A Novel Dynamic S-Box Generation Scheme Based on Quantum Random Walks Controlled by a Hyper-Chaotic Map

Lijun Zhang, Caochuan Ma, Yuxiang Zhao and Wenbo Zhao ()
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Lijun Zhang: School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741000, China
Caochuan Ma: School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741000, China
Yuxiang Zhao: School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741000, China
Wenbo Zhao: School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741000, China

Mathematics, 2023, vol. 12, issue 1, 1-22

Abstract: For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems. In this paper, a new model (compound chaotic system) of quantum random walks controlled by a hyper-chaotic map is constructed and a novel scheme for constructing a dynamic S-Box based on the new model is proposed. Through aperiodic evaluation and statistical complexity measurement, it is shown that the compound chaotic system has features such as complex structure and stronger randomness than classical chaotic systems. Based on the chaotic sequence generated by the composite system, we design a dynamic S-Box generation mechanism. The mechanism can quickly generate high-security S-Boxes. Then, an example of randomly generating S-Boxes is given alongside an analytical evaluation of S-Box standard performance criteria such as bijection, boomerang uniformity, bit independence, nonlinearity, linear approximate probability, strict avalanche effect, differential uniformity, the and generalized majority logic criterion. The evaluation results confirm that the performance of the S-Box is excellent. Thus, the proposed dynamic S-Box construction technique can be used to generate cryptographically strong substitution-boxes in practical information security systems.

Keywords: compound chaotic system; quantum random walk; S-Box generation mechanism; standard performance criteria; information security (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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