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International Conference on Cryptology and Network Security

CANS 2006: Cryptology and Network Security pp 270–285Cite as

Chaotic Keystream Generator Using Coupled NDFs with Parameter Perturbing

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4301))

Abstract

Chaotic cryptology has been widely investigated recently. This paper analyzes the security pitfalls existing in digital chaotic stream ciphers, which work on the well characterized one-dimensional(1-D) chaotic systems. As a practical solution to these problems caused by 1-D chaotic systems, a chaotic keystream generator using nonlinear digital filters with n-D uniform distribution is proposed. To improve system security further and overcome the effects of finite wordlength, the coupling method with parameter perturbing is considered. Detailed theoretical analyses show that it has perfect cryptographic properties, and can be used to construct stream ciphers with higher security than other 1-D chaotic ciphers. Finally, some numeric experiments are made and the experimental results coincide well with the theoretical analyses.

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References

  1. Matthews, R.: On the derivation of a chaotic encryption algorithm. Cryptologia XIII(1), 29–42 (1989)

    Article  MathSciNet  Google Scholar 

  2. Forré, R.: The Hénon attractor as a keystream generator. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 0547, pp. 76–81. Springer, Heidelberg (1991)

    Google Scholar 

  3. Zhou, H., Ling, X.: Generating chaotic secure sequence with desired statistical properties and high security. Int. J. Bifurcation and Chaos 7, 205–213 (1997)

    Article  MATH  Google Scholar 

  4. Habutsu, T., Nishio, Y., Sasase, I., Mori, S.: A Secret Key Cryptosystem by Iterating a Chaotic Map. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 0547, pp. 127–140. Springer, Heidelberg (1991)

    Google Scholar 

  5. Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcation and Chaos. 8, 1259–1284 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Protopopescu, V.A., Santoro, R.T., Tollover, J.S.: Fast and secure encryption-decryption method based on chaotic dynamics. US Patent No.5479513 (1995)

    Google Scholar 

  7. Zbigniew, K., Janusz, S.: Application of discrete chaotic dynamical systems in cryptography-dcc method. Int. J. Bifurcation and Chaos 9, 1121–1135 (1999)

    Article  MATH  Google Scholar 

  8. Ghobad, H.B., Clare, D.: A chaotic direct-sequence spread-spectrum communication system. IEEE Trans. Communication 42, 1524–1527 (1994)

    Article  Google Scholar 

  9. Erdmann, D., Murphy, S.: Hénon stream cipher. Electronics Letters 28, 893–895 (1992)

    Article  Google Scholar 

  10. Bruce, S.: Applied Cryptography-Protocols, algorithms, and source code, 2nd edn. John Wiley & Sons, Inc., New York (1996)

    MATH  Google Scholar 

  11. Lu, H., Wang, S., Hu, G.: Pseudo-random number generator based on coupled map lattices. Int. J. Mod Phys B. 18, 2409–2414 (2004)

    Article  Google Scholar 

  12. Kohda, T., Tsuneda, A.: Stream cipher systems based on chaotic binary sequences. In: Proc. SCIS 1996-11C (1996)

    Google Scholar 

  13. Kocarev, L., Jakimoski, G., Stojanovski, T., Parlitz, U.: From chaotic maps to encryption schemes. In: Proc. IEEE Int. Symposium Circuits and Systems, vol. 4, pp. 514–517 (1998)

    Google Scholar 

  14. Li, S., Mou, X., Cai, Y.: Pseudo-Random Bit Generator Based on Couple Chaotic Systems and its Applications in Stream-Cipher Cryptography. In: Pandu Rangan, C., Ding, C. (eds.) INDOCRYPT 2001. LNCS, vol. 2247, pp. 316–329. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Chen, G., Mao, Y., Chui, C.: A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos, Solitons & Fractals 12, 749–761 (2004)

    Article  MathSciNet  Google Scholar 

  16. Chua, L.O., Lin, T.: Chaos in digital filters. IEEE Trans. CAS 35, 648–658 (1988)

    MathSciNet  Google Scholar 

  17. Lin, T., Chua, L.O.: On chaos of digital filters in the real world. IEEE Trans. CAS 38, 557–558 (1991)

    Google Scholar 

  18. Li, S., Li, Q., Li, W., Mou, X., Cai, Y.: Statistical properties of digital piecewise linear chaotic maps and their roles in cryptography and pseudo-random coding. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, p. 205. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Kelber, K.: N-Dimensional Uniform Probability Distribution in Nonlinear Autoregressive Filter Structures. IEEE Trans. CAS-I 47, 1413–1417 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  20. Alvarez, G., Li, S.: Some Basic Cryptographic Requirements for Chaos-based Cryptosystems. I. J. Bifurcation and Chaos (2005)

