Все подряд

.venv2/Lib/site-packages/telethon/crypto/factorization.py

@@ -0,0 +1,67 @@
+"""
+This module holds a fast Factorization class.
+"""
+from random import randint
+
+
+class Factorization:
+    """
+    Simple module to factorize large numbers really quickly.
+    """
+    @classmethod
+    def factorize(cls, pq):
+        """
+        Factorizes the given large integer.
+
+        Implementation from https://comeoncodeon.wordpress.com/2010/09/18/pollard-rho-brent-integer-factorization/.
+
+        :param pq: the prime pair pq.
+        :return: a tuple containing the two factors p and q.
+        """
+        if pq % 2 == 0:
+            return 2, pq // 2
+
+        y, c, m = randint(1, pq - 1), randint(1, pq - 1), randint(1, pq - 1)
+        g = r = q = 1
+        x = ys = 0
+
+        while g == 1:
+            x = y
+            for i in range(r):
+                y = (pow(y, 2, pq) + c) % pq
+
+            k = 0
+            while k < r and g == 1:
+                ys = y
+                for i in range(min(m, r - k)):
+                    y = (pow(y, 2, pq) + c) % pq
+                    q = q * (abs(x - y)) % pq
+
+                g = cls.gcd(q, pq)
+                k += m
+
+            r *= 2
+
+        if g == pq:
+            while True:
+                ys = (pow(ys, 2, pq) + c) % pq
+                g = cls.gcd(abs(x - ys), pq)
+                if g > 1:
+                    break
+
+        p, q = g, pq // g
+        return (p, q) if p < q else (q, p)
+
+    @staticmethod
+    def gcd(a, b):
+        """
+        Calculates the Greatest Common Divisor.
+
+        :param a: the first number.
+        :param b: the second number.
+        :return: GCD(a, b)
+        """
+        while b:
+            a, b = b, a % b
+
+        return a