytes2int('\x80@\x0f')
8405007
'''
return int(binascii.hexlify(raw_bytes), 16)
def bytes_leading(raw_bytes, needle=ZERO_BYTE):
'''
Finds the number of prefixed byte occurrences in the haystack.
Useful when you want to deal with padding.
:param raw_bytes:
Raw bytes.
:param needle:
The byte to count. Default \000.
:returns:
The number of leading needle bytes.
'''
leading = 0
# Indexing keeps compatibility between Python 2.x and Python 3.x
_byte = needle[0]
for x in raw_bytes:
if x == _byte:
leading += 1
else:
break
return leading
def int2bytes(number, fill_size=None, chunk_size=None, overflow=False):
'''
Convert an unsigned integer to bytes (base-256 representation)::
Does not preserve leading zeros if you don't specify a chunk size or
fill size.
.. NOTE:
You must not specify both fill_size and chunk_size. Only one
of them is allowed.
:param number:
Integer value
:param fill_size:
If the optional fill size is given the length of the resulting
byte string is expected to be the fill size and will be padded
with prefix zero bytes to satisfy that length.
:param chunk_size:
If optional chunk size is given and greater than zero, pad the front of
the byte string with binary zeros so that the length is a multiple of
``chunk_size``.
:param overflow:
``False`` (default). If this is ``True``, no ``OverflowError``
will be raised when the fill_size is shorter than the length
of the generated byte sequence. Instead the byte sequence will
be returned as is.
:returns:
Raw bytes (base-256 representation).
:raises:
``OverflowError`` when fill_size is given and the number takes up more
bytes than fit into the block. This requires the ``overflow``
argument to this function to be set to ``False`` otherwise, no
error will be raised.
'''
if number < 0:
raise ValueError("Number must be an unsigned integer: %d" % number)
if fill_size and chunk_size:
raise ValueError("You can either fill or pad chunks, but not both")
# Ensure these are integers.
number & 1
raw_bytes = b('')
# Pack the integer one machine word at a time into bytes.
num = number
word_bits, _, max_uint, pack_type = get_word_alignment(num)
pack_format = ">%s" % pack_type
while num > 0:
raw_bytes = pack(pack_format, num & max_uint) + raw_bytes
num >>= word_bits
# Obtain the index of the first non-zero byte.
zero_leading = bytes_leading(raw_bytes)
if number == 0:
raw_bytes = ZERO_BYTE
# De-padding.
raw_bytes = raw_bytes[zero_leading:]
length = len(raw_bytes)
if fill_size and fill_size > 0:
if not overflow and length > fill_size:
raise OverflowError(
"Need %d bytes for number, but fill size is %d" %
(length, fill_size)
)
raw_bytes = raw_bytes.rjust(fill_size, ZERO_BYTE)
elif chunk_size and chunk_size > 0:
remainder = length % chunk_size
if remainder:
padding_size = chunk_size - remainder
raw_bytes = raw_bytes.rjust(length + padding_size, ZERO_BYTE)
return raw_bytes
# ===========================================================================
#'''RSA key 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.
#'''
class PublicKey():
'''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)
class PrivateKey():
'''Represents a private RSA key.
This key is also known as the 'decryption key'. It contains the 'n', 'e',
'd'.
Supports attributes as well as dictionary-like access. Attribute accesss is
faster, though.
>>> PrivateKey(3247, 65537, 833)
PrivateKey(3247, 65537, 833)
'''
__slots__ = ('n', 'e', 'd')
def __init__(self, n, e, d):
self.n = n
self.e = e
self.d = d
def __getitem__(self, key):
return getattr(self, key)
def __repr__(self):
return 'PrivateKey(%(n)i, %(e)i, %(d)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)
def __ne__(self, other):
return not (self == other)
# ===========================================================================
#'''Functions for PKCS#1 version 1.5 encryption and signing
#This module implements certain functionality from PKCS#1 version 1.5. For a
#very clear example, read http://www.di-mgt.com.au/rsa_alg.html#pkcs1schemes
#At least 8 bytes of random padding is used when encrypting a message. This makes
#these methods much more secure than the ones in the ``rsa`` module.
#WARNING: this module leaks information when decryption or verification fails.
#The exceptions that are raised contain the Python traceback information, which
#can be used to deduce where in the process the failure occurred. DO NOT PASS
#SUCH INFORMATION to your users.
#'''
class CryptoError(Exception):
'''Base class for all exceptions in this module.'''
class DecryptionError(CryptoError):
'''Raised when decryption fails.'''
def _pad_for_encryption(message, target_length):
r'''Pads the message for encryption, returning the padded message.
