First attempt at TelegramClient. Added fixes and doc

crypto/factorizator.py

@@ -0,0 +1,64 @@
+# This file is based on TLSharp
+# https://github.com/sochix/TLSharp/blob/master/TLSharp.Core/MTProto/Crypto/Factorizator.cs
+from random import randint
+
+
+class Factorizator:
+    @staticmethod
+    def find_small_multiplier_lopatin(what):
+        """Finds the small multiplier by using Lopatin's method"""
+        g = 0
+        for i in range(3):
+            q = (randint(0, 127) & 15) + 17
+            x = randint(0, 1000000000) + 1
+            y = x
+            lim = 1 << (i + 18)
+            for j in range(1, lim):
+                a, b, c = x, x, q
+                while b != 0:
+                    if (b & 1) != 0:
+                        c += a
+                        if c >= what:
+                            c -= what
+                    a += a
+                    if a >= what:
+                        a -= what
+                    b >>= 1
+
+                x = c
+                z = y - x if x < y else x - y
+                g = Factorizator.gcd(z, what)
+                if g != 1:
+                    break
+
+                if (j & (j - 1)) == 0:
+                    y = x
+
+            if g > 1:
+                break
+
+        p = what // g
+        return min(p, g)
+
+    @staticmethod
+    def gcd(a, b):
+        """Calculates the greatest common divisor"""
+        while a != 0 and b != 0:
+            while b & 1 == 0:
+                b >>= 1
+
+            while a & 1 == 0:
+                a >>= 1
+
+            if a > b:
+                a -= b
+            else:
+                b -= a
+
+        return a if b == 0 else b
+
+    @staticmethod
+    def factorize(pq):
+        """Factorizes the given number and returns both the divisor and the number divided by the divisor"""
+        divisor = Factorizator.find_small_multiplier_lopatin(pq)
+        return divisor, pq // divisor