Add doctests to cryptomath_module

Added comprehensive doctests for find_mod_inverse function.

Contributes to #9943

Author: adrian-cancio

ciphers/cryptomath_module.py

@@ -1,7 +1,41 @@
+"""
+Cryptographic mathematics module for modular arithmetic operations.
+
+This module provides utilities for cryptographic computations,
+particularly modular multiplicative inverse.
+"""
+
 from maths.greatest_common_divisor import gcd_by_iterative
 
 
 def find_mod_inverse(a: int, m: int) -> int:
+    """
+    Find the modular multiplicative inverse of a modulo m.
+
+    The modular multiplicative inverse of a modulo m is an integer x
+    such that (a * x) % m == 1. This only exists when gcd(a, m) == 1.
+
+    Args:
+        a: The number to find the inverse of
+        m: The modulus
+
+    Returns:
+        The modular multiplicative inverse of a modulo m
+
+    Raises:
+        ValueError: If gcd(a, m) != 1 (inverse doesn't exist)
+
+    >>> find_mod_inverse(7, 26)
+    15
+    >>> find_mod_inverse(3, 11)
+    4
+    >>> find_mod_inverse(5, 17)
+    7
+    >>> find_mod_inverse(1, 5)
+    1
+    >>> find_mod_inverse(2, 7)
+    4
+    """
     if gcd_by_iterative(a, m) != 1:
         msg = f"mod inverse of {a!r} and {m!r} does not exist"
         raise ValueError(msg)