68 lines
1.6 KiB
Python
68 lines
1.6 KiB
Python
"""
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This module holds a fast Factorization class.
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"""
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from random import randint
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class Factorization:
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"""
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Simple module to factorize large numbers really quickly.
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"""
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@classmethod
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def factorize(cls, pq):
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"""
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Factorizes the given large integer.
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Implementation from https://comeoncodeon.wordpress.com/2010/09/18/pollard-rho-brent-integer-factorization/.
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:param pq: the prime pair pq.
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:return: a tuple containing the two factors p and q.
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"""
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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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p, q = g, pq // g
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return (p, q) if p < q else (q, p)
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@staticmethod
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def gcd(a, b):
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"""
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Calculates the Greatest Common Divisor.
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:param a: the first number.
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:param b: the second number.
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:return: GCD(a, b)
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"""
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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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