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ISSN 2542-1905 (Online)

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Isaeva O. B., Lubchenko D. O. Comparative analysis of the secure communication schemes based on the generators of hyperbolic strange attractor and strange nonchaotic attractor. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, iss. 1, pp. 31-41. DOI: 10.18500/0869-6632-003078, EDN: VEFEDZ

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Comparative analysis of the secure communication schemes based on the generators of hyperbolic strange attractor and strange nonchaotic attractor

Isaeva Olga Borisovna, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Lubchenko Dmitry Olegovich, Kotel'nikov Institute of Radioengineering and Electronics of Russian Academy of Sciences

The purpose of this work is to analyse qualitative features of the information transmission process via several communication schemes based on the synchronization of transmitter and receiver, both being complex signal generators. For this purpose generators of the hyperbolic chaos and generators with the strange nonchaotic attractor are employed. Evaluation of advantages and disadvantages of such schemes is made comparing themselves with each other as well as with schemes based on the nonhyperbolic chaotic generators.

Methods. The power spectra and the distributions of the largest finite-time Lyapunov exponent are used to confirm the complexity of the dynamics of the generators in use and to verify the wide-bandness, robustness and stochasticity of their signals. Confidentiality of the informational signal transmission is achieved using its nonlinear mixing to the dynamics of the transmitter. The special phase mixing is used since the model generators employed for the research demonstrate nontrivial dynamics for the angular variable — oscillations phase shift. The digital image is used as an information for transmission. Visual control during the transmission process allows to carry out the qualitative analysis of the success of the signal coding and its detecting by the receiver.

Results. Successful transmission and decoding of information for all schemes under investigation are demonstrated for the case of identical transmitter and receiver. Parameter detuning of these generators leads to difficulties in separation of the informational signal from the chaotic/complex carrier due to loss of the full synchronization. For the nonhyperbolic chaos detuning of the parameter responsible for the amplitude of the signal leads to the bad quality of the detection while frequency detuning makes detection absolutely impossible. Schemes with the hyperbolic chaos and strange nonchaotic dynamics appear to demonstrate much better results. The information detection is much better in this case because of the robustness of the generalized synchronization.

Conclusion. Robust chaotic and complex nonchaotic generators appear to have significant advantages for communication systems comparing to the chaotic generators of nonhyperbolic type.

Supported by Russian Science Foundation, Grant No. 21-12-00121. We acknowledge PhD D. V. Savin for usefull discussion.
  1. Dmitriev AS, Panas AI. Dynamical Chaos: New Information Carriers for Communication Systems. Moscow: Fizmatlit; 2002. 252 p. (in Russian).
  2. Koronovskii AA, Moskalenko OI, Hramov AE. On the use of chaotic synchronization for secure communication. Physics-Uspekhi. 2009;52(12):1213–1238. DOI: 10.3367/UFNe.0179. 200912c.1281.
  3. Pikovsky A, Rosenblum M, Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences. New York: Cambridge University Press; 2001. 432 p. DOI: 10.1017/CBO9780511755743.
  4. Prokhorov MD, Ponomarenko VI, Kulminskiy DD, Koronovskii AA, Moskalenko OI, Hramov AE. Resistant to noise chaotic communication scheme exploiting the regime of generalized synchronization. Nonlinear Dynamics. 2017;87(3):2039–2050. DOI: 10.1007/s11071-016-3174-6.
  5. Kuznetsov SP. Example of a physical system with a hyperbolic attractor of the Smale-Williams type. Phys. Rev. Lett. 2005;95(14):144101. DOI: 10.1103/PhysRevLett.95.144101.
  6. Jalnine AY, Kuznetsov SP. On the realization of the Hunt-Ott strange nonchaotic attractor in a physical system. Tech. Phys. 2007;52(4):401–408. DOI: 10.1134/S1063784207040020.
  7. Kuznetsov SP. Hyperbolic Chaos: A Physicist’s View. Berlin, Heidelberg: Springer; 2012. 320 p. DOI: 10.1007/978-3-642-23666-2.
  8. Kuptsov PV, Kuznetsov SP. Transition to a synchronous chaos regime in a system of coupled non-autonomous oscillators presented in terms of amplitude equations. Russian Journal of Nonlinear Dynamics. 2006;2(3):307–331 (in Russian). DOI: 10.20537/nd0603005.
  9. Pikovsky AS. Synchronization of oscillators with hyperbolic chaotic phases. Izvestiya VUZ. Applied Nonlinear Dynamics 2021;29(1):78–87. DOI: 10.18500/0869-6632-2021-29-1-78-87.
  10. Isaeva OB, Jalnine AY, Kuznetsov SP. Chaotic communication with robust hyperbolic transmitter and receiver. In: 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS). 22-25 May 2017, St. Petersburg, Russia. IEEE; 2017. P. 3129–3136. DOI: 10.1109/PIERS.2017.8262295.
  11. Feudel U, Kuznetsov S, Pikovsky A. Strange Nonchaotic Attractors: Dynamics between Order and Chaos in Quasiperiodically Forced Systems. Singapore: World Scientific; 2006. 228 p. DOI: 10.1142/6006.
  12. Ramaswamy R. Synchronization of strange nonchaotic attractors. Phys. Rev. E. 1997;56(6): 7294–7296. DOI: 10.1103/PhysRevE.56.7294.
  13. Zhou CS, Chen TL. Robust communication via synchronization between nonchaotic strange attractors. Europhys. Lett. 1997;38(4):261–265. DOI: 10.1209/epl/i1997-00235-7.
  14. Rizwana R, Raja Mohamed I. Applicability of strange nonchaotic Wien-bridge oscillators for secure communication. Pramana. 2018;91(1):10. DOI: 10.1007/s12043-018-1582-5.
  15. Volkovskii AR, Rulkov NF. Synchronous chaotic response of a nonlinear oscillator system as a principle for the detection of the information component of chaos. Tech. Phys. Lett. 1993; 19(2):97–99.
  16. Behnia S, Akhshani A, Mahmodi H, Akhavan A. A novel algorithm for image encryption based on mixture of chaotic maps. Chaos, Solitons & Fractals. 2008;35(2):408–419. DOI: 10.1016/j.chaos. 2006.05.011.
  17. Jalnine AY. A new information transfer scheme based on phase modulation of a carrier chaotic signal. Izvestiya VUZ. Applied Nonlinear Dynamics. 2014;22(5):3–12 (in Russian). DOI: 10.18500/ 0869-6632-2014-22-5-3-12.
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