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83 lines
1.7 KiB
Python
83 lines
1.7 KiB
Python
'''
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This module implements simple prime generation and primality testing.
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'''
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from random import SystemRandom
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random = SystemRandom()
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from os import urandom
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def exp(x, n, m):
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'''Efficiently compute x ** n mod m'''
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y = 1
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z = x
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while n > 0:
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if n & 1:
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y = (y * z) % m
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z = (z * z) % m
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n //= 2
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return y
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# Miller-Rabin-Test
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def prime(n, k):
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'''Checks whether n is probably prime (with probability 1 - 4**(-k)'''
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if n % 2 == 0:
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return False
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d = n - 1
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s = 0
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while d % 2 == 0:
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s += 1
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d /= 2
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for i in xrange(k):
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a = long(2 + random.randint(0, n - 4))
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x = exp(a, d, n)
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if (x == 1) or (x == n - 1):
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continue
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for r in xrange(1, s):
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x = (x * x) % n
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if x == 1:
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return False
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if x == n - 1:
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break
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else:
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return False
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return True
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# Generate and Test Algorithms
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def get_prime(size, accuracy):
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'''Generate a pseudorandom prime number with the specified size (bytes).'''
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while 1:
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# read some random data from the operating system
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rstr = urandom(size - 1)
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r = 128 | ord(urandom(1)) # MSB = 1 (not less than size)
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for c in rstr:
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r = (r << 8) | ord(c)
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r |= 1 # LSB = 1 (odd)
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# test whether this results in a prime number
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if prime(r, accuracy):
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return r
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def get_prime_upto(n, accuracy):
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'''Find largest prime less than n'''
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n |= 1
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while n > 0:
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n -= 2
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if prime(n, accuracy):
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return n
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