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64 lines
2.0 KiB
Python
64 lines
2.0 KiB
Python
# Primality Testing with the Rabin-Miller Algorithm
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import random
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def rabinMiller(num):
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s = num - 1
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t = 0
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while s % 2 == 0:
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s = s // 2
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t += 1
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for trials in range(5):
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a = random.randrange(2, num - 1)
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v = pow(a, s, num)
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if v != 1:
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i = 0
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while v != (num - 1):
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if i == t - 1:
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return False
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else:
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i = i + 1
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v = (v ** 2) % num
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return True
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def isPrime(num):
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if (num < 2):
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return False
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lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
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61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
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131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191,
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193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257,
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263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331,
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337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401,
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409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
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479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563,
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569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631,
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641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709,
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719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
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809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
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881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967,
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971, 977, 983, 991, 997]
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if num in lowPrimes:
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return True
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for prime in lowPrimes:
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if (num % prime) == 0:
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return False
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return rabinMiller(num)
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def generateLargePrime(keysize = 1024):
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while True:
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num = random.randrange(2 ** (keysize - 1), 2 ** (keysize))
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if isPrime(num):
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return num
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if __name__ == '__main__':
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num = generateLargePrime()
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print(('Prime number:', num))
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print(('isPrime:', isPrime(num)))
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