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Effects of Limited Computational Precision on the Discrete Chaotic Sequences and the Design of Related Solutions

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  • Chunlei Fan
  • Qun Ding

Abstract

In this paper, we analyzed the periodicity of discrete Logistic and Tent sequences with different computational precision in detail. Further, we found that the process of iterations of the Logistic and Tent mapping is composed of transient and periodic stages. Surprisingly, for the different initial iterative values, we first discovered that all periodic stages have the same periodic limit cycles. This phenomenon has seriously affected the security of chaotic cipher. To solve this problem, we designed a novel discrete chaotic sequence generator based on m-sequence and discrete chaotic mapping. The experimental results indicated that the chaotic sequence generator can generate pseudorandom chaotic sequences with large periodicity and good performance under the condition of limited computational precision.

Suggested Citation

  • Chunlei Fan & Qun Ding, 2019. "Effects of Limited Computational Precision on the Discrete Chaotic Sequences and the Design of Related Solutions," Complexity, Hindawi, vol. 2019, pages 1-10, January.
    • Handle: RePEc:hin:complx:3510985
    DOI: 10.1155/2019/3510985
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    References listed on IDEAS

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    1. Hu, Hanping & Xu, Ya & Zhu, Ziqi, 2008. "A method of improving the properties of digital chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 439-446.
    2. Wafaa S. Sayed & Ahmed G. Radwan & Ahmed A. Rezk & Hossam A. H. Fahmy, 2017. "Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications," Complexity, Hindawi, vol. 2017, pages 1-21, February.
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