This file is indexed.

/usr/lib/python3/dist-packages/rsa/common.py is in python3-rsa 3.4.2-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
185
186
187
188
# -*- 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
#
#      https://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 https://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()