513 lines
15 KiB
Python
513 lines
15 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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"""Deprecated version of the RSA module
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.. deprecated:: 3.0
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This submodule is deprecated and will be completely removed as of version 4.0.
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"""
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__author__ = "Sybren Stuvel, Marloes de Boer, Ivo Tamboer, and Barry Mead"
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__date__ = "2010-02-08"
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__version__ = '2.0'
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import math
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import os
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import random
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import sys
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import types
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from rsa._compat import byte
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# Display a warning that this insecure version is imported.
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import warnings
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warnings.warn('Insecure version of the RSA module is imported as %s' % __name__)
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warnings.warn('This submodule is deprecated and will be completely removed as of version 4.0.',
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DeprecationWarning)
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def bit_size(number):
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"""Returns the number of bits required to hold a specific long number"""
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return int(math.ceil(math.log(number,2)))
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def gcd(p, q):
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"""Returns the greatest common divisor of p and q
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>>> gcd(48, 180)
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12
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"""
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# Iterateive Version is faster and uses much less stack space
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while q != 0:
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if p < q: (p,q) = (q,p)
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(p,q) = (q, p % q)
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return p
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def bytes2int(bytes):
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r"""Converts a list of bytes or a string to an integer
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"""
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if not (type(bytes) is types.ListType or type(bytes) is types.StringType):
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raise TypeError("You must pass a string or a list")
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# Convert byte stream to integer
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integer = 0
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for byte in bytes:
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integer *= 256
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if type(byte) is types.StringType: byte = ord(byte)
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integer += byte
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return integer
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def int2bytes(number):
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"""
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Converts a number to a string of bytes
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"""
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if not (type(number) is types.LongType or type(number) is types.IntType):
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raise TypeError("You must pass a long or an int")
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string = ""
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while number > 0:
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string = "%s%s" % (byte(number & 0xFF), string)
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number /= 256
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return string
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def to64(number):
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"""Converts a number in the range of 0 to 63 into base 64 digit
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character in the range of '0'-'9', 'A'-'Z', 'a'-'z','-','_'.
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"""
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if not (type(number) is types.LongType or type(number) is types.IntType):
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raise TypeError("You must pass a long or an int")
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if 0 <= number <= 9: #00-09 translates to '0' - '9'
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return byte(number + 48)
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if 10 <= number <= 35:
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return byte(number + 55) #10-35 translates to 'A' - 'Z'
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if 36 <= number <= 61:
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return byte(number + 61) #36-61 translates to 'a' - 'z'
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if number == 62: # 62 translates to '-' (minus)
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return byte(45)
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if number == 63: # 63 translates to '_' (underscore)
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return byte(95)
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raise ValueError('Invalid Base64 value: %i' % number)
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def from64(number):
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"""Converts an ordinal character value in the range of
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0-9,A-Z,a-z,-,_ to a number in the range of 0-63.
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"""
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if not (type(number) is types.LongType or type(number) is types.IntType):
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raise TypeError("You must pass a long or an int")
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if 48 <= number <= 57: #ord('0') - ord('9') translates to 0-9
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return(number - 48)
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if 65 <= number <= 90: #ord('A') - ord('Z') translates to 10-35
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return(number - 55)
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if 97 <= number <= 122: #ord('a') - ord('z') translates to 36-61
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return(number - 61)
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if number == 45: #ord('-') translates to 62
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return(62)
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if number == 95: #ord('_') translates to 63
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return(63)
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raise ValueError('Invalid Base64 value: %i' % number)
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def int2str64(number):
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"""Converts a number to a string of base64 encoded characters in
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the range of '0'-'9','A'-'Z,'a'-'z','-','_'.
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"""
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if not (type(number) is types.LongType or type(number) is types.IntType):
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raise TypeError("You must pass a long or an int")
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string = ""
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while number > 0:
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string = "%s%s" % (to64(number & 0x3F), string)
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number /= 64
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return string
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def str642int(string):
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"""Converts a base64 encoded string into an integer.
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The chars of this string in in the range '0'-'9','A'-'Z','a'-'z','-','_'
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"""
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if not (type(string) is types.ListType or type(string) is types.StringType):
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raise TypeError("You must pass a string or a list")
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integer = 0
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for byte in string:
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integer *= 64
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if type(byte) is types.StringType: byte = ord(byte)
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integer += from64(byte)
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return integer
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def read_random_int(nbits):
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"""Reads a random integer of approximately nbits bits rounded up
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to whole bytes"""
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nbytes = int(math.ceil(nbits/8.))
