Cryptography Assignment: Cipher Techniques and Probability Analysis

This document presents a comprehensive solution to a cryptography assignment, addressing a range of topics including Caesar and Vigenère ciphers, shift ciphers, and probability calculations. The solution includes step-by-step explanations for encrypting and decrypting messages using different ciphers, determining cipher keys, and analyzing ciphertext probabilities under various conditions (case-sensitive and insensitive). Furthermore, the assignment delves into key security, analyzing the impact of processor speed and key length on the time and probability of breaking an encryption scheme. The document also covers group theory concepts, specifically focusing on the members of groups Z5, Z7, Z9, Z5*, Z7*, and Z9*, and identifying primitive roots for modular arithmetic. The solutions provided are detailed and thorough, offering a complete understanding of each concept and problem.