IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v45y2012i3p238-245.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077911002384
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2011.12.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ren, Haijun & Wang, Yong & Xie, Qing & Yang, Huaqian, 2009. "A novel method for one-way hash function construction based on spatiotemporal chaos," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2014-2022.
    2. Mahmoud, Emad E. & Abo-Dahab, S.M., 2018. "Dynamical properties and complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 273-284.
    3. Zaher, Ashraf A., 2009. "An improved chaos-based secure communication technique using a novel encryption function with an embedded cipher key," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2804-2814.
    4. Akhavan, A. & Samsudin, A. & Akhshani, A., 2009. "Hash function based on piecewise nonlinear chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1046-1053.
    5. Asgari Chenaghlu, Meysam & Jamali, Shahram & Nikzad Khasmakhi, Narjes, 2016. "A novel keyed parallel hashing scheme based on a new chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 216-225.
    6. Zhiqin Qiao & Xianyi Li, 2014. "Dynamical analysis and numerical simulation of a new Lorenz-type chaotic system," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 20(3), pages 264-283, May.
    7. Akhshani, A. & Behnia, S. & Akhavan, A. & Jafarizadeh, M.A. & Abu Hassan, H. & Hassan, Z., 2009. "Hash function based on hierarchy of 2D piecewise nonlinear chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2405-2412.
    8. Khan, Muhammad Khurram & Zhang, Jiashu & Wang, Xiaomin, 2008. "Chaotic hash-based fingerprint biometric remote user authentication scheme on mobile devices," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 519-524.
    9. Li, Lixiang & Peng, Haipeng & Yang, Yixian & Wang, Xiangdong, 2009. "On the chaotic synchronization of Lorenz systems with time-varying lags," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 783-794.
    10. Yang, Huaqian & Wong, Kwok-Wo & Liao, Xiaofeng & Wang, Yong & Yang, Degang, 2009. "One-way hash function construction based on chaotic map network," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2566-2574.
    11. Rasool, Masrat & Belhaouari, Samir Brahim, 2023. "From Collatz Conjecture to chaos and hash function," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    12. Han, Song, 2008. "Security of a key agreement protocol based on chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 764-768.
    13. Tutueva, Aleksandra V. & Karimov, Artur I. & Moysis, Lazaros & Volos, Christos & Butusov, Denis N., 2020. "Construction of one-way hash functions with increased key space using adaptive chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Amin, Mohamed & Faragallah, Osama S. & Abd El-Latif, Ahmed A., 2009. "Chaos-based hash function (CBHF) for cryptographic applications," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 767-772.
    15. Wang, Yu & Chen, Liquan & Wang, Xingyuan & Wu, Ge & Yu, Kunliang & Lu, Tianyu, 2021. "The design of keyed hash function based on CNN-MD structure," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    16. Xiang, Tao & Wong, Kwok-Wo & Liao, Xiaofeng, 2009. "On the security of a novel key agreement protocol based on chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 672-675.
    17. Arroyo, David & Li, Chengqing & Li, Shujun & Alvarez, Gonzalo, 2009. "Cryptanalysis of a computer cryptography scheme based on a filter bank," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 410-413.
    18. Zhao, Liang & Liao, Xiaofeng & Xiao, Di & Xiang, Tao & Zhou, Qing & Duan, Shukai, 2009. "True random number generation from mobile telephone photo based on chaotic cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1692-1699.
    19. Chu, Yan-Dong & Chang, Ying-Xiang & Zhang, Jian-Gang & Li, Xian-Feng & An, Xin-Lei, 2009. "Full state hybrid projective synchronization in hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1502-1510.
    20. Tigan, Gheorghe & Opriş, Dumitru, 2008. "Analysis of a 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1315-1319.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:45:y:2012:i:3:p:238-245. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.