:return: 00 02 RANDOM_DATA 00 MESSAGE
>>> block = _pad_for_encryption('hello', 16)
>>> len(block)
16
>>> block[0:2]
'\x00\x02'
>>> block[-6:]
'\x00hello'
'''
max_msglength = target_length - 11
msglength = len(message)
if msglength > max_msglength:
raise OverflowError('%i bytes needed for message, but there is only'
' space for %i' % (msglength, max_msglength))
# Get random padding
padding = b('')
padding_length = target_length - msglength - 3
# We remove 0-bytes, so we'll end up with less padding than we've asked for,
# so keep adding data until we're at the correct length.
while len(padding) < padding_length:
needed_bytes = padding_length - len(padding)
# Always read at least 8 bytes more than we need, and trim off the rest
# after removing the 0-bytes. This increases the chance of getting
# enough bytes, especially when needed_bytes is small
new_padding = os.urandom(needed_bytes + 5)
new_padding = new_padding.replace(b('\x00'), b(''))
padding = padding + new_padding[:needed_bytes]
assert len(padding) == padding_length
return b('').join([b('\x00\x02'),
padding,
b('\x00'),
message])
def encrypt(message, pub_key):
'''Encrypts the given message using PKCS#1 v1.5
:param message: the message to encrypt. Must be a byte string no longer than
``k-11`` bytes, where ``k`` is the number of bytes needed to encode
the ``n`` component of the public key.
:param pub_key: the :py:class:`rsa.PublicKey` to encrypt with.
:raise OverflowError: when the message is too large to fit in the padded
block.
>>> pub_key = PublicKey(n, e)
>>> message = 'hello'
>>> crypto = encrypt(message, pub_key)
The crypto text should be just as long as the public key 'n' component:
'''
keylength = byte_size(pub_key.n)
padded = _pad_for_encryption(message, keylength)
payload = bytes2int(padded)
encrypted = encrypt_int(payload, pub_key.e, pub_key.n)
block = int2bytes(encrypted, keylength)
return block
def decrypt(crypto, priv_key):
r'''Decrypts the given message using PKCS#1 v1.5
The decryption is considered 'failed' when the resulting cleartext doesn't
start with the bytes 00 02, or when the 00 byte between the padding and
the message cannot be found.
:param crypto: the crypto text as returned by :py:func:`rsa.encrypt`
:param priv_key: the :py:class:`rsa.PrivateKey` to decrypt with.
:raise DecryptionError: when the decryption fails. No details are given as
to why the code thinks the decryption fails, as this would leak
information about the private key.
>>> pub_key = PublicKey(n, e)
>>> priv_key = PrivateKey(n,e,d)
It works with strings:
>>> crypto = encrypt('hello', pub_key)
>>> decrypt(crypto, priv_key)
'hello'
And with binary data:
>>> crypto = encrypt('\x00\x00\x00\x00\x01', pub_key)
>>> decrypt(crypto, priv_key)
'\x00\x00\x00\x00\x01'
.. warning::
Never display the stack trace of a
:py:class:`rsa.pkcs1.DecryptionError` exception. It shows where in the
code the exception occurred, and thus leaks information about the key.
It's only a tiny bit of information, but every bit makes cracking the
keys easier.
>>> crypto = encrypt('hello', pub_key)
>>> crypto = crypto[0:5] + 'X' + crypto[6:] # change a byte
>>> decrypt(crypto, priv_key)
Traceback (most recent call last):
...
DecryptionError: Decryption failed
'''
blocksize = byte_size(priv_key.n)
encrypted = bytes2int(crypto)
decrypted = decrypt_int(encrypted, priv_key.d, priv_key.n)
cleartext = int2bytes(decrypted, blocksize)
# If we can't find the cleartext marker, decryption failed.
if cleartext[0:2] != b('\x00\x02'):
raise DecryptionError('Decryption failed')
# Find the 00 separator between the padding and the message
try:
sep_idx = cleartext.index(b('\x00'), 2)
except ValueError:
raise DecryptionError('Decryption failed')
return cleartext[sep_idx+1:]
# ===========================================================================
大概就是这个样子啦(✿◡‿◡)
额，下面放一个简单的应用示例：
因为RSA加密后不一定是可读的，所以在这个例子里，我在RSA后加了一个base64为了方便显示传输~
# /usr/bin/env python
#-*- coding:utf8 -*-
import rsalite
import base64
import datetime
"""
rsalite pkcs#1 v1.5 + base64
"""
def encrypt(message, n, e):
pub_key = rsalite.PublicKey(n, e)
return base64.b64encode(rsalite.encrypt(message, pub_key))
def decrypt(crypto, n, e, d):
priv_key = rsalite.PrivateKey(n, e, d)
return rsalite.decrypt(base64.b64decode(crypto), priv_key)
if __name__=="__main__":
message = "睡个午觉好咯"
n = 110945963084729473086130203053960579550327729658653847757740988437942109564961023146972997505984588276879603057313266311940033330197319153582130175907476828376116030185974931539273268251822428164938194795044377834219803829324792738562530352716088675074468303811597376036491268631231669325065321536138026294537
e = 65537
d = 30172114989382080333461992600069264832468546404415635878758832978766837340377196324953838816991368491978960973045674130303602759419973744210053956165203764840228493876500545273584837106269531589946013642765942133471280266654547841324173913630308073510056590061826558556761211357514740191416959593086511172993
crypto = encrypt(message, n, e)
print "A :", message
print "B :", crypto
print "A~:", decrypt(crypto, n, e, d)