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miller_rabin.py
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miller_rabin.py
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'''
Created on Dec 4, 2011
@author: andrewkittredge
'''
from exponentiation import fast_exponentiation
import logging
import random
def miller_rabin(n, b):
'''Miller-Rabin test for primality.
'''
r = 0
m = n - 1
while m % 2 == 0:
r += 1
m = m / 2
if fast_exponentiation(b, m, n) in (n - 1, 1):
return True
power = 1
while power < r - 1:
b_m_squared_mod_n = fast_exponentiation(b, m * (2 ** power), n)
if b_m_squared_mod_n == 1:
return False
elif b_m_squared_mod_n == n - 1:
return True
else:
power = power * 2
return False
def check_primality_miller_rabin(n, attempts=20):
for _ in range(0, attempts):
b = random.randint(1, n - 1)
prime = miller_rabin(n, b)
if not prime:
break
return prime
import unittest
class Test(unittest.TestCase):
def test_miller_rabin(self):
for composite, base in ((1281, 41),
(1729, 10),
(3073, 1146),
(3201, 1163),
(3201, 1163),
(3585, 434),
(5377, 848)):
self.assertTrue(miller_rabin(composite, base))