Chaotic Communication – An Overview

1. Chaotic Communication – An Overview Rupak Kharel NCRLab, Northumbria University Supervisors Dr. Krishna Busawon, Prof. Z. Ghassemlooy

2. Outline of the presentation • Chaos – • Introduction • Examples • Application to cryptography & secure communication • Chaos Synchronization • Why/How (??) • Different Types/Methods • Secure communication using chaos • Different methods, problems(!!!) • Different attack methods • Methods proposed, results and analysis • Future works

3. Chaos – introduction • Deterministic system • system has no random or noisy inputs or parameters. The irregular behaviour arises from the system’s nonlinearity rather than from the noisy driving forces. • Aperiodic long term behaviour • trajectories that do not settle down to fixed points, periodic orbits or quasiperiodic orbits as t →∞. • Sensitive dependence on initial conditions & parameters • nearby trajectories separate exponentially fast - the system has positive Lyapunov exponent.

4. Chaos – example • The Lorenz system

5. Chaos – example • The Chua System f(x) is a 3-segment piecewise linear function.

6. Chaos – example • The Duffing system

7. Chaos – application to secure communication • has a broadband spectrum – message does not change the properties of transmitted signal. • Constant output power even when the message is included • Little affect by multi-path fading • cheaper alternative solution to traditional spread spectrum systems. • Aperiodic - limited predictability. • High security at physical level.

8. Chaotic synchronization why/how(??) • Essential in communication systems • Chaotic systems are very sensitive: • to initial conditions and initial parameters - slight different initial condition leads to totally different trajectories • Even the smallest error between Tx and Rx can be expected to grow exponentially. Q1: How can one achieve synchronization? Q2: Can sensitive chaotic systems be used in communications? • Pecora & Carroll1: showed that it is possible to synchronize two chaotic system if they are coupled with common signals • Cuomo & Oppenheim2: practically utilized chaotic synchronization for transmitting message signal 1) L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett., 64, pp. 821-824, 1990 2) K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phy. Rev. Lett., 71, pp. 65-68, 1993.

9. Chaotic synchronization – types One or more driving signals is required to be transmitted sent from source (driving/master) chaotic system to the chaotic system (slave) • Complete Synchronization • Generalized Synchronization • Projective Synchronization • Phase Synchronization • Lag Synchronization • Impulsive Synchronization • Adaptive Synchronization – trajectories of master and slave systems converges to be exactly the same. – slave system trajectory converges to masters trajectory in one-to-one mapping f. – slave system phase converges to masters but their trajectory may not be the same. – In this case, driving signal from master system is not sent continuously but sent as impulses determined by a fixed or time varying interval τ. – special case of generalized, where one-to-one mapping is a simple linear funtionf(x)=ax. – slave system trajectory converges to masters trajectory after a time delay. This is special case of complete synchronization. – Synchronization is adaptive, this is important for attacks as well.

10. Chaotic synchronization – methods • Drive-Response Principle • Active Passive Decomposition • Observer Based Synchronization • Extended Kalman Filtering Method • etc. Driving signal is always transmitted from master to the slave chaotic oscillator for synchronization. Does this means communication??

11. Observer based synchronization • Concept borrowed from the control theory • Chaotic oscillator defined as: • An observer can be defined as: • Therefore, if the error is , then • Therefore, if Kpis chosen such that eigen value of (A-KpC) is negative, then error converges to zero thus achieving synchronization.

12. P & pi-observers • Performance comparison of proportional (P) and proportional-integral (PI) observer under noisy environment. • P-observer will amplify the noise with the value of gain values chosen. • PI-observer will add degree of freedom to the system.

13. Results • Duffing system used as chaotic oscillator • Additive white Gaussian noise (AWGN) channel with signal-to-noise ratio (SNR) of 25 dB Synchronization using PI-observer Synchronization using P-observer My opinion: Secure communication is related with how message is mixed with chaotic carrier but not the method used for synchronization.

14. Chaotic COMMUNICATION– methods • Chaotic Masking Technique • Chaotic Parameter Modulation Technique • Message Inclusion Technique • Chaotic Shift Keying (CSK) Almost all other methods falls into one or more of these categories.