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randomdata = os.urandom(nbytes)
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return bytes2int(randomdata)
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def randint(minvalue, maxvalue):
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"""Returns a random integer x with minvalue <= x <= maxvalue"""
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# Safety - get a lot of random data even if the range is fairly
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# small
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min_nbits = 32
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# The range of the random numbers we need to generate
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range = (maxvalue - minvalue) + 1
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# Which is this number of bytes
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rangebytes = ((bit_size(range) + 7) / 8)
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# Convert to bits, but make sure it's always at least min_nbits*2
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rangebits = max(rangebytes * 8, min_nbits * 2)
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# Take a random number of bits between min_nbits and rangebits
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nbits = random.randint(min_nbits, rangebits)
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return (read_random_int(nbits) % range) + minvalue
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def jacobi(a, b):
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"""Calculates the value of the Jacobi symbol (a/b)
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where both a and b are positive integers, and b is odd
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"""
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if a == 0: return 0
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result = 1
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while a > 1:
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if a & 1:
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if ((a-1)*(b-1) >> 2) & 1:
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result = -result
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a, b = b % a, a
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else:
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if (((b * b) - 1) >> 3) & 1:
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result = -result
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a >>= 1
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if a == 0: return 0
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return result
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def jacobi_witness(x, n):
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"""Returns False if n is an Euler pseudo-prime with base x, and
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True otherwise.
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"""
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j = jacobi(x, n) % n
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f = pow(x, (n-1)/2, n)
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if j == f: return False
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return True
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def randomized_primality_testing(n, k):
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"""Calculates whether n is composite (which is always correct) or
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prime (which is incorrect with error probability 2**-k)
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Returns False if the number is composite, and True if it's
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probably prime.
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"""
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# 50% of Jacobi-witnesses can report compositness of non-prime numbers
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for i in range(k):
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x = randint(1, n-1)
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if jacobi_witness(x, n): return False
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return True
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def is_prime(number):
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"""Returns True if the number is prime, and False otherwise.
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"""
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if randomized_primality_testing(number, 6):
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# Prime, according to Jacobi
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return True
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# Not prime
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return False
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def getprime(nbits):
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"""Returns a prime number of max. 'math.ceil(nbits/8)*8' bits. In
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other words: nbits is rounded up to whole bytes.
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"""
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while True:
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integer = read_random_int(nbits)
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# Make sure it's odd
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integer |= 1
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# Test for primeness
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if is_prime(integer): break
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# Retry if not prime
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return integer
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def are_relatively_prime(a, b):
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"""Returns True if a and b are relatively prime, and False if they
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are not.
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>>> are_relatively_prime(2, 3)
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1
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>>> are_relatively_prime(2, 4)
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0
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"""
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d = gcd(a, b)
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return (d == 1)
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def find_p_q(nbits):
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"""Returns a tuple of two different primes of nbits bits"""
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pbits = nbits + (nbits/16) #Make sure that p and q aren't too close
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qbits = nbits - (nbits/16) #or the factoring programs can factor n
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p = getprime(pbits)
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while True:
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q = getprime(qbits)
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#Make sure p and q are different.
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if not q == p: break
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return (p, q)
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def extended_gcd(a, b):
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"""Returns a tuple (r, i, j) such that r = gcd(a, b) = ia + jb
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"""
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# r = gcd(a,b) i = multiplicitive inverse of a mod b
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# or j = multiplicitive inverse of b mod a
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# Neg return values for i or j are made positive mod b or a respectively
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# Iterateive Version is faster and uses much less stack space
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x = 0
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y = 1
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lx = 1
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ly = 0
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oa = a #Remember original a/b to remove
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ob = b #negative values from return results
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while b != 0:
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q = long(a/b)
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(a, b) = (b, a % b)
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(x, lx) = ((lx - (q * x)),x)
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(y, ly) = ((ly - (q * y)),y)
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if (lx < 0): lx += ob #If neg wrap modulo orignal b
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if (ly < 0): ly += oa #If neg wrap modulo orignal a
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return (a, lx, ly) #Return only positive values
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# Main function: calculate encryption and decryption keys
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def calculate_keys(p, q, nbits):
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"""Calculates an encryption and a decryption key for p and q, and
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returns them as a tuple (e, d)"""
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n = p * q
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phi_n = (p-1) * (q-1)
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while True:
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# Make sure e has enough bits so we ensure "wrapping" through
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# modulo n
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e = max(65537,getprime(nbits/4))
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if are_relatively_prime(e, n) and are_relatively_prime(e, phi_n): break
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(d, i, j) = extended_gcd(e, phi_n)
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if not d == 1:
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raise Exception("e (%d) and phi_n (%d) are not relatively prime" % (e, phi_n))
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if (i < 0):
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raise Exception("New extended_gcd shouldn't return negative values")
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if not (e * i) % phi_n == 1:
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raise Exception("e (%d) and i (%d) are not mult. inv. modulo phi_n (%d)" % (e, i, phi_n))
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return (e, i)
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def gen_keys(nbits):
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"""Generate RSA keys of nbits bits. Returns (p, q, e, d).
