Fuzzy Chaotic Synchronization and Communication — Signal Masking and Encryption

  • Kuang-Yow Lian
  • Peter Liu
  • Chian-Song Chiu
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 136)

Abstract

In this chapter, we address synthesis approaches for signal synchronization and secure communications of chaotic systems by using LMIbased fuzzy system design methods. Following a general form of TakagiSugeno fuzzy chaotic models, the structure of the response system is firstly proposed. Synthesizing from the observer and controller points of view, two developed drive-response systems achieve asymptotic synchronization. For chaotic communications, the asymptotical recovering of messages is ensured by the same framework. As a further application, a chaotic cryptosystem is proposed. The synchronization design is applied to transmit and decrypt the ciphertext. The combination of both chaotic signal and cyptosystem characteristics achieves communication with a higher level of security. Finally, several well-known chaotic systems are used in numerical simulations and DSP-based experiments.

Keywords

Chaotic synchronization Chaotic communication Cryptosystem T-S fuzzy model 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15: 116–132MATHCrossRefGoogle Scholar
  2. 2.
    Wang HO, Tanaka K, Griffin MF (1996) An approach to fuzzy control of nonlinear systems: stability and design issues.IEEE Trans Fuzzy Systems 4: 14–23CrossRefGoogle Scholar
  3. 3.
    Tanaka K, Ikeda T, Wang HO (1998) A unified approach to controlling chaos via an LMI-based fuzzy control system design.IEEE Trans Circuits Syst 45: 1021–1040MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Tanaka K, Ikeda T, Wang HO (1998) Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs. IEEE Trans Fuzzy Systems 6: 250–265CrossRefGoogle Scholar
  5. 5.
    Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaMATHCrossRefGoogle Scholar
  6. 6.
    Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 38: 821–824MathSciNetCrossRefGoogle Scholar
  7. 7.
    Carroll TL, Pecora LM (1991) Synchronizing chaotic circuits. IEEE Trans Circuits Syst 38: 453–456CrossRefGoogle Scholar
  8. 8.
    Chen C, Dong X (1998) From chaos to order methodologies, perspectives and applications. World Scientific, SingaporeMATHGoogle Scholar
  9. 9.
    Lakshmanan M, Murali K (1996) Chaos in nonlinear oscillators: controlling and synchronization. World Scientific, SingaporeMATHGoogle Scholar
  10. 10.
    Morgiil O, Solak E (1996) Observer based synchronization of chaotic systems. Phys Rev E 54: 4803–4811CrossRefGoogle Scholar
  11. 11.
    Huijberts HJC, Nijmeijer H, Pogromsky AYu(2000) An observer point of view on synchronization of discrete-time systems. Proc ISCAS 2000: 491–494.Google Scholar
  12. 12.
    Grassi G, Mascolo S (1999) Synchronizing hyperchaotic systems by observer design. IEEE Trans Circuits Syst II 46 : 478–483MATHCrossRefGoogle Scholar
  13. 13.
    Cuomo KM, Oppenheim AV, Strogatz SH (1993) Synchronization of Lorenzbased chaotic circuits with applicatons to communications. IEEE Trans Circuits Syst II 40: 626–633CrossRefGoogle Scholar
  14. 14.
    Kocarev LJ, Halle KD, Eckert K, Chua LO, Parlitz U (1992) Experimental demonstration of secure communications via chaotic synchronization. Int J Bifurcation Chaos 2: 709–713MATHCrossRefGoogle Scholar
  15. 15.
    Liao TL, Huang NS (1999) An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Trans Circuits Syst I 46: 1144–1150MATHCrossRefGoogle Scholar
  16. 16.
    Wu CW, Chua LO (1993) A simple way to synchronize chaotic systems with applications to secure communication systems. Int J Bifurcation Chaos 3: 1619–1627MATHCrossRefGoogle Scholar
  17. 17.
    Halle KS, Wu CW, Itoh M, Chua LO (1993) Spread spectrum communication through modulation of chaos. Int J Bifurcation Chaos 3: 469–477MATHCrossRefGoogle Scholar
  18. 18.
    Lian KY, Chiang TS, Liu P (2000) Discrete-time chaotic systems: applications in secure communications. Int J Bifurcation Chaos 10: 2193–2206MathSciNetMATHGoogle Scholar
  19. 19.
    Lian KY, Chiang TS, Liu P, Chiu CS (2001) LMI-based fuzzy chaotic synchronization and communication. IEEE Trans Fuzzy Systems 9: 539 - 553CrossRefGoogle Scholar
  20. 20.
    Lian KY, Chiang TS, Chiu CS, Liu P (2001) Synthesis of fuzzy modelbased design to synchronization and secure communication for chaotic systems. IEEE Trans Syst Man Cybern Part B 31: 66–83CrossRefGoogle Scholar
  21. 21.
    Short K (1994) Steps toward unmasking secure communications. Int J Bifurcation Chaos 4: 959–977MATHCrossRefGoogle Scholar
  22. 22.
    Garey MR, Johnson DS (1976) Computers and intractability: a guide to the theory of NP-completeness. WH Freeman & Co, San FranciscoGoogle Scholar
  23. 23.
    Denning DER (1982) Cryptography and data security. Addison Wesley, New YorkMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kuang-Yow Lian
    • 1
  • Peter Liu
    • 1
  • Chian-Song Chiu
    • 1
  1. 1.Department of Electrical EngineeringChung-Yuan Christian UniversityChung-LiTaiwan

Personalised recommendations