Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding
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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.
- Andrzej Lasota and Michael C. Mackey. Chaos, Fractals, and Noise-Stochastic Aspects of Dynamics. Springer-Verlag, New York, second edition, 1997.
- Ljupčo Kocarev, Goce Jakimoski, Toni Stojanovski, and Ulrich Parlitz. From chaotic maps to encryption schemes. In Proc. IEEE Int. Symposium Circuits and Systems 1998, volume 4, pages 514–517. IEEE, 1998.
- Jiri Fridrich. Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcation and Chaos, 8(6):1259–1284, 1998. CrossRef
- R. Brown and L. O. Chua. Clarifying chaos: Examples and counterexamples. Int. J. Bifurcation and Chaos, 6(2):219–249, 1996. CrossRef
- R. Matthews. On the derivation of a ‘chaotic’ encryption algorithm. Cryptologia, XIII(1):29–42, 1989. CrossRef
- Zhou Hong and Ling Xieting. Generating chaotic secure sequences with desired statistical properties and high security. Int. J. Bifurcation and Chaos, 7(1):205–213, 1997. CrossRef
- T. Habutsu, Y. Nishio, I. Sasase, and S. Mori. A secret key cryptosystem by iterating a chaotic map. In Advances in Cryptology-EuroCrypt’91, Lecture Notes in Computer Science 0547, pages 127–140, Berlin, 1991. Spinger-Verlag.
- Hong Zhou and Xie-Ting Ling. Problems with the chaotic inverse system encryption approach. IEEE Trans. Circuits and Systems I, 44(3):268–271, 1997. CrossRef
- Sang Tao, Wang Ruili, and Yan Yixun. Perturbance-based algorithm to expand cycle length of chaotic key stream. Electronics Letters, 34(9):873–874, 1998. CrossRef
- D. D. Wheeler. Problems with chaotic cryptosystems. Cryptologia, XIII(3):243–250, 1989. CrossRef
- D. D. Wheeler and R. Matthews. Supercomputer investigations of a chaotic encryption algorithm. Cryptologia, XV(2):140–151, 1991. CrossRef
- E. Biham. Cryptoanalysis of the chaotic-map cryptosystem suggested at Euro-Crypt’91. In Advances in Cryptology-EuroCrypt’91, Lecture Notes in Computer Science 0547, pages 532–534, Berlin, 1991. Spinger-Verlag.
- Ghobad Heidari-Bateni and Clare D. McGillem. A chaotic direct-sequence spreadspectrum communication system. IEEE Trans. Communications, 42(2/3/4):1524–1527, 1994. CrossRef
- Shin’ichi Oishi and Hajime Inoue. Pseudo-random number generators and chaos. Trans. IECE Japan, E 65(9):534–541, 1982.
- Tohru Kohda and Akio Tsuneda. Statistics of chaotic binary sequences. IEEE Trans. Information Theory, 43(1):104–112, 1997. CrossRef
- Jorge A. González and Ramiro Pino. A random number generator based on unpredictable chaotic functions. Computer Physics Communications, 120:109–114, 1999. CrossRef
- A. Baranovsky and D. Daems. Design of one-dimensional chaotic maps with prescribed statistical properties. Int. J. Bifurcation and Chaos, 5(6):1585–1598, 1995. CrossRef
- Bruce Schneier. Applied Cryptography — Protocols, algorithms, and souce code in C. John Wiley & Sons, Inc., New York, second edition, 1996.
- Julian Palmore and Charles Herring. Computer arithmetic, chaos and fractals. Physica D, D 42:99–110, 1990. CrossRef
- Zhou Hong and Ling Xieting. Realizing finite precision chaotic systems via perturbation of m-sequences. Acta Eletronica Sinica(In Chinese), 25(7):95–97, 1997.
- Hu Guanhua. Applied Modern Algebra. Tsinghua University Press, Beijing, China, second edition, 1999.
- Pan Chengdong and Pan Chengbiao. Concise Number Theory. Beijing University Press, Beijing, China, 1998.
- The Committee of Modern Applied Mathematics Handbook. Modern Applied Mathematics Handbook-vol. Probability Theory and Stochastic Process. Tsinghua University Press, Beijing, China, 2000.
- Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding
- Book Title
- Cryptography and Coding
- Book Subtitle
- 8th IMA International Conference Cirencester, UK, December 17–19, 2001 Proceedings
- pp 205-221
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- Springer-Verlag Berlin Heidelberg
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- Bahram Honary (4)
- Editor Affiliations
- 4. Faculty of Applied Sciences, Department of Communication Systems, Lancaster University
- Author Affiliations
- 5. Institute of Image Processing, School of Electronics and Information Engineering, Xi’an Jiaotong University, 710049, Xi’an, Shaanxi, P. R. China
- 6. Department of Electrical Engineering and Electronics, The University of Liverpool, L69 3GJ, Liverpool, Brownlow Hill, UK
- 7. Department of Electircal and Electronic Engeering, Imperial College, Exhibition Road, SW7 2BT, London, UK
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