CHAOTIC COMMUNICATION – AN OVERVIEWRupak Kharel

NCRLab, Northumbria University

Supervisors

Dr. Krishna Busawon, Prof. Z. Ghassemlooy

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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

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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.

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CHAOS – EXAMPLE

The Lorenz system

010

2030

4050

-20

-10

0

10

20-30

-20

-10

0

10

20

30

z(t)x(t)

y(t)

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CHAOS – EXAMPLE

The Chua System

-4-2

02

4

-5

0

5-1

-0.5

0

0.5

1

x(t)z(t)

y(t)

f(x) is a 3-segment piecewise linear function.

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CHAOS – EXAMPLE

The Duffing system

-5 0 5-15

-10

-5

0

5

10

15

x1(t)

x 2(t)

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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.

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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.

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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.– 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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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??

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 Kp is chosen such that eigen value of (A- KpC) is negative, then error converges to zero thus achieving synchronization.

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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.

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RESULTS

Duffing system used as chaotic oscillator Additive white Gaussian noise (AWGN) channel

with signal-to-noise ratio (SNR) of 25 dB

-150 -100 -50 0 50 100 150-150

-100

-50

0

50

100

150

x1

x 1h

-5 0 5-5

0

5

x1

x 1h

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.

CHAOTIC COMMUNICATION – METHODS

CHAOTIC MASKING TECHNIQUE

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Message spectrum is hidden in the broad chaos spectrum

Observer should show robustness even if it is driven by message + chaotic carrier

PARAMETER MODULATION TECHNIQUE

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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

CHAOTIC SHIFT KEYING (CSK)

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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.

MESSAGE INCLUSION TECHNIQUE

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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.

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.

1) K. M. Short, "Steps toward unmasking secure communications," International Journal of Bifurcation and Chaos, vol. 4, pp. 959-977, 1994.

2) 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.

3) 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.

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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.

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CASCADED CHAOTIC MASKING – RESULTS

Lorenz system was employed for both oscillators and drive response principle as used for achieving synchronization.

Fig. 1: Output ym after first level of masking

Fig. 2: Output yt after second level of masking (transmitted signal)

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RESULTS (CONTD...)

Input and output waveforms

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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.

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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.

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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???

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PROPOSED CHAOTIC CRYPTOSYSTEM

kr(t)

Chaotic Transmitter (T)

Chaotic Key Generator (A)

Encryption Rule e(.)

m(t)

+yt (t)

ChannelChaotic Receiver (R)

Chaotic Key Generator (B)

Decryption Rule d(.)

y't (t)

mr(t)

y1(t)y1 (t)r

k(t)

e(m(t)) e(m (t))r

Fig. Block diagram of the proposed chaotic communication based on cryptography.

y2 (t) y2 (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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RESULTS

Ideal Channel AWGN Channel with SNR = 40dB

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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.

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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.

ztrtYiytChaotic

Oscillator

mt

A/D Digital Encoder

Channel h(t)

ŋt

Matched Filter

D/AChaotic Observer

Fig. Block diagram of proposed chaotic communication system using digitization

SamplerThreshold DetectorLPF

Yirytr

x1

x1r

mr

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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.

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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

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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

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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.

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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.

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Thank You. Any Questions !!!