Dynamical Discrete-Time Rössler Map with Variable Delay

  • Madalin FrunzeteEmail author
  • Anca Andreea Popescu
  • Jean-Pierre Barbot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9155)


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".


Dynamical-systems Cryptography Chaotic map Identifiability Chaotic-discrete system with delay 


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  1. 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. 2.
    Baptista, M.S.: Cryptography with chaos. Physics Letters A 240(1–2), 50–54 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 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. 4.
    Bhat, K., Koivo, H.: Modal characterizations of controllability and observability in time delay systems 21(2), 292–293 (1976)Google Scholar
  5. 5.
    Carroll, T.L., Pecora, L.M.: Synchronizing chaotic circuits 38(4), 453–456 (1991)Google Scholar
  6. 6.
    Cicarella, G., Dalla Mora, M., Germani, A.: A robust observer for discrete time nonlinear systems. Sys. Contr. Lett. 24(10), 291–300 (1995)CrossRefGoogle Scholar
  7. 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. 8.
    Fliess, M.: Automatique en temps discret et algbre aux diffrences. Mathematicum 2, 213–232 (1990)zbMATHMathSciNetGoogle Scholar
  9. 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. 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).
  11. 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) CrossRefGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 13.
    Larger, L., Goedgebuer, J-P.: Le chaos chiffrant. Pour la science (36) (2002)Google Scholar
  14. 14.
    Ljung, L.: System Identification - Theory for the User, 2nd edn. Prentice-Hall, Upper Saddle River (2002) Google Scholar
  15. 15.
    Nijmeijer, H., van der Schaft, A.: Nonlinear dynamical control systems. Springer-Verlag New York Inc., New York (1990) zbMATHCrossRefGoogle Scholar
  16. 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. 17.
    Perruquetti, W., Barbot, J.-P.: Chaos in automatic control. CRC Press, Taylor & Francis Group (2006)Google Scholar
  18. 18.
    Richard, J.-P.: Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  19. 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)MathSciNetGoogle Scholar
  20. 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) CrossRefGoogle Scholar
  21. 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)zbMATHMathSciNetCrossRefGoogle Scholar
  22. 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

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Madalin Frunzete
    • 1
    • 2
    Email author
  • Anca Andreea Popescu
    • 1
  • Jean-Pierre Barbot
    • 2
    • 3
  1. 1.Faculty of Electronics, Telecommunications and Information TechnologyPOLITEHNICA University of BucharestBucharest 6Romania
  2. 2.Electronique Et Commande des Systmes LaboratoireEA 3649 (ECS-Lab/ENSEA), ENSEACergy-pontoiseFrance
  3. 3.EPI Non-A INRIALyonFrance

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