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A new chaotic map and analysis of properties of “Reciprocal difference twice modular maps” on Z(pn)

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Abstract

The chaotic maps on the real number fields certainly cause the degenerate of the chaotic characters because of the finite precision when realized on computers. And its complexity is very high. In this paper a new class of 1-D nonlinear chaotic map on the real number fields is proposed. This map is chaotic in the whole range of parameters. The Lyapunov exponents of this map tend to ln 2. It has complex dynamical properties and high sensitivity to initial values; the iterative sequences obey a uniform distribution. Then we propose the concept of “reciprocal difference twice modular maps” based on this map which is realized on Z(pn) and avoids the defects above. The properties of the generating sequences by the new maps are analyzed, including periods and long chains and so on. The analysis and numeral experiments show that reciprocal difference twice modular maps can be widely applied in the pseudo-random number generators, cryptography, spread spectrum communication and so on.

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Acknowledgements

This work was supported by the Scientific Research Program of Department of Education of Hubei Province (Grant No. D20202801) and the Scientific Research Foundation for PhD of Hubei University of Science and Technology(Grant No. BK202030).

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  1. School of Computer Science and Technology, Hubei University of Science and Technology, Xianning, 437100, China

    LI Yong-Kui

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  1. LI Yong-Kui
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Correspondence to LI Yong-Kui.

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Yong-Kui, L. A new chaotic map and analysis of properties of “Reciprocal difference twice modular maps” on Z(pn). Multimed Tools Appl 81, 40371–40383 (2022). https://doi.org/10.1007/s11042-022-13074-w

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  • DOI: https://doi.org/10.1007/s11042-022-13074-w

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