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Dynamical Discrete-Time Rössler Map with Variable Delay

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Computational Science and Its Applications -- ICCSA 2015 (ICCSA 2015)

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Abstract

This paper presents an improvement to an existing method used in security data transmission based on discrete time hyperchaotic cryptography. The technique is implemented for a Rössler hyperchaotic generator. The improvement consists in modifying the structure of the existing generator in order to increase the robustness of the new cryptosystem with respect to known plain text attack, particularly the "identification technique".

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References

  1. Anstett, F., Millerioux, G., Bloch, G.: Message-embedded cryptosystems: cryptanalysis and identifiability. In: 44th IEEE Conf. on Proc. and 2005 European Control Conf. Decision and Control CDC-ECC 2005, pp. 2548–2553 (2005)

    Google Scholar 

  2. Baptista, M.S.: Cryptography with chaos. Physics Letters A 240(1–2), 50–54 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Belmouhoub, I., Djemai, M., Barbot, J.-P.: Cryptography by discrete-time hyperchaotic systems. In: Proc. 42nd IEEE Conf. Decision and Control, vol. 2, pp. 1902–1907 (2003)

    Google Scholar 

  4. Bhat, K., Koivo, H.: Modal characterizations of controllability and observability in time delay systems 21(2), 292–293 (1976)

    Google Scholar 

  5. Carroll, T.L., Pecora, L.M.: Synchronizing chaotic circuits 38(4), 453–456 (1991)

    Google Scholar 

  6. Cicarella, G., Dalla Mora, M., Germani, A.: A robust observer for discrete time nonlinear systems. Sys. Contr. Lett. 24(10), 291–300 (1995)

    Article  Google Scholar 

  7. Diop, S., Fliess, M.: Nonlinear observability, identifiability, and persistent trajectories. In: Proc. 30th IEEE Conf. Decision and Control, pp. 714–719 (1991)

    Google Scholar 

  8. Fliess, M.: Automatique en temps discret et algbre aux diffrences. Mathematicum 2, 213–232 (1990)

    MATH  MathSciNet  Google Scholar 

  9. Frunzete, M., Florea, B.C., Stefanescu, V., Stoichescu, D.A.: Image enciphering by using rossler map. In: Proceedings of the 2011 IEEE International Conference on Intelligent Computer Communication and Processing, pp. 307–310 (2011)

    Google Scholar 

  10. Frunzete, M., Luca, A., Vlad, A.: On the statistical independence in the context of the rössler map. In: 3rd Chaotic Modeling and Simulation International Conference (CHAOS2010), Chania, Greece (2010). http://cmsim.net/sitebuildercontent/sitebuilderfiles/

  11. Frunzete, M., Luca, A., Vlad, A., Barbot, J.-P.: Statistical behaviour of discrete-time rössler system with time varying delay. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part I. LNCS, vol. 6782, pp. 706–720. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Frunzete, M., Barbot, J.-P., Letellier, C.: Influence of the singular manifold of nonobservable states in reconstructing chaotic attractors. Physical Review E 86(2), 026205 (2012)

    Article  Google Scholar 

  13. Larger, L., Goedgebuer, J-P.: Le chaos chiffrant. Pour la science (36) (2002)

    Google Scholar 

  14. Ljung, L.: System Identification - Theory for the User, 2nd edn. Prentice-Hall, Upper Saddle River (2002)

    Google Scholar 

  15. Nijmeijer, H., van der Schaft, A.: Nonlinear dynamical control systems. Springer-Verlag New York Inc., New York (1990)

    Book  MATH  Google Scholar 

  16. Nomm, S., Moog, C.H.: Identifiability of discrete-time nonlinear systems. In: Proc. of the 6th IFAC Symposium on Nonlinear Control Systems, pp. 477–489. NOLCOS, Stuttgart (2004)

    Google Scholar 

  17. Perruquetti, W., Barbot, J.-P.: Chaos in automatic control. CRC Press, Taylor & Francis Group (2006)

    Google Scholar 

  18. Richard, J.-P.: Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  19. Stefanescu, V., Stoichescu, D., Frunzete, M., Florea, B.: Influence of computer computation precision in chaos analysis. University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics 75(1), 151–162 (2013)

    MathSciNet  Google Scholar 

  20. Vlad, A., Luca, A., Frunzete, M.: Computational measurements of the transient time and of the sampling distance that enables statistical independence in the logistic map. In: Gervasi, O., Taniar, D., Murgante, B., Laganà, A., Mun, Y., Gavrilova, M.L. (eds.) ICCSA 2009, Part II. LNCS, vol. 5593, pp. 703–718. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Vo Tan, P., Millerioux, G., Daafouz, J.: Left invertibility, flatness and identifiability of switched linear dynamical systems: a framework for cryptographic applications. International Journal of Control 83(1), 145–153 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  22. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining lyapunov exponents from a time series. Physica, 285–317 (1985)

    Google Scholar 

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Correspondence to Madalin Frunzete .

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Frunzete, M., Popescu, A.A., Barbot, JP. (2015). Dynamical Discrete-Time Rössler Map with Variable Delay. In: Gervasi, O., et al. Computational Science and Its Applications -- ICCSA 2015. ICCSA 2015. Lecture Notes in Computer Science(), vol 9155. Springer, Cham. https://doi.org/10.1007/978-3-319-21404-7_32

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  • DOI: https://doi.org/10.1007/978-3-319-21404-7_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21403-0

  • Online ISBN: 978-3-319-21404-7

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