    Google Scholar 

  21. Wheeler, D.: Problems with chaotic cryptosystems. Cryptologia XIII(3), 243–250 (1989)

    Article  Google Scholar 

  22. Wheeler, D., Mattews, R.: Supercomputer investigations of a chaotic encryption algorithm. Cryptologic XV(2), 140–151 (1991)

    Article  Google Scholar 

  23. Biham, E.: Cryptoanalysis of the chaotic-map cryptosystem suggested at EuroCrypt 1991. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 0547, pp. 532–534. Springer, Heidelberg (1991)

    Google Scholar 

  24. Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Cryptanalysis of a chaotic encryption system. Physics Letters A, 7, 191–196 (2000)

    MathSciNet  Google Scholar 

  25. Short, K.M.: Signal extraction from chaotic communications. Int. J. Bifurcation and Chaos 7, 1579–1597 (1997)

    Article  MATH  Google Scholar 

  26. Yang, T., Yang, L., Yang, C.M.: Cryptanalyzing chaotic secure communications using return maps. Physics Letters A, 245, 495–510 (1998)

    Google Scholar 

  27. Yang, Y.X., Lin, X.D.: Coding Theory and Cryptology. People’s Post and Telecomm. Press, Beijing (1992) (in Chinese)

    Google Scholar 

  28. Wang, X., Zhang, M., Lai, C., et al.: Error function attack of chaos synchronization based encryption schemes. Chaos 14, 128–137 (2004)

    Article  Google Scholar 

  29. Kelber, K., Götz, M., Schwarz, W.: Generation of chaotic signals with n-dimensional uniform probability distribution by digital filter structure. In: Proc. of the 7th IEEE Digital Signal Processing Workshop (DSPWS 1996), pp. 486–489. Loen, Norway (1996)

    Chapter  Google Scholar 

  30. Sang, T., Wang, R., Yan, Y.: Perturbance-based algorithm to expand cycle length of chaotic key stream. Electronics Letters 34, 873–874 (1998)

    Article  Google Scholar 

  31. Sang, T., Wang, R., Yan, Y.: Clock-controlled chaotic keystream generators. Electronics Letters 34, 1932–1934 (1998)

    Article  Google Scholar 

  32. Bernstein, G., Lieberman, M.: Secure random number generation using chaotic circuits. IRRR Trans. CAS 37, 1157–1164 (1990)

    MathSciNet  Google Scholar 

  33. Baptista, M.S.: Cryptography with chaos. Physics Letters A 240, 50–54 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  34. Alvarez, E., Fernández, A., García, P., et al.: New approach to chaotic encryption. Physics Letters A9, 263, 373–375 (1999)

    Google Scholar 

  35. Rueppel, R.: Analysis and design of stream ciphers. Springer, Berlin (1986)

    MATH  Google Scholar 

  36. Frey, D.R.: Chaotic digital encoding: An approach to secure communication. IEEE Trans. CAS-II 40, 660–666 (1993)

    MathSciNet  Google Scholar 

  37. Andrew, R., Juan, S., James, N., et al.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800-22 (2001), http://csrc.nist.gov/rng/

  38. Available Online at: http://stat.fsu.edu/~geo/diehard.html

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Author information

Authors and Affiliations

  1. Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu, 610031, P.R. China

    Xiaomin Wang & Jiashu Zhang

  2. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 610031, P.R. China

    Wenfang Zhang

Authors
  1. Xiaomin Wang
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  2. Jiashu Zhang
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  3. Wenfang Zhang
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Editor information

Editors and Affiliations

  1. Ecole Normale Supérieure – LIENS/CNRS/INRIA,, France

    David Pointcheval

  2. Centre for Computer and Information Security Research School of Computer Science and Software Engineering, University of Wollongong, Australia

    Yi Mu

  3. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

    Kefei Chen

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© 2006 Springer-Verlag Berlin Heidelberg

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Wang, X., Zhang, J., Zhang, W. (2006). Chaotic Keystream Generator Using Coupled NDFs with Parameter Perturbing. In: Pointcheval, D., Mu, Y., Chen, K. (eds) Cryptology and Network Security. CANS 2006. Lecture Notes in Computer Science, vol 4301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11935070_19

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  • DOI: https://doi.org/10.1007/11935070_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49462-1

  • Online ISBN: 978-3-540-49463-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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