1. 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. 2  Chaos  Secure Communication  Chaotic Generator  Conclusions Outline

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

4. 4 Lorenz strange attractor

5. 5 Three planar charged particles

6. 6

7. 7

8. 8 Henon map

9. 9 Discrete predator-prey map

10. 10 Logistic map

11. 11 Secure Communication

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

13. 13 Applications - 1 CommunicationInformation EntertainmentTransaction

14. 14 Applications - 2

15. 15 Chaotic Generator

16. 16 Logistic map

17. 17 Modified Logistic map

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

19. 19 MLM: chaotic map

20. 20 MLM: no windows

21. 21 MLM: no windows

22. 22 MLM: uniform distribution r = 5.9

23. 23 MLM: uniform distribution r = 10.8

24. 24 MLM: equivalent

25. 25 MLM: equivalent

26. 26 MLM: pseudorandom

27. 27 MLM: pseudorandom

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

29. 29 Thank you for your attention!

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

31. 31 Random vs. Chaos Observable : Temporal Average for (1): Perturbation : Temporal Average for (2): 3. Stability ：

32. 32 Random vs. Chaos Distinction ：

33. 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. 34 Digital secure communication TransmitterReceiver Source Digital Data MLHCS Encryption Unit Acquire Digital Data Ciphertext Plaintext Encryption Decryption ASMLHCS Decryption Unit

35. 35 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. References