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Output Choice of a Chaotic Jerk Circuit Used as Transmitter in Data Secure CommunicationsDATCU, O. , STANCIU, M. , TAULEIGNE, R. , BURILEANU, C. , BARBOT, J.-P.
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chaotic communication, nonlinear dynamical systems, observers, signals analysis, sliding mode control
chaotic(11), chaos(11), systems(9), cryptography(5), circuits(5), system(4), review(4), physical(4), control(4), barbot(4)
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About this article
Date of Publication: 2015-11-30
Volume 15, Issue 4, Year 2015, On page(s): 63 - 68
ISSN: 1582-7445, e-ISSN: 1844-7600
Digital Object Identifier: 10.4316/AECE.2015.04008
Web of Science Accession Number: 000368499800008
SCOPUS ID: 84949960782
Usually, when analyzing a data series, dynamical systems theory is used to reconstruct the state space of the original system. This work aims to determine which of a chaotic system's states is best suited as output when transmitting secret messages. This is the first step prior to designing an actual communication scheme. As an example, the three states of Sprott's jerk circuit are analyzed in terms of the local observability they ensure for the original dynamics when transmitted as a scalar data series. Results show that its first two states enable accurate estimation of the transmitter's dynamics at the receiving end. However, its third state generates, in some regions of the state space, a non-invertible transformation between the original state space and the one the receiver sees. This is due to the exponential nonlinearities present in this state's derivatives. Given that these nonlinearities remain inaccessible to the receiver, they are neglected in order to allow the partial reconstruction of the dynamics of the transmitter. But, since these nonlinearities are essential for the chaotic behavior, this makes the third state unusable for cryptographic purposes. This analysis may be applied to any bipolar junction transistor or diode based chaotic circuit.
|References|||||Cited By «-- Click to see who has cited this paper|
| L. Kocarev, "Chaos-based cryptography: a brief overview", Circuits and Systems Magazine, IEEE 1 (3), 6-21. Inst. for Nonlinear Sci., California Univ., San Diego, La Jolla, 09/2002. |
[CrossRef] [SCOPUS Times Cited 579]
 G. Jakimoski, L. Kocarev, "Chaos and Cryptography: Block Encryption Ciphers Based on Chaotic Maps", IEEE Transactions On Circuits And SystemsI: Fundamental Theory And Applications, Vol. 48, No. 2, February 2001.
[CrossRef] [Web of Science Times Cited 405] [SCOPUS Times Cited 477]
 C. Pellicer-Lostao, R. Lopez-Ruiz, "Notions of Chaotic Cryptography: Sketch of a Chaos Based Cryptosystem", Chapter 12 from Applied Cryptography and Network Security, edited by Jaydip Sen, ISBN 978-953-51-0218-2, Published: March 14, 2012 under CC BY 3.0 license,
 R. L. Devaney, "An introduction to Chaotic Dynamical Systems", Perseus Books (Second Ed. 1989).
 V. Grigoras, C. Grigoras, "A Novel Chaotic System for Random Pulse Generation", Advances in Electrical and Computer Engineering: AECE, Vol. 14, Issue: 2, 2014, ISSN: 1582-7445, eISSN: 1844-7600.
[CrossRef] [Full Text] [Web of Science Times Cited 2] [SCOPUS Times Cited 3]
 S. Vlad, S-Gh. Pentiuc, "Searching of Chaotic Elements in Hydrology", Journal of Applied Computer Science & Mathematics, no. 16 (32), 2014, Suceava.
 S. Vlad, P. Pascu, N. Morariu, "Chaos Models in Economics", Journal of Computing, Vol. 2, Issue 1, January 2010, ISSN 2151-9617, pp. 79-83.
 G. Mahalu, A. Graur, "The Fractal Techniques Applied in Pattern Recognition", The Eighth All-Ukrainian International Conference, Ukrobrez'2006, 28-31 August, 2006, Kyjiv, Ukraine, ISSB/ISBN: ISBN 966-02-4096-1, pp. 35-38, (2006).
 S. Pohoata, O. German, A. Graur, "Dual tasking: gait and tremor in Parkinson's disease - acquisition, processing and clustering", Rev. Roum. Sci. Techn. - Électrotechn. et Énerg., 58, 3, p. 324-334, Bucharest, 2013.
 G. Alvarez, S. Li, "Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems", International Journal of Bifurcation and Chaos, vol. 16, no. 8, pp. 2129-2151, 2006.
[CrossRef] [Web of Science Times Cited 788] [SCOPUS Times Cited 944]
 G. Jakimoski, L. Kocarev, "Analysis of some recently proposed chaos-based encryption algorithms", Physics Letters A 291 (2001) 381-384, 17 December 2001.
[CrossRef] [Web of Science Times Cited 112] [SCOPUS Times Cited 133]
 G. Alvarez, J.- M. Amigo, D. Arroyo, S. Li, "Lessons learnt from the cryptanalysis of chaos-based ciphers", Chapter 8, Chaos-Based Cryptography: Theory, Algorithms and Applications, pp. 257-295, Springer-Verlag GmbH, 2011.
[CrossRef] [SCOPUS Times Cited 55]
 J. C. Sprott, "A new chaotic jerk circuit", J. C. IEEE Transactions on Circuits and Systems-II: Express Briefs 58, 240-243, 2011.
