Abstract
This chapter introduces nonlinear dynamical systems known as chaotic systems and describes their suitability for application to secure communications. A nonlinear or chaotic signal is characterised by its high sensitivity to parameter and initial condition perturbations, the random like nature and broadband spectrum [1]. From a nonlinear dynamical perspective, chaotic motion is a motion which possesses at least one positive Lyapunov exponent. Furthermore, for a given set of parameters and initial conditions chaotic motion is highly deterministic. Among other applications, these properties make chaotic systems suitable for the application in secure communications [2-9]. One of the main reasons for the increased security of communication provided by the chaotic signals is their broadband nature. In many cases the broadband nature of a chaotic system allows for the effective spectral cover up of the message by the chaotic carrier. In addition, the high sensitivity of chaotic signals to parameter and initial condition perturbations often can act as the encryption keys. In this chapter, the distinguishing features of chaotic systems are first presented and some approaches, used to identify chaotic behavior, are introduced. Furthermore, the approaches and the suitability of chaotic systems to the implementation within secure communication systems are examined. Finally, some of the noise reduction techniques, used to filter chaotic communication systems, are introduced.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Sprott, J.C.: Chaos and Time-Series Analysis, pp. 230–440. Oxford University Press, Oxford (2003)
Stavroulakis, P.: Introduction. In: Stavroulakis, P. (ed.) Chaos Applications in Telecommunications, pp. 1–12. CRC Press LLC, Boca Raton (2006)
Kennedy, M.P., Kolumban, G., Jako, Z.: Chaotic Modulation Schemes. In: Kennedy, M.P., Rovatti, R., Setti, G. (eds.) Chaotic Electronics in Telecommunications, pp. 163–175. CRC Press LLC, Boca Raton (2000)
Chen, G., Dong, X.: From chaos to order: Methodologies, Perspectives and Applications, pp. 598–614. World Scientific Publishing Co. Pte. Ltd., Singapore (1998)
Lau, F.C.M., Tse, C.K.: Chaos-Based Digital Communication Systems, ch. 1, pp. 1–20. Springer, Berlin (2004)
Kolumban, G., Kennedy, M.P.: Correlator-Based Chaotic Communications: Attainable Noise and Multipath Performance. In: Chen, G., Ueta, T. (eds.) Chaos in Circuits and Systems, pp. 443–485. World Scientific Publishing Co. Pte. Ltd., New Jersey (2002)
Kennedy, M.P., Kolumban, G.: Digital Communications Using Chaos. In: Chen, G. (ed.) Controlling Chaos and Bifurcations in Engineering Systems, pp. 477–500. CRC Press LLC, Boca Raton (1999)
Wu, C.W.: Synchronization in coupled chaotic circuits and systems, pp. 13–33. World Scientific Publishing Co. Pte. Ltd., New Jersey (2002)
Setti, G., Rovatti, R., Mazzini, G.: Control of Chaos Statistics for Optimization of DS-CDMA Systems. In: Chen, G., Yu, X. (eds.) Chaos Control Theory and Applications, pp. 295–319. Springer, Berlin (2003)
Abraham, R., Ueda, Y.: The chaos avant – garde memories of the early days of chaos theory, pp. 23–80. World Scientific Publishing Co. Pte. Ltd., Singapore (2000)
Moon, F.C.: Chaotic Vibrations - An Introduction for Applied Scientists and Engineers, pp. 24–36. Wiley Interscience, New York (1987)
Rossler, O.E.: An equation for continuous chaos. Physics Letters A 57A(5), 397–398 (1976)
Rucklidge, A.M.: Chaos in models of double convection. Journal of Fluid Mechanics 237, 209–229 (1992)
Parlitz, U., Ergezinger, S.: Robust communication based on chaotic spreading sequences. Physics Letters A 188(2), 146–150 (1994)
Zhou, C.S., Chen, T.L.: Extracting information masked by chaos and contaminated with noise: Some considerations on the security of communication approaches using chaos. Physics Letters A 234(6), 429–435 (1997)
Moon, F.C.: Chaotic and Fractal Dynamics - An Introduction for Applied Scientists and Engineers, pp. 307–309. Wiley Interscience, New York (1992)
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Physical Review Letters 64(8), 821–824 (1990)
Jovic, B., Unsworth, C.P.: Chaos based multi-user time division multiplexing communication system. IET Communications 1(4), 549–555 (2007)
Jordan, D.W., Smith, P.: Mathematical Techniques: An introduction for the engineering, physical, and mathematical sciences, 2nd edn., p. 8. Oxford University Press, Oxford (1997)
Jovic, B., Unsworth, C.P., Berber, S.M.: De-noising ‘Initial Condition Modulation’ Wideband Chaotic Communication Systems with Linear & Wavelet Filters. In: Proceedings of the First IEEE International Conference on Wireless Broadband and Ultra Wideband Communications (AusWireless 2006), Sydney, Australia, March 13-16, pp. 1–6 (2006)
Grzesiak, M.: Wavelet filtering of chaotic data. Nonlinear processes in geophysics 7, 111–116 (2000)
Broomhead, D., Huke, J., Muldoon, M.: Linear Filters and Nonlinear Systems. Journal of the Royal Statistical Society 54(2), 373–382 (1992)
Roy, M., Kumar, V., Kulkarni, B., Sanderson, J., Rhodes, M., Stappen, M.: Simple denoising algorithm using wavelet transform. AIChE Journal 45(11), 2461–2466 (1999)
Constantine, W., Reinhall, P.: Wavelet-based in-band denoising technique for chaotic sequences. International Journal of Bifurcation and Chaos 11(2), 483–495 (2000)
Boccalleti, S., Guiaquinta, A., Arecchi, F.: Adaptive recognition and filtering of noise using wavelets. Physical Review E 55(5), 5393–5397 (1997)
Lee, C.: Noise reduction methods for chaotic signals with application to secure communications, PhD thesis, Georgia institute of technology (1995)
Carroll, T.L.: Approximating chaotic time series through unstable periodic orbits. Physical Review E 59(2), 1615–1621 (1999)
Nievergelt, Y.: Wavelets made easy, ch. 1, 2 and 3. Birkhauser, Boston (1999)
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Jovic, B. (2011). Chaotic Signals and Their Use in Secure Communications. In: Synchronization Techniques for Chaotic Communication Systems. Signals and Communication Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21849-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-21849-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21848-4
Online ISBN: 978-3-642-21849-1
eBook Packages: EngineeringEngineering (R0)