Digital Cosine Chaotic Map for Cryptographic Applications

Abstract

Despite having many similar characteristics with cryptography, existing chaotic systems have many security issues that negatively affect the chaos-based cryptographic algorithms that utilize them. This paper proposes a new chaotification method that enhances the chaotic complexity of existing chaotic maps to surmount these issues. The proposed method uses a cosine function alongside a chaotic map in a cascade system. To depict its advantages, we apply it to enhance logistic and Henon maps before analyzing their chaotic properties. Results and comparisons indicate that the new chaotic maps have a wider chaotic range, elevated sensitivity, complex characteristics, high nonlinearity, and an extended cycle length as compared to the original (seed) maps as well as other chaotic maps. We then utilize the modified maps (and their corresponding seed maps) to design simple pseudorandom number generators to study their feasibility when used in cryptographic algorithms. We perform comparisons between the generators derived from both the original and seed maps. Results show that generators based on the new maps outperform their seed counterparts in nearly every aspect. This finding demonstrates the capability of the proposed method in improving the performance of chaos-based cryptographic algorithms.