[CrossRef] [Web of Science Times Cited 111] [SCOPUS Times Cited 128]
 Z. Fu and J. Heidel, "Non-chaotic behaviour in three-dimensional quadratic systems", Nonlinearity 10 (1997) 1289-1303, Printed in the UK, PII: S0951-7715(97)78288-4.
[CrossRef] [Web of Science Times Cited 50] [SCOPUS Times Cited 50]
 B. Mumuangsaen, B. Srisuchinwong, J.C. Sprott (2011), "Generalization of the Simplest Autonomous Chaotic System", Physics Letters A, Vol. 375, No. 12, March, pp. 1445-1450.
[CrossRef] [Web of Science Times Cited 51] [SCOPUS Times Cited 55]
 A. Wolf, J. B. Swift, H. L. Swinney, J. A. Vastano, "Determining Lyapunov exponents from a time series", Physica D, Vol. 16, pp. 285-317, 1985.
[CrossRef] [Web of Science Times Cited 5998] [SCOPUS Times Cited 5663]
 H.-T. Yau, Y.-C. Pu, S. Cimin Li, "Application of a Chaotic Synchronization System to Secure Communication", ISSN 1392 - 124 X Information Technology And Control, 2012, Vol.41, No.3.
 D. I. R. Almeida, J. Alvarez, J. G. Barajas, "Robust synchronization of Sprott circuits using sliding mode control", Chaos, Solitons and Fractals Vol. 30(1), 2006, 11-18.
[CrossRef] [Web of Science Times Cited 40] [SCOPUS Times Cited 54]
 A. Levant, "Robust exact differentiation via sliding mode technique", Automatica, vol. 34, no. 3, pp. 379-384, 1998.
[CrossRef] [Web of Science Times Cited 1207] [SCOPUS Times Cited 1532]
 N. H. Packard, J. P. Crutchfield, J. D. Farmer, R. S. Shaw, "Geometry from a time series", Physical Review Letters, 45 (25), pp.712-716, 1980.
[CrossRef] [Web of Science Times Cited 2703] [SCOPUS Times Cited 2926]
 G. Gouesbet, "Reconstruction of Standard and Inverse Vector Fields Equivalent to a Rössler system", Physical Review A, 44 (26), pp. 6264-6280, 1991.
[CrossRef] [Web of Science Times Cited 27] [SCOPUS Times Cited 28]
 G. B. Mindlin, H. G. Solari, M. A. Natiello, R. Gilmore, X. J. Hou, "Topological Analysis of Chaotic Time Series Data from the Belousov-Zhabotinski", Journal of Nonlinear Sciences, 1, pp. 147-173, 1991.
[CrossRef] [SCOPUS Times Cited 118]
 C. Letellier, L. A. Aguirre and J. Maquet, "How the choice of the observable may influence the analysis of non linear dynamical systems", Communications in Nonlinear Science and Numerical Simulation, Vol. 11 (5), 555-576, 2006.
[CrossRef] [SCOPUS Times Cited 30]
 C. Letellier and L. A. Aguirre, "Interplay between synchronization, observability, and dynamics", Physical Review E, Vol. 82, 016204, 2010.
[CrossRef] [Web of Science Times Cited 29] [SCOPUS Times Cited 32]
 M. Demazure, "Catastrophes et Bifurcations", Ellipse, Paris, 1989.
 R. Hermann and A. Krener, "Nonlinear controllability and observ-ability", IEEE Transactions on Automatic Control, vol. 22, no. 5, pp.728-740, 1977.
[CrossRef] [Web of Science Times Cited 1142] [SCOPUS Times Cited 1420]
 A. Trautman, "Remarks on the history of the notion of Lie differentiation", Variations, Geometry and Physics in honour of Demeter Krupkas sixty-fifth birthday O. Krupkova and D. J. Saunders (Editors) Nova Science Publishers, pp. 297-302, 2008.
 M. Frunzete, J.-P. Barbot, and C. Letellier, "Influence of the singular manifold of observable states in reconstructing chaotic attractors", Physical Review E, vol. 86, 2012. PMid:23005843
 J.-P. Barbot, D. Boutat, and T. Floquet, "An observation algorithm for nonlinear systems with unknown inputs", Automatica, vol. 45, no. 8, pp.1970-1974, 2009.
[CrossRef] [Web of Science Times Cited 36] [SCOPUS Times Cited 49]
 H. Hamiche, M. Ghanes, J. P. Barbot, K. Kemih, S. Djennoune, "Hybrid dynamical systems for private digital communication", International Journal of Modelling Identification and Control 01/2013; 20(2):99-113.
[CrossRef] [SCOPUS Times Cited 14]
 T. Boukhobza and J-P Barbot, "High Order Sliding Modes Observer", Proceeding of the 37th IEEE CDC, Tampa USA, pp. 1912-1917, 1998. [Online]
 R. Tauleigne, O. Datcu, and M. Stanciu, "Thwarting cryptanalytic attacks based on the correlation function", The 10th International Conference on Communications (COMM 2014), Bucharest, May 2014.
[CrossRef] [SCOPUS Times Cited 1]
 M. P. Kennedy, "Chaos in the Colpitts oscillator", IEEE Transactions On Circuits and Systems - 1 CAS, 41 (27):771-774, 1994.
[CrossRef] [Web of Science Times Cited 261] [SCOPUS Times Cited 306]
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