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Chaotic Generator for Digital Secure Communication

This paper discusses the use of chaotic generators in digital secure communication and proposes a modified logistic map as a chaotic map for encryption. It also explores the applications and concludes with the distinction between random and chaotic signals.

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Chaotic Generator for Digital Secure Communication

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  1. Chaotic Generator in Digital Secure Communication 張 書 銘 交通大學應用數學系 smchang@math.nctu.edu.tw 2008 年 12 月 20 日

  2. Outline • Chaos • Secure Communication • Chaotic Generator • Conclusions

  3. Chaos • Chaos is “ mess, disorder, uncontrollable ! ? • Smoke of Cigarette Mike in coffee

  4. Lorenz strange attractor

  5. Three planar charged particles

  6. Three planar charged particles

  7. Three planar charged particles

  8. Henon map

  9. Discrete predator-prey map

  10. Logistic map

  11. Secure Communication

  12. Digital secure communication Transmitter Receiver Encryption Decryption Chaotic Encryption Unit Chaotic Decryption Unit Acquire Digital Data Source Digital Data Ciphertext Plaintext

  13. Applications - 1 VoIP e-mail PSTN/PLMN Communication Information Ineternet/Intranet Wifi/WiMAX WEB Service ADSL/ISDN Transaction Entertainment ETC Digital content providor e-ATM Game/MOD Database

  14. Applications - 2

  15. Chaotic Generator

  16. Logistic map

  17. Modified Logistic map

  18. Properties of MLM • Chaotic map • No windows • Uniform distribution • Equivalent • Pseudorandom

  19. MLM: chaotic map

  20. MLM: no windows

  21. MLM: no windows

  22. MLM: uniform distribution r = 5.9

  23. MLM: uniform distribution r = 10.8

  24. MLM: equivalent

  25. MLM: equivalent

  26. MLM: pseudorandom

  27. MLM: pseudorandom

  28. Conclusions • Propose Modified Logistic Map (MLM) • Show that MLM is a chaotic map • (Devaney's definition) • No windows • Uniform distribution, equivalent • Pseudorandom

  29. Thank you for your attention!

  30. Random vs. Chaos Random numbers: Chaotic signals: Identity： 1. Continuous Spectrum 2. Correlation Function：

  31. Random vs. Chaos 3. Stability： Observable: TemporalAveragefor (1): Perturbation: TemporalAveragefor (2):

  32. Random vs. Chaos Distinction：

  33. Further • Based on MLMs, we establish Modified Logistic Hyper-Chaotic System (MLHCS) • Apply MLHCS to develop a symmetric cryptography algorithm • Asymptotic Synchronization of Modified Logistic Hyper-Chaotic System (ASMLHCS)

  34. Digital secure communication Transmitter Receiver Encryption Decryption MLHCS Encryption Unit ASMLHCS Decryption Unit Acquire Digital Data Source Digital Data Ciphertext Plaintext

  35. References • S. M. Chang, M. C. Li and W. W. Lin, Asymptotic synchronization of modified logistic hyper-chaotic systems and its applications. Nonlinear Analysis: Real World Applications, Vol. 10, Issue 2 (2009), pp. 869–880. • S. M. Chang, T. C. Lin and W. W. Lin, Chaotic and Quasiperiodic Motions of Three Planar Charged Particles.Int. J. Bifurcation Chaos, Vol. 11, No. 7 (2001), pp. 1937–1951. • S. L. Chen, S. M. Chang, T. T. Hwang and W. W. Lin, Digital secure-communication using robust hyper-chaotic systems. Int. J. Bifurcation Chaos, Vol. 18, No. 11 (2008), pp. 1–14.

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