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Chaotical PRNG based on composition of logistic and tent maps using deep-zoom

Author

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  • Valle, João
  • Machicao, Jeaneth
  • Bruno, Odemir M.

Abstract

We propose the deep-zoom analysis of the composition of the logistic map and the tent map, which are well-known discrete one-dimensional chaotic maps. The deep-zoom technique transforms each point of a given chaotic orbit by removing the first k-digits after decimal separator. We found that the pseudo-random qualities of the composition map as a pseudo-random number generator (PRNG) improve as the k parameter increases. This was evidenced by the fact that it successfully passed the randomness tests and even outperformed the k-logistic map and the k-tent map PRNG. These dynamic properties show that the application of deep-zoom to the composition of chaotic maps, at least to these two well-known maps, is suitable for better randomization for PRNG purposes as well as for cryptographic systems.

Suggested Citation

  • Valle, João & Machicao, Jeaneth & Bruno, Odemir M., 2022. "Chaotical PRNG based on composition of logistic and tent maps using deep-zoom," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005069
    DOI: 10.1016/j.chaos.2022.112296
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    References listed on IDEAS

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    1. González, C.M. & Larrondo, H.A. & Rosso, O.A., 2005. "Statistical complexity measure of pseudorandom bit generators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 281-300.
    2. Larrondo, H.A. & González, C.M. & Martín, M.T. & Plastino, A. & Rosso, O.A., 2005. "Intensive statistical complexity measure of pseudorandom number generators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 133-138.
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    Cited by:

    1. García-Grimaldo, Claudio & Campos-Cantón, Eric, 2023. "Exploring a family of Bernoulli-like shift chaotic maps and its amplitude control," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Weichao He & Yuemin Zheng & Jin Tao & Yujuan Zhou & Jiayan Wen & Qinglin Sun, 2023. "A Novel Fractional-Order Active Disturbance Rejection Load Frequency Control Based on An Improved Marine Predator Algorithm," Sustainability, MDPI, vol. 15(13), pages 1-23, June.
    3. Li, Ze & Guo, Junfei & Gao, Xinyu & Yang, Xiaohu & He, Ya-Ling, 2023. "A multi-strategy improved sparrow search algorithm of large-scale refrigeration system: Optimal loading distribution of chillers," Applied Energy, Elsevier, vol. 349(C).
    4. 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).
    5. Fan, Chunlei & Ding, Qun, 2023. "Constructing n-dimensional discrete non-degenerate hyperchaotic maps using QR decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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