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