Chaotification Methods For Enhancing One-Dimension Digital Chaotic Maps For Applications In Cryptography - Alawida, Moatsum Khalif Oduh (2022)
Digital one-dimensional chaotic maps are becoming increasingly popular in the area of cryptography due to their commonalities and their simple structures. However, these maps have well-known drawbacks which contribute negatively towards the security of the cryptographic algorithms that utilize them. Thus, enhancing digital one-dimensional chaotic maps in terms of their chaoticity and statistical properties will contribute towards the improvement of chaos-based cryptography. Many chaotification methods have been recently proposed to address these issues. However, most of these methods are dependent on an external entropy source to enhance the characteristics of one-dimensional chaotic maps. In this study, four novel chaotification methods are proposed to address these issues without the need of external entropy sources. The first method hybridizes deterministic finite state automata with one-dimensional chaotic maps under control the existing chaotification methods. The aim of this method is to weaken dynamical degradation issue through prolonging cycle length. To increase chaotic complexity and enlarge chaotic parameter range, the second method is proposed based on modifying chaotic state values by reversing the order of their fractional bits. To take advantage of the first two proposed methods, the third method is proposed based on a one-dimensional chaotic map and deterministic finite state machine under the control of bitwise permutations. The fourth method is introduced based on cascade and combination methods as a simple framework to enlarge the chaotic parameter range and to enhance chaotic performance.