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Note: this can take a long time, depending on the key size.
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"""
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(p, q) = find_p_q(nbits)
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(e, d) = calculate_keys(p, q, nbits)
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return (p, q, e, d)
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def newkeys(nbits):
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"""Generates public and private keys, and returns them as (pub,
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priv).
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The public key consists of a dict {e: ..., , n: ....). The private
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key consists of a dict {d: ...., p: ...., q: ....).
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"""
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nbits = max(9,nbits) # Don't let nbits go below 9 bits
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(p, q, e, d) = gen_keys(nbits)
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return ( {'e': e, 'n': p*q}, {'d': d, 'p': p, 'q': q} )
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def encrypt_int(message, ekey, n):
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"""Encrypts a message using encryption key 'ekey', working modulo n"""
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if type(message) is types.IntType:
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message = long(message)
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if not type(message) is types.LongType:
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raise TypeError("You must pass a long or int")
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if message < 0 or message > n:
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raise OverflowError("The message is too long")
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#Note: Bit exponents start at zero (bit counts start at 1) this is correct
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safebit = bit_size(n) - 2 #compute safe bit (MSB - 1)
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message += (1 << safebit) #add safebit to ensure folding
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return pow(message, ekey, n)
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def decrypt_int(cyphertext, dkey, n):
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"""Decrypts a cypher text using the decryption key 'dkey', working
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modulo n"""
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message = pow(cyphertext, dkey, n)
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safebit = bit_size(n) - 2 #compute safe bit (MSB - 1)
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message -= (1 << safebit) #remove safebit before decode
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return message
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def encode64chops(chops):
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"""base64encodes chops and combines them into a ',' delimited string"""
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chips = [] #chips are character chops
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for value in chops:
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chips.append(int2str64(value))
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#delimit chops with comma
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encoded = ','.join(chips)
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return encoded
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def decode64chops(string):
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"""base64decodes and makes a ',' delimited string into chops"""
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chips = string.split(',') #split chops at commas
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chops = []
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for string in chips: #make char chops (chips) into chops
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chops.append(str642int(string))
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return chops
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def chopstring(message, key, n, funcref):
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"""Chops the 'message' into integers that fit into n,
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leaving room for a safebit to be added to ensure that all
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messages fold during exponentiation. The MSB of the number n
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is not independant modulo n (setting it could cause overflow), so
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use the next lower bit for the safebit. Therefore reserve 2-bits
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in the number n for non-data bits. Calls specified encryption
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function for each chop.
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Used by 'encrypt' and 'sign'.
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"""
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msglen = len(message)
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mbits = msglen * 8
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#Set aside 2-bits so setting of safebit won't overflow modulo n.
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nbits = bit_size(n) - 2 # leave room for safebit
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nbytes = nbits / 8
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blocks = msglen / nbytes
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if msglen % nbytes > 0:
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blocks += 1
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cypher = []
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for bindex in range(blocks):
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offset = bindex * nbytes
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block = message[offset:offset+nbytes]
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value = bytes2int(block)
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cypher.append(funcref(value, key, n))
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return encode64chops(cypher) #Encode encrypted ints to base64 strings
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def gluechops(string, key, n, funcref):
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"""Glues chops back together into a string. calls
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funcref(integer, key, n) for each chop.
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Used by 'decrypt' and 'verify'.
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"""
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message = ""
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chops = decode64chops(string) #Decode base64 strings into integer chops
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for cpart in chops:
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mpart = funcref(cpart, key, n) #Decrypt each chop
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message += int2bytes(mpart) #Combine decrypted strings into a msg
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return message
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def encrypt(message, key):
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"""Encrypts a string 'message' with the public key 'key'"""
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if 'n' not in key:
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raise Exception("You must use the public key with encrypt")
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return chopstring(message, key['e'], key['n'], encrypt_int)
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def sign(message, key):
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"""Signs a string 'message' with the private key 'key'"""
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if 'p' not in key:
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raise Exception("You must use the private key with sign")
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return chopstring(message, key['d'], key['p']*key['q'], encrypt_int)
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def decrypt(cypher, key):
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"""Decrypts a string 'cypher' with the private key 'key'"""
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if 'p' not in key:
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raise Exception("You must use the private key with decrypt")
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return gluechops(cypher, key['d'], key['p']*key['q'], decrypt_int)
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def verify(cypher, key):
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"""Verifies a string 'cypher' with the public key 'key'"""
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if 'n' not in key:
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raise Exception("You must use the public key with verify")
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return gluechops(cypher, key['e'], key['n'], decrypt_int)
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# Do doctest if we're not imported
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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__all__ = ["newkeys", "encrypt", "decrypt", "sign", "verify"]
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