40 lines
924 B
Python
40 lines
924 B
Python
# Python Miller-Rabin implementation
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import random
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import lib.arithmetics as arithm
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def get_d_and_s(n: int) -> (int, int):
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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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d //= 2
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s += 1
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return (d, s)
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def rabin_witness(n: int, a: int) -> bool:
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d, s = get_d_and_s(n)
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x = arithm.modpow(a, d, n)
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if x == 1 or x == n - 1:
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return False
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for _ in range(s - 1):
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x = arithm.modpow(x, 2, n)
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if x == n - 1:
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return False
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return True
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def miller_rabin(n: int, k: int) -> bool:
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if n < 3: return False
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for _ in range(k):
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a = random.randint(2, n - 1)
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if rabin_witness(n, a): return False
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return True
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def is_prime(n: int) -> bool:
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return miller_rabin(n, 25)
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def get_random_prime(n: int) -> int:
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a = random.randint(2**(n-1), 2**(n) - 1)
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while not is_prime(a):
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a = random.randint(2**(n-1), 2**(n) - 1)
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return a
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