Add bin expo functions and update docs

Cryptotools/Utils/utils.py

@@ -31,4 +31,54 @@ def egcd(a, b):
     x = y1 - (b // a) * x1
     y = x1
     return gcd, x, y
-    
+
+def bin_expo(n, e) -> int:
+    """
+        This function perform an binary exponentiation, also known as Exponentiation squaring.
+        A binary exponentiation is the process for computing an integer power of a number, such as a ** n.
+        For doing that, the first step is to convert the exponent into a binary representation
+        And for each 1 bit, we compute the exponent.
+
+        Args:
+            n (Integer): it's the base
+            e (Integer): it's the exponent
+
+        Returns:
+            Return the result of the exponentation of n ** e
+
+    """
+    binary = bin(e)[2:] # Remove the prefix 0b
+
+    r = 1
+    exp = 1
+    # We need to reverse, and to start from the right to left
+    # Otherwise, we do on left to the right
+    # It's dirty, maybe we can find another way to do that
+    for b in binary[::-1]:
+        if b == '1':
+            r *= n ** exp
+            print(n ** exp, exp)
+        exp *= 2
+    return r
+
+def exponent_squaring(n, e):
+    """
+        This function perform an exponentiation squaring, which compute an integer power of a number based on the following algorithm:
+            n ** e = {
+                1                               # if n is 0
+                (n ** (e / 2)) ** 2             # if n is even
+                ((n ** (e - 1 / 2)) ** 2) * n   # if n is odd
+            }
+
+        Args:
+            n (Integer): n is the base of n ** e
+            e (Integer): e is the exponent
+    """
+    if e < 0:
+        return exponent_squaring(1 / n, -e)
+    elif e == 0:
+        return 1
+    elif e % 2 == 1: # n is odd
+        return exponent_squaring(n * n, (e - 1) / 2) * n
+    elif e % 2 == 0: # n is even
+        return exponent_squaring(n * n, e / 2)