From a8b05c2320a68cb82a26c697914e53cf32bfcfda Mon Sep 17 00:00:00 2001
From: geoffrey <geoffrey.bucchino@protonmail.com>
Date: Wed, 11 Feb 2026 17:18:55 +0100
Subject: [PATCH] Add bin expo functions and update docs

---
 Cryptotools/Utils/utils.py |  52 ++++++++++++++++++++++++++++++++++++-
 docs/index.md              |   2 ++
 docs/utils.md              |   3 +++
 mkdocs.yml                 |   2 ++
 site/index.html            |   2 +-
 site/sitemap.xml.gz        | Bin 127 -> 127 bytes
 6 files changed, 59 insertions(+), 2 deletions(-)
 create mode 100644 docs/utils.md

diff --git a/Cryptotools/Utils/utils.py b/Cryptotools/Utils/utils.py
index 9090efe..4b87c04 100644
--- a/Cryptotools/Utils/utils.py
+++ b/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)
diff --git a/docs/index.md b/docs/index.md
index b575c8e..f434fae 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -7,6 +7,8 @@
     * [Group Theory](/group-theory)
 * Public Keys:
     * [RSA](/rsa)
+* Utils
+    * [Utils](/utils)
 * Examples:
     * [Generating RSA keys](/examples-rsa-keys)
 
diff --git a/docs/utils.md b/docs/utils.md
new file mode 100644
index 0000000..d97e9fd
--- /dev/null
+++ b/docs/utils.md
@@ -0,0 +1,3 @@
+CryptoTools provides several utils function wich can be used for cryptography purposes
+
+::: Cryptotools.Utils.utils
diff --git a/mkdocs.yml b/mkdocs.yml
index 04cebae..f04ea4d 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -13,5 +13,7 @@ nav:
     - Group theory: group-theory.md
   - Public Keys:
     - RSA: rsa.md
+  - Utils:
+    - Utils: utils.md
   - Examples:
     - Generating RSA Keys: examples-rsa-keys.md 
diff --git a/site/index.html b/site/index.html
index b2600a2..87dfc67 100644
--- a/site/index.html
+++ b/site/index.html
@@ -144,5 +144,5 @@
 
 <!--
 MkDocs version : 1.6.1
-Build Date UTC : 2026-01-06 07:48:31.465035+00:00
+Build Date UTC : 2026-02-11 16:14:17.229949+00:00
 -->
diff --git a/site/sitemap.xml.gz b/site/sitemap.xml.gz
index d0bfde9ed880dae009f7fc1d8bb38efd3a74e72b..a7f3a5c62b68f6f7e0866da58ffd8d36aedca294 100644
GIT binary patch
delta 13
Ucmb=gXP58h;AlA3J(0Zv03MYDp#T5?

delta 13
Ucmb=gXP58h;AjYlnaExN02_+~`~Uy|