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Design and geometric control of polynomial chaotic maps with any desired positive Lyapunov exponents

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  • Fan, Chunlei
  • Ding, Qun

Abstract

Digital chaotic maps are severely hampered by the finite calculation accuracy of the hardware device that is used to implement them, and their applications in cryptography and information assurance are seriously degraded. To resolve this issue, we put forward a universal iterative model to construct non-degenerate polynomial chaotic maps with any desired number of positive Lyapunov exponents. In addition, we innovatively propose the geometric control methods of polynomial chaotic maps, including amplitude control, offset boosting, plane rotation, shape control, and combined regulation. Furthermore, to assess the effectiveness and feasibility of the proposed method, a microcontroller-based platform was developed to demonstrate the hardware implementation and geometric control of the proposed polynomial chaotic map. Finally, a PRNG is constructed by interval quantization. Numerical experiments are performed to verify the desirable statistical properties of the PRNG in terms of local weak random test, discrete Fourier transform test, linear complexity and NIST SP800-22 test.

Suggested Citation

  • Fan, Chunlei & Ding, Qun, 2023. "Design and geometric control of polynomial chaotic maps with any desired positive Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001595
    DOI: 10.1016/j.chaos.2023.113258
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    References listed on IDEAS

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    Cited by:

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    2. Ding, Dawei & Zhu, Haifei & Zhang, Hongwei & Yang, Zongli & Xie, Dong, 2024. "An n-dimensional polynomial modulo chaotic map with controllable range of Lyapunov exponents and its application in color image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).

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