15. Chaotic masking technique • Message spectrum is hidden in the broad chaos spectrum • Observer should show robustness even if it is driven by message + chaotic carrier

16. Parameter modulation technique • Message is used to vary the parameters of the chaotic system • Care should be taken so that change in parameters do not affect the chaotic nature of the system

17. Chaotic shift keying (csk) • Used for transmitting digital message signal. • Two statistically similar chaotic attractor are respectively used to encode bit ‘1’ or ‘0’. • Two attractors are generated by two chaotic systems having the same structure but slightly different parameters.

18. Message inclusion technique • Rather than changing the chaotic parameter, the message is included in one of the states of the chaotic oscillator. By doing this, we are directly changing the chaotic attractor at phase space. • A transmitted signal will be different than the state where the message will be included. • Encryption rule can also be applied.

19. PROBLEMS • Masking, parametric modulation technique and CSK has been proved to be insecure1,2,3. • Breaking methods were based on forecasting and predicting the carrier values, which when subtracted revealed the spectrum of message. • Inclusion method can be secure, however presents a problem of left invertibility. • Hence, the need to improve the security of the above techniques. • K. M. Short, "Steps toward unmasking secure communications," International Journal of Bifurcation and Chaos, vol. 4, pp. 959-977, 1994. • G. Alvarez, F. Montoya, M. Romera, and G. Pastor, "Breaking parameter modulated chaotic secure communication systems," Chaos Solitons & Fractals, vol. 21, pp. 783-787, 2004. • T. Yang, L. B. Yang, and C. M. Yang, "Application of neural networks to unmasking chaotic secure communication," Physica D, vol. 124, pp. 248-257, 1998.

20. Our proposed solutions • Cascaded Chaotic Masking • Two chaotic signal of similar powers are added together to create of carrier of sufficient complexity, where the message is masked.

21. Cascaded chaotic masking – results • Lorenz system was employed for both oscillators and drive response principle as used for achieving synchronization. Fig. 2: Output ytafter second level of masking (transmitted signal) Fig. 1: Output ymafter first level of masking

22. Results (Contd...) • Input and output waveforms

23. Yang’s method based on cryptography • T. Yang et. al proposed a chaotic communication system based on cryptography where they extended the method of masking1. • One chaotic signal was chosen as carrier where an encrypted message signal is masked. • Encryption is performed by using a chaotic key stream different from chaotic carrier. • Method was resistant for various attacks including Short’s method. 1) T. Yang, C. W. Wu, and L. O. Chua, "Cryptography based on chaotic systems," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 44, pp. 469-472, 1997.

24. So what is the problem? • Later, work done by Parker & Short showed that it is still possible to generate the keystream from transmitted chaotic carrier1. • The fact that the dynamics of chaotic keystream was in the transmitted chaotic signal, it was possible to estimate the keystream. • After seeing all these methods to be insecure, does this mean, it is pessimistic to think that chaotic signals after all cannot be used for secure communication??? • My answer will be NO. 1) A. T. Parker and K. M. Short, "Reconstructing the keystream from a chaotic encryption," IEEE Transaction on Circuit and Systems-I: Fundamental Theory And Applications, vol. 48, pp. 624-630, 2001.

25. Our proposed chaotic cryptosystem • Chaotic keystream is generated which is not part of the chaotic dynamics of the transmitter oscillator. • Separate chaotic oscillator is used • Encryption of message signal using this key • Resulting encrypted message signal is masked with chaotic carrier from the chaotic transmitter. • At receiver side, chaotic synchronization is performed and encrypted signal is recovered where same chaotic keystream is applied to decrypt the message signal back. Q: How to generate same keystream in Tx and Rx???

