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Applied Intelligence

, Volume 10, Issue 1, pp 71–84 | Cite as

A New Symmetric Probabilistic Encryption Scheme Based on Chaotic Attractors of Neural Networks

  • Donghui Guo
  • L.M. Cheng
  • L.L. Cheng
Article

Abstract

A new probabilistic symmetric-key encryption scheme based on chaotic-classified properties of Hopfield neural networks is described. In an overstoraged Hopfield Neural Network (OHNN) the phenomenon of chaotic-attractors is well documented and messages in the attraction domain of an attractor are unpredictably related to each other. By performing permutation operations on the neural synaptic matrix, several interesting chaotic-classified properties of OHNN were found and these were exploited in developing a new cryptography technique. By keeping the permutation operation of the neural synaptic matrix as the secret key, we introduce a new probabilistic encryption scheme for a symmetric-key cryptosystem. Security and encryption efficiency of the new scheme are discussed.

encryption chaotic attractors neural networks symmetric-key 

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References

  1. 1.
    C.E. Shannon, “Communication theory and secrecy system,” Bell Syst. Tech. J., vol. 28, pp. 656–715, 1949.Google Scholar
  2. 2.
    J. Seberry and J. Pieprzyk, Crytography—An Introduction to Computer Security, Prentice Hall, 1989, ISBN 0–13–194986–1.Google Scholar
  3. 3.
    M. Hellman, “An extension of the Shannon theory approach to cryptography,” IEEE Trans. Inform. Theory, vol. IT-23,no. 2, pp. 289–297, 1977.Google Scholar
  4. 4.
    W. Diffie and M.E. Hellman, “New direction in cryptography,” IEEE Trans. Inform. Theory, vol. IT-22,no. 3, pp. 644–654, 1976.Google Scholar
  5. 5.
    G. Brassard, Modern Cryptology, Springer-Verlag, 1988.Google Scholar
  6. 6.
    M.E. Bianco and D.A. Reed, “Encryption system based on chaos theory,” US Patent No. 5,048,086, September, 1991.Google Scholar
  7. 7.
    H.A. Gutowitz, “Method and apparatus for encryption, decryption and authentication using dynamic systems,” US Patent No. 5,365,589, February, 1992.Google Scholar
  8. 8.
    R.L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Comm. ACM, vol. 21, pp. 120–126, 1978.Google Scholar
  9. 9.
    J.J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” in Proc. Natl. Acad. Sci. USA, 1982, vol. 79, pp. 2554–2558.Google Scholar
  10. 10.
    Donghui Guo, Zhenxiang Chen, Ruitang Liu, and Boxi Wu, “A modified Hopfield model of neural network,” Journal of Xiamen University (Natural), vol. 32,no. 1, pp. 33–40, 1993.Google Scholar
  11. 11.
    R.J. McEliece, E.C. Posner, E.R. Rodemich, and S.S. Vankatesh, “The capacity of the Hopfield associative memory,” IEEE Trans. Inform. Theory, vol. IT-33,no. 4, pp. 461–482, 1987.Google Scholar
  12. 12.
    W.S. McCulloch and W. Pitts, “A logical calculus of the ideas immanent in nervous activity,” Bull. Math. Biophys., vol. 5, pp. 115–133, 1943.Google Scholar
  13. 13.
    E. Davalo and P. Naim, Neural Network, MacMillan, 1991.Google Scholar
  14. 14.
    E. Gardner, “Maximinum storage capacity in neural networks,” Europhys. Lett., vol. 4,no. 4, pp. 481–485, 1987.Google Scholar
  15. 15.
    D.O. Hebb, The Organisation of Behaviour, Wiley: New York, NY, 1949.Google Scholar
  16. 16.
    D.J. Amit, H. Gutfreund, and H. Sompolinsky, “Statistical mechanics of neural networks near saturation,” Ann. Phys., vol. 173, pp. 30–67, 1987.Google Scholar
  17. 17.
    H. Sompolinsky, A. Crisanti, and H.J. Sommer, “Chaos in random neural networks,” Physical Review Letters, vol. 61,no. 3, pp. 259–262, 1988.Google Scholar
  18. 18.
    M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman: San Francisco, 1979.Google Scholar
  19. 19.
    Certicom White Paper, “Current public key cytographic systems,” http://www.certicom.com/ecc/wecc2.htm, 1997.Google Scholar
  20. 20.
    National Bureau of Standards, DES Modes of Operation, U.S.A. Department of Commerce, FIPS pub.81, December 1980.Google Scholar
  21. 21.
    Eli Biham and Adi Shamir, “Differential cryptoanalysis of DES-like cryptosystems,” Journal of Cryptology, vol. 4,no. 1, pp. 3–72, 1991.Google Scholar
  22. 22.
    R.C. Merkle, “On the security of multiple encryption,” Comm. of ACM, vol. 24,no. 7, pp. 465–467, July 1981.Google Scholar
  23. 23.
    T. Kaneko, K. Koyama, and R. Terada, “Dynamic swapping schemes and differential cryptanalysis,” IEICE Trans. Fundamentals, vol. E-77-A,no. 8, August 1994.Google Scholar
  24. 24.
    C.K. Chan and L.M. Cheng, “Configurable non-linear filter generator,” Electronics Letters, vol. 34,no. 4, p. 349, 1998.Google Scholar
  25. 25.
    R.A. Rueppel, “Stream ciphers,” in Contemporary Cryptology, edited by L. Shaw, IEEE: New York, pp. 65–134, 1992.Google Scholar
  26. 26.
    S. Wolfram, “Cryptography with cellular automata,” in Proc. Crypto'85, 1986, pp. 523–534.Google Scholar
  27. 27.
    R.A. Rueppel and O. Staffelbach, “Products of sequences with maximum linear complexity,” IEEE Trans. on Inform. Theory, vol. IT-33,no. 1, pp. 124–131, 1987.Google Scholar
  28. 28.
    Xiao Guo-Zhen and J.L. Massey, “A spectral characterization of correlation-immune combining functions,” IEEE Trans. on Info. Theory, vol. IT-34,no. 3, pp. 569–571, 1988.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Donghui Guo
    • 1
    • 2
  • L.M. Cheng
    • 3
  • L.L. Cheng
    • 3
  1. 1.Department of Electronic EngineeringCity University of Hong KongHong Kong, and
  2. 2.Department of PhysicsXiamen UniversityXiamenP.R. China. dhguo@jingxian.xmu.edu.cn
  3. 3.Department of Electronic EngineeringCity University of Hong KongHong Kong

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