Enhancing unimodal digital chaotic maps through hybridisation
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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.
KeywordsChaotic map Dynamical degradation Pseudorandom number generator Unimodal map Sine map Logistic map
This work has been partially supported by Universiti Sains Malaysia under Grant No. 304/PKOMP/6316280 and the National Natural Science Foundation of China under Grant No. 61702212.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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