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C HAOTIC C OMMUNICATION – A N O VERVIEW Rupak Kharel NCRLab, Northumbria University Supervisors Dr. Krishna Busawon, Prof. Z. Ghassemlooy

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O UTLINE 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 2

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C HAOS – 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. 3

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C HAOS – EXAMPLE The Lorenz system 4

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C HAOS – EXAMPLE The Chua System 5 f(x) is a 3-segment piecewise linear function.

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C HAOS – EXAMPLE The Duffing system 6

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C HAOS – 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. 7

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C HAOTIC 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 & Carroll 1 : showed that it is possible to synchronize two chaotic system if they are coupled with common signals Cuomo & Oppenheim 2 : 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 , ) K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phy. Rev. Lett., 71, pp ,

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C HAOTIC 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 9 – 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. – special case of generalized, where one-to-one mapping is a simple linear funtion f ( x )= ax. – slave system phase converges to masters but their trajectory may not be the same. – slave system trajectory converges to masters trajectory after a time delay. This is special case of complete synchronization. – 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. – Synchronization is adaptive, this is important for attacks as well.

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C HAOTIC 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?? 10

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O BSERVER 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 K p is chosen such that eigen value of ( A - K p C ) is negative, then error converges to zero thus achieving synchronization. 11

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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. 12

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

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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. 14 C HAOTIC COMMUNICATION – METHODS

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C HAOTIC MASKING TECHNIQUE 15 Message spectrum is hidden in the broad chaos spectrum Observer should show robustness even if it is driven by message + chaotic carrier

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P ARAMETER MODULATION TECHNIQUE 16 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

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C HAOTIC SHIFT KEYING ( CSK ) 17 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.

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M ESSAGE INCLUSION TECHNIQUE 18 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.

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P ROBLEMS Masking, parametric modulation technique and CSK has been proved to be insecure 1,2,3. 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. 1) K. M. Short, "Steps toward unmasking secure communications," International Journal of Bifurcation and Chaos, vol. 4, pp , ) G. Alvarez, F. Montoya, M. Romera, and G. Pastor, "Breaking parameter modulated chaotic secure communication systems," Chaos Solitons & Fractals, vol. 21, pp , ) T. Yang, L. B. Yang, and C. M. Yang, "Application of neural networks to unmasking chaotic secure communication," Physica D, vol. 124, pp ,

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O UR 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. 20

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C ASCADED CHAOTIC MASKING – RESULTS Lorenz system was employed for both oscillators and drive response principle as used for achieving synchronization. 21 Fig. 1: Output y m after first level of masking Fig. 2: Output y t after second level of masking (transmitted signal)

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R ESULTS (C ONTD...) Input and output waveforms 22

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Y ANG ’ S METHOD BASED ON CRYPTOGRAPHY T. Yang et. al proposed a chaotic communication system based on cryptography where they extended the method of masking 1. 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. 23 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 , 1997.

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S O WHAT IS THE PROBLEM ? Later, work done by Parker & Short showed that it is still possible to generate the keystream from transmitted chaotic carrier 1. 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. 24 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 , 2001.

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O UR 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??? 25

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P ROPOSED CHAOTIC CRYPTOSYSTEM 26 k r (t) Chaotic Transmitter (T) Chaotic Key Generator (A) Encryption Rule e(.) m(t ) + y t (t) Channel Chaotic Receiver (R) Chaotic Key Generator (B) Decryption Rule d(.) y' t (t) m r (t) y1(t)y1(t) y 1 (t) r k(t ) e(m(t)) e(m (t)) r Fig. Block diagram of the proposed chaotic communication based on cryptography. y 2 (t) y 2 (t) r 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.

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R ESULTS 27 Ideal Channel AWGN Channel with SNR = 40dB

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G ENERAL 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. 28

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D IGITIZATION 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. 29 ztzt rtrt YiYi ytyt Chaotic Oscillator mtmt A/D Digital Encoder Channel h(t) ŋtŋt Matched Filter D/A Chaotic Observer Fig. Block diagram of proposed chaotic communication system using digitization Sampler Threshold Detector LPF Y ir y tr x1x1 x 1r mrmr

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D IGITIZATION 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.

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C ONCLUSIONS 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 31

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F UTURE 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 32

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P UBLICATION 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 , A chaos-based communication scheme using proportional and proportional-integral observers 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: , pp. Sa1.2 (1-6), Marrakech, Morocco, Dec., Invited Plenary Paper. Digitization of chaotic signal for reliable communication in non-ideal channels”, proceeding of International Conference on Transparent Optical Networks 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 , Liverpool, UK, pp , June Novel cascaded chaotic masking for secure communication 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: , pp , Graz, Austria, July A new chaos-based communication scheme using observers Kharel, R., Busawon, K. and Ghassemlooy, Z.: “ A Novel Chaotic Encryption Technique for Secure Communication ”, Submitted. A Novel Chaotic Encryption Technique for Secure Communication 33

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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. 34

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Thank You. Any Questions !!! 35

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