Enhancing Playfair Cipher Security Using Chaotic Maps: A Comparative Analysis of Logistic, Hénon, and Arnold Cat Maps

Abstract

Today, classical encryption systems such as the Playfair cipher are easily broken in the current computing environment. Traditional ciphers based on digraph interactions cannot resist attacks using frequency analysis and pattern recognition, making them unsuitable for modern security. This work presents an improved Playfair cipher by integrating three chaotic maps—Logistic, Hénon, and Arnold Cat—to generate encryption keys dynamically and distort ciphertext. This integration creates a hybrid system that is highly secure yet computationally efficient. Experimental results using Shannon entropy and Lyapunov exponent metrics show clear performance advantages. The Hénon Map proves superior in randomness, achieving a Shannon entropy of 4.11257. The Arnold Cat Map, with a Lyapunov exponent of 0.89813, demonstrates strong sensitivity to initial conditions, preventing brute-force attacks. The Logistic Map provides a balanced compromise (entropy: 3.97695, Lyapunov: 0.63663) between security and resource efficiency. This approach augments the traditional Playfair cipher into a robust modern security solution, showing how classical cryptographic techniques combined with chaos theory can effectively meet contemporary digital security demands.