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Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding

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Cryptography and Coding (Cryptography and Coding 2001)

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Abstract

The applications of digital chaotic maps in discrete-time chaotic cryptography and pseudo-random coding are widely studied recently. However, the statistical properties of digital chaotic maps are rather different from the continuous ones, which impedes the theoretical analyses of the digital chaotic ciphers and pseudo-random coding. This paper detailedly investigates the statistical properties of a class of digital piecewise linear chaotic map (PLCM), and rigorously proves some useful results. Based on the proved results, we further discuss some notable problems in chaotic cryptography and pseudo-random coding employing digital PLCM-s. Since the analytic methods proposed in this paper can essentially extended to a large number of PLCM-s, they will be valuable for the research on the performance of such maps in chaotic cryptography and pseudo-random coding.

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Author information

Authors and Affiliations

  1. Institute of Image Processing, School of Electronics and Information Engineering, Xi’an Jiaotong University, 710049, Xi’an, Shaanxi, P. R. China

    Shujun Li, Xuanqin Mou & Yuanlong Cai

  2. Department of Electrical Engineering and Electronics, The University of Liverpool, L69 3GJ, Liverpool, Brownlow Hill, UK

    Qi Li

  3. Department of Electircal and Electronic Engeering, Imperial College, Exhibition Road, SW7 2BT, London, UK

    Wenmin Li

Authors
  1. Shujun Li
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  2. Qi Li
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  3. Wenmin Li
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  4. Xuanqin Mou
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  5. Yuanlong Cai
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Editor information

Editors and Affiliations

  1. Faculty of Applied Sciences, Department of Communication Systems, Lancaster University, LA1 4YR, Lancaster, UK

    Bahram Honary

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© 2001 Springer-Verlag Berlin Heidelberg

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Li, S., Li, Q., Li, W., Mou, X., Cai, Y. (2001). Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding. In: Honary, B. (eds) Cryptography and Coding. Cryptography and Coding 2001. Lecture Notes in Computer Science, vol 2260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45325-3_19

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  • DOI: https://doi.org/10.1007/3-540-45325-3_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43026-1

  • Online ISBN: 978-3-540-45325-3

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