/usr/lib/python3/dist-packages/rsa/common.py is in python3-rsa 3.2.3-1.1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 | # -*- 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.
'''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 _bit_size(number):
'''
Returns the number of bits required to hold a specific long number.
'''
if number < 0:
raise ValueError('Only nonnegative numbers possible: %s' % number)
if number == 0:
return 0
# This works, even with very large numbers. When using math.log(number, 2),
# you'll get rounding errors and it'll fail.
bits = 0
while number:
bits += 1
number >>= 1
return bits
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))
def extended_gcd(a, b):
'''Returns a tuple (r, i, j) such that r = gcd(a, b) = ia + jb
'''
# r = gcd(a,b) i = multiplicitive inverse of a mod b
# or j = multiplicitive inverse of b mod a
# Neg return values for i or j are made positive mod b or a respectively
# Iterateive Version is faster and uses much less stack space
x = 0
y = 1
lx = 1
ly = 0
oa = a #Remember original a/b to remove
ob = b #negative values from return results
while b != 0:
q = a // b
(a, b) = (b, a % b)
(x, lx) = ((lx - (q * x)),x)
(y, ly) = ((ly - (q * y)),y)
if (lx < 0): lx += ob #If neg wrap modulo orignal b
if (ly < 0): ly += oa #If neg wrap modulo orignal a
return (a, lx, ly) #Return only positive values
def inverse(x, n):
'''Returns x^-1 (mod n)
>>> inverse(7, 4)
3
>>> (inverse(143, 4) * 143) % 4
1
'''
(divider, inv, _) = extended_gcd(x, n)
if divider != 1:
raise ValueError("x (%d) and n (%d) are not relatively prime" % (x, n))
return inv
def crt(a_values, modulo_values):
'''Chinese Remainder Theorem.
Calculates x such that x = a[i] (mod m[i]) for each i.
:param a_values: the a-values of the above equation
:param modulo_values: the m-values of the above equation
:returns: x such that x = a[i] (mod m[i]) for each i
>>> crt([2, 3], [3, 5])
8
>>> crt([2, 3, 2], [3, 5, 7])
23
>>> crt([2, 3, 0], [7, 11, 15])
135
'''
m = 1
x = 0
for modulo in modulo_values:
m *= modulo
for (m_i, a_i) in zip(modulo_values, a_values):
M_i = m // m_i
inv = inverse(M_i, m_i)
x = (x + a_i * M_i * inv) % m
return x
if __name__ == '__main__':
import doctest
doctest.testmod()
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