Enhancing unimodal digital chaotic maps through hybridisation

Abstract

Despite sharing many similar properties with cryptography, digitizing chaotic maps for the purpose of developing chaos-based cryptosystems leads to dynamical degradation, causing many security issues. This paper introduces a hybrid chaotic system that enhances the dynamical behaviour of these maps to overcome this problem. The proposed system uses cascade and combination methods as a nonlinear chaotification function. To depict the capability of the proposed system, we apply it to classical chaotic maps and analyse them using theoretical analysis, conventional, fractal and randomness evaluations. Results show that the enhanced maps have a larger chaotic range, low correlation, uniform data distribution and better chaotic properties. As a proof of concept, simple pseudorandom number generators are then designed based on a classical map and its enhanced variant. Security comparisons between the two generators indicate that the generator based on the enhanced map has better statistical properties as compared to its classical counterpart. This finding showcases the capability of the proposed system in improving the performance of chaos-based algorithms.