/usr/lib/python3/dist-packages/rsa/prime.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 | # -*- 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.
'''Numerical functions related to primes.
Implementation based on the book Algorithm Design by Michael T. Goodrich and
Roberto Tamassia, 2002.
'''
__all__ = [ 'getprime', 'are_relatively_prime']
import rsa.randnum
def gcd(p, q):
'''Returns the greatest common divisor of p and q
>>> gcd(48, 180)
12
'''
while q != 0:
if p < q: (p,q) = (q,p)
(p,q) = (q, p % q)
return p
def jacobi(a, b):
'''Calculates the value of the Jacobi symbol (a/b) where both a and b are
positive integers, and b is odd
:returns: -1, 0 or 1
'''
assert a > 0
assert b > 0
if a == 0: return 0
result = 1
while a > 1:
if a & 1:
if ((a-1)*(b-1) >> 2) & 1:
result = -result
a, b = b % a, a
else:
if (((b * b) - 1) >> 3) & 1:
result = -result
a >>= 1
if a == 0: return 0
return result
def jacobi_witness(x, n):
'''Returns False if n is an Euler pseudo-prime with base x, and
True otherwise.
'''
j = jacobi(x, n) % n
f = pow(x, n >> 1, n)
if j == f: return False
return True
def randomized_primality_testing(n, k):
'''Calculates whether n is composite (which is always correct) or
prime (which is incorrect with error probability 2**-k)
Returns False if the number is composite, and True if it's
probably prime.
'''
# 50% of Jacobi-witnesses can report compositness of non-prime numbers
# The implemented algorithm using the Jacobi witness function has error
# probability q <= 0.5, according to Goodrich et. al
#
# q = 0.5
# t = int(math.ceil(k / log(1 / q, 2)))
# So t = k / log(2, 2) = k / 1 = k
# this means we can use range(k) rather than range(t)
for _ in range(k):
x = rsa.randnum.randint(n-1)
if jacobi_witness(x, n): return False
return True
def is_prime(number):
'''Returns True if the number is prime, and False otherwise.
>>> is_prime(42)
False
>>> is_prime(41)
True
'''
return randomized_primality_testing(number, 6)
def getprime(nbits):
'''Returns a prime number that can be stored in 'nbits' bits.
>>> p = getprime(128)
>>> is_prime(p-1)
False
>>> is_prime(p)
True
>>> is_prime(p+1)
False
>>> from rsa import common
>>> common.bit_size(p) == 128
True
'''
while True:
integer = rsa.randnum.read_random_int(nbits)
# Make sure it's odd
integer |= 1
# Test for primeness
if is_prime(integer):
return integer
# Retry if not prime
def are_relatively_prime(a, b):
'''Returns True if a and b are relatively prime, and False if they
are not.
>>> are_relatively_prime(2, 3)
1
>>> are_relatively_prime(2, 4)
0
'''
d = gcd(a, b)
return (d == 1)
if __name__ == '__main__':
print('Running doctests 1000x or until failure')
import doctest
for count in range(1000):
(failures, tests) = doctest.testmod()
if failures:
break
if count and count % 100 == 0:
print('%i times' % count)
print('Doctests done')
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