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Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation

Author

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  • Persohn, K.J.
  • Povinelli, R.J.

Abstract

Because of the mixing and aperiodic properties of chaotic maps, such maps have been used as the basis for pseudorandom number generators (PRNGs). However, when implemented on a finite precision computer, chaotic maps have finite and periodic orbits. This manuscript explores the consequences finite precision has on the periodicity of a PRNG based on the logistic map. A comparison is made with conventional methods of generating pseudorandom numbers. The approach used to determine the number, delay, and period of the orbits of the logistic map at varying degrees of precision (3 to 23 bits) is described in detail, including the use of the Condor high-throughput computing environment to parallelize independent tasks of analyzing a large initial seed space. Results demonstrate that in terms of pathological seeds and effective bit length, a PRNG based on the logistic map performs exponentially worse than conventional PRNGs.

Suggested Citation

  • Persohn, K.J. & Povinelli, R.J., 2012. "Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 238-245.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:3:p:238-245
    DOI: 10.1016/j.chaos.2011.12.006
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    References listed on IDEAS

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    1. Xiao, Di & Liao, Xiaofeng & Deng, Shaojiang, 2005. "One-way Hash function construction based on the chaotic map with changeable-parameter," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 65-71.
    2. Álvarez, G. & Li, Shujun & Montoya, F. & Pastor, G. & Romera, M., 2005. "Breaking projective chaos synchronization secure communication using filtering and generalized synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 775-783.
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    Cited by:

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    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.
    3. Zheng, Jun & Hu, Hanping & Ming, Hao & Liu, Xiaohui, 2020. "Theoretical design and circuit implementation of novel digital chaotic systems via hybrid control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Eduarda T. C. Chagas & Marcelo Queiroz‐Oliveira & Osvaldo A. Rosso & Heitor S. Ramos & Cristopher G. S. Freitas & Alejandro C. Frery, 2022. "White Noise Test from Ordinal Patterns in the Entropy–Complexity Plane," International Statistical Review, International Statistical Institute, vol. 90(2), pages 374-396, August.
    5. De Micco, L. & Antonelli, M. & Larrondo, H.A., 2017. "Stochastic degradation of the fixed-point version of 2D-chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 477-484.

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