/usr/lib/python3/dist-packages/rsa/prime.py is in python3-rsa 3.4.2-1.
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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 | # -*- 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.
"""Numerical functions related to primes.
Implementation based on the book Algorithm Design by Michael T. Goodrich and
Roberto Tamassia, 2002.
"""
import rsa.randnum
__all__ = ['getprime', 'are_relatively_prime']
def gcd(p, q):
"""Returns the greatest common divisor of p and q
>>> gcd(48, 180)
12
"""
while q != 0:
(p, q) = (q, p % q)
return p
def miller_rabin_primality_testing(n, k):
"""Calculates whether n is composite (which is always correct) or prime
(which theoretically is incorrect with error probability 4**-k), by
applying Miller-Rabin primality testing.
For reference and implementation example, see:
https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
:param n: Integer to be tested for primality.
:type n: int
:param k: Number of rounds (witnesses) of Miller-Rabin testing.
:type k: int
:return: False if the number is composite, True if it's probably prime.
:rtype: bool
"""
# prevent potential infinite loop when d = 0
if n < 2:
return False
# Decompose (n - 1) to write it as (2 ** r) * d
# While d is even, divide it by 2 and increase the exponent.
d = n - 1
r = 0
while not (d & 1):
r += 1
d >>= 1
# Test k witnesses.
for _ in range(k):
# Generate random integer a, where 2 <= a <= (n - 2)
a = rsa.randnum.randint(n - 4) + 2
x = pow(a, d, n)
if x == 1 or x == n - 1:
continue
for _ in range(r - 1):
x = pow(x, 2, n)
if x == 1:
# n is composite.
return False
if x == n - 1:
# Exit inner loop and continue with next witness.
break
else:
# If loop doesn't break, n is composite.
return False
return True
def is_prime(number):
"""Returns True if the number is prime, and False otherwise.
>>> is_prime(2)
True
>>> is_prime(42)
False
>>> is_prime(41)
True
>>> [x for x in range(901, 1000) if is_prime(x)]
[907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
"""
# Check for small numbers.
if number < 10:
return number in [2, 3, 5, 7]
# Check for even numbers.
if not (number & 1):
return False
# According to NIST FIPS 186-4, Appendix C, Table C.3, minimum number of
# rounds of M-R testing, using an error probability of 2 ** (-100), for
# different p, q bitsizes are:
# * p, q bitsize: 512; rounds: 7
# * p, q bitsize: 1024; rounds: 4
# * p, q bitsize: 1536; rounds: 3
# See: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
return miller_rabin_primality_testing(number, 7)
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
"""
assert nbits > 3 # the loop wil hang on too small numbers
while True:
integer = rsa.randnum.read_random_odd_int(nbits)
# 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)
True
>>> are_relatively_prime(2, 4)
False
"""
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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