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46 lines
1001 B
Python
46 lines
1001 B
Python
from random import randint
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class Factorization:
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@classmethod
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def factorize(cls, pq):
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if pq % 2 == 0:
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return 2, pq // 2
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y, c, m = randint(1, pq - 1), randint(1, pq - 1), randint(1, pq - 1)
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g = r = q = 1
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x = ys = 0
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while g == 1:
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x = y
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for i in range(r):
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y = (pow(y, 2, pq) + c) % pq
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k = 0
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while k < r and g == 1:
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ys = y
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for i in range(min(m, r - k)):
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y = (pow(y, 2, pq) + c) % pq
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q = q * (abs(x - y)) % pq
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g = cls.gcd(q, pq)
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k += m
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r *= 2
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if g == pq:
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while True:
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ys = (pow(ys, 2, pq) + c) % pq
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g = cls.gcd(abs(x - ys), pq)
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if g > 1:
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break
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return g, pq // g
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@staticmethod
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def gcd(a, b):
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while b:
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a, b = b, a % b
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return a
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