Novel Cascaded Chaotic Masking for Secure Communications

1. Novel Cascaded Chaotic Masking for SecureCommunications Rupak Kharel, Krishna Busawon & Zabi Ghassemloy Northumbria Communication Research Lab Northumbria University

2. Outline • Chaos – Introduction • Application to communication • Different techniques for chaotic communication • Problem statement • Cascaded chaotic masking technique • Results • Final Comments

3. CHAOS – INTRODUCTION • Deterministic system • means that the 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 • means that there should be trajectories which do not settle down to fixed points, periodic orbits or quasiperiodic orbits as t →∞. • Sensitive dependence on initial conditions • means that nearby trajectories separate exponentially fast, which means the system has positive Liapunov exponent.

4. CHAOS – EXAMPLE; LORENZ EQUATIONS • Are dynamical system exhibiting chaotic property • Three dimensional system given as: • States are evolving in a complex non repetitive pattern over time.

5. CHAOS – APPLICATIONS IN COMMUNICATION • Chaotic signal has a broadband spectrum, hence the presence of information does not necessarily change the properties of transmitted signal. • Power output remains constant regardless of the information content. • It is resistant against multi-path fading and offers cheaper solution to traditional spread spectrum systems. • Chaotic signal are aperiodic therefore limited predictability. • Hence, chaotic signal can be used for providing security at physical level.

6. CHAOTIC SYNCHRONIZATION (HOW???) • Chaotic systems are very sensitive: • Slightly different initial conditions and initial parameters lead to totally different trajectories. • slight errors between transmitter and receiver can be expected to grow exponentially. Q1: How can one achieve synchronization? Q2: Can this sensitive chaotic system be used in communication? • 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.

7. CHAOTIC COMMUNICATION –TECHNIQUES • 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.

8. Chaotic masking technique • Message signal (m) is buried in the broad chaos spectrum by adding m to a chaotic mask y. • At receiver, the chaotic mask that is estimated from chaotic synchronization, is removed from received signal to obtain m.

9. Parameter modulation technique • Some parameters of chaotic system are varied by adding the message signal. • At receiver an adaptive controller is used to tune the chaotic system parameters to ensure zero synchronization error .

10. 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.

11. Chaotic shift keying (csk) • Used for transmitting digital message signal. • Two statistically similar chaotic attractor are respectively used to encode bit ‘1’ or ‘0’. • These two attractors are generated by two chaotic systems having the same structure but slightly different parameters. • At receiver, the received signal is used to drive a chaotic system similar to one of the transmitters. • The message is recovered by thresholding the synchronization error signal.

12. CHAOS – TECHNIQUES 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 is secure, however presents a problem of inversion. • 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.

13. CHAOS – PROBABLE SOLUTION • Cascaded Masking Technique (CMT). • Two chaotic signals (generated by two oscillators) are added together at roughly equal power to generate a carrier of sufficient complexity. • Forecasting and predicting carrier behaviour is hence not possible. • Simpler masking technique thus can be extended as cascaded structure for more secure links.

14. Cascaded masking technique (cmt) • Chaotic receiver ‘B’ synchronizes with oscillator ‘B’ to estimate and recover ym to drive chaotic receiver ‘A’ to synchronize with oscillator ‘A’.

15. CMT – APPLICATION USING LORENZ SYSTEM • Transmitter A • Transmitter B • Receiver B • Receiver A Note: A scaled Lorenz equation is used as done by Cuomo & Oppenheim for favourable electronic implementation, otherwise wide dynamic range of the solution will exceed typical power supply limit.

16. CMT – RESULTS • Parameters adopted and assumption made • σ, r, b = 16,45.6 and 4 • m(t) = 0.1 sin(2πt) • All the gains are set to zero • Arbitrary Initial conditions • Ideal channel and no noise Fig. 2: Output ymafter first level of masking (transmitted signal) Fig. 1: Output ymafter first level of masking

17. CMT – RESULTS (CONTD…) • Input and output waveforms

18. Limitations & future work • Taking into consideration non-ideal channel with noise. • The synchronization robustness of receiver B is critical for the proper synchronization of receiver A and proper message extraction. • Expanding the system to work with other chaotic oscillator such Chua’s circuit, Duffing oscillator, Colpitts oscillator, etc. • Hardware implementation.

19. Conclusion • A novel cascaded masking technique to increase the security of the chaotic communication system was presented. • Theoretical analysis was given. Simulation results presented demonstrated successful recovery of the message signal. • Limitation and future works were also outlined.

20. acknowledgements • I would like to thank • Northumbria University for providing me with PhD studentship to carry out the research. • My supervisors Dr. Krishna Busawon and Prof. Zabi Ghassemlooy. • My collegues in NCRLab.

21. Thank you. (Any questions !!!)