26. y1 (t)r y1(t) y't (t) yt (t) Chaotic Receiver (R) Chaotic Transmitter (T) Channel + e(m (t))r e(m(t)) kr(t) k(t) Chaotic Key Generator (A) Chaotic Key Generator (B) Decryption Rule d(.) Encryption Rule e(.) mr(t) m(t) Fig. Block diagram of the proposed chaotic communication based on cryptography. Proposed chaotic cryptosystem • Non-coupled synchronization is obtained between two chaotic key generator oscillators where both are driven by equivalent chaotic carriers. • No dynamics of the chaotic keystream is present on the transmitted chaotic carrier, hence impossible to estimate the keystream and decrypt the message signal back. y2 (t) y2 (t)r

27. Results Ideal Channel AWGN Channel with SNR = 40dB

28. General issues • The channel through which the signal is transmitted will not be ideal ― most of the researcher tend to assume ideal channel when proposing a new method. • Therefore, the method might not be feasible when implemented practically. • Also, significant development has already been made on digital communication where channel equalization, error correction methods, etc are well developed. • Therefore, parallel development of these techniques on chaotic communication is impractical. • Chaotic communication should therefore complement existing digital communication.

29. ŋt mt yt Yi zt rt Chaotic Oscillator Digital Encoder Channelh(t) Matched Filter A/D Chaotic Observer Threshold Detector D/A Sampler LPF Fig. Block diagram of proposed chaotic communication system using digitization Digitization of chaotic signals • Chaotic signal is converted to digital format with uniform sampling and encoding. • Simple baseband modulation technique on-off keying with 100% duty cycle is used. • We study the performance of this system with respect to bit error rate (BER). • Once optimum BER is set, error control coding can be applied to improve the BER performance. x1 x1r ytr Yir mr

30. Digitization of chaotic signals... • The message recovery is good up to BER>10-4 • AWGN channel was considered here, but dispersion in dispersive channels can easily be compensated using equalizers such as linear equalizer or Wavelet and ANN based equalizers.

31. Conclusions • Chaotic property of a system has a lot of potential in secure communication • Lots of methods has been proposed, but most of them are broken by one method or other • We proposed few methods for realizing potential secure communication links • Digitization concept was implemented on chaotic signals, where already made developments on digital communication is readily available

32. Future works • Hardware realization of the proposed encryption method • Security analysis of the proposed method under various attack methods • Hardware realization of the proposed digitization of chaotic signal, may be by using a DSP board • Implement channel equalization and error control codes

33. Publication list Journal • Kharel, R., Busawon, K. and Ghassemlooy, Z.: "A chaos-based communication scheme using proportional and proportional-integral observers", Iranian Journal of Electrical & Electronic Engineering, Vol. 4, No. 4, pp. 127-139, 2008. Conferences • Kharel, R., Rajbhandari, S., Busawon, K., and Ghassemlooy, Z.: “Digitization of chaotic signal for reliable communication in non-ideal channels”, proceeding of International Conference on Transparent Optical Networks’’, Mediterranean Winter’’ 2008 (ICTON-MW'08), ISBN: 978-1-4244-3485-5, pp. Sa1.2 (1-6), Marrakech, Morocco, 11-13 Dec., 2008. Invited Plenary Paper. • Kharel, R., Busawon, K. and Ghassemlooy, Z.: “Novel cascaded chaotic masking for secure communication“, The 9th annual Postgraduate Symposium on the convergence of Telecommunications , Networking & Broadcasting (PGNET 2008), ISBN 978-1-902560-19-9, Liverpool, UK, pp 295-298, June 2008. • Busawon, K., Kharel, R., and Ghassemlooy, Z.: “A new chaos-based communication scheme using observers”, proceeding of the 6th Symposium on Communication Systems, Networks and Digital Signal Processing 2008 (CSNDSP 2008), ISBN: 978-1-4244-1876-3, pp. 16-20, Graz, Austria, July 2008. • Kharel, R., Busawon, K. and Ghassemlooy, Z.: “A Novel Chaotic Encryption Technique for Secure Communication”, Submitted.

34. acknowledgement • Northumbria University for providing studentship to carry out my Ph.D research work. • My supervisors Dr. Krishna Busawon & Prof. Fary Ghassemlooy for their support and invaluable guidance. • All my colleagues in NCRLab.

35. Thank You. • Any Questions !!!