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Analysis and resistance of dynamic degradation of digital chaos via functional graphs

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Abstract

To analyze the effects of finite computational precision on the dynamical degradation of digital chaotic maps, we designed a periodic orbit detection algorithm that is based on a functional graph. The algorithm can calculate the transient length of each chaotic orbit, weak secret keys, fixed points and the period distribution of digital chaotic systems with various limited computational precisions accurately. Furthermore, an effective method based on quadratic congruential generator is proposed to counteract the performance degradation of digital chaos. Based on the method, a new chaotic model can be constructed with full cycle. Numerical experiments are carried out to evaluate the feasibility of the proposed scheme in terms of phase portrait, autocorrelation function, complexity and periodicity analysis. Finally, as an application, a pseudorandom bit generator with satisfactory performance is designed for chaotic secure communication.

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Acknowledgements

This work was supported by the Natural Science Foundation of China (No. 61471158) and Natural Science Foundation of Heilongjiang Province (LH2019F048).

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  1. Electrical Engineering College, Heilongjiang University, Harbin, 150080, China

    Chunlei Fan & Qun Ding

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  1. Chunlei Fan
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  2. Qun Ding
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Correspondence to Qun Ding.

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Fan, C., Ding, Q. Analysis and resistance of dynamic degradation of digital chaos via functional graphs. Nonlinear Dyn 103, 1081–1097 (2021). https://doi.org/10.1007/s11071-020-06160-x

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  • DOI: https://doi.org/10.1007/s11071-020-06160-x

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