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A new secure communication scheme using fractional order delayed chaotic system: design and electronics circuit simulation

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Abstract

In this paper, a new approach to secure in perturbed receiver based on the Chen fractional order delayed chaotic system is developed and the electronics circuit is simulated with Multisim. The main idea of this approach is the injection of the transmitted message in the dynamics of the Chen fractional order delayed chaotic system in the transmitter. To recover the message from the perturbed receiver, we use the H-infinity to establish the synchronization between the transmitter and the receiver and to recover the transmitted signal. Little paper in the literature presents the electronic circuit of the secure communication using fractional order delayed chaotic system due to the difficulty of realization, for it, the electronic circuit is detailed using Multisim software to demonstrate the feasibility of the proposed approach.

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References

  1. Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130–141.

    Article  MathSciNet  MATH  Google Scholar 

  2. Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64(8), 821.

    Article  MathSciNet  MATH  Google Scholar 

  3. Fallahi, K., & Leung, H. (2010). A chaos secure communication scheme based on multiplication modulation. Communications in Nonlinear Science and Numerical Simulation, 15(2), 368–383.

    Article  MATH  Google Scholar 

  4. Mata-Machuca, J. L., Martínez-Guerra, R., Aguilar-López, R., & Aguilar-Ibañez, C. (2012). A chaotic system in synchronisation and secure communications. Communications in Nonlinear Science and Numerical Simulation, 17(4), 1706–1713.

    Article  MathSciNet  Google Scholar 

  5. Senouci, A., Boukabou, A., Busawon, K., et al. (2015). Robust chaotic communication based on indirect coupling synchronisation. Circuits, Systems, and Signal Processing, 34(2), 393–418.

    Article  Google Scholar 

  6. Hamiche, H., Megherbi, O., Kara, R., Saddaoui, R., Laghrouche, M., & Djennoune, S. (2017). A new implementation of an impulsive synchronization of two discrete-time hyperchaotic systems using Arduino-Uno boards. International Journal of Modeling, Identification and Control, 28(02), 177–186.

    Article  Google Scholar 

  7. Bouhous, A., & Kemih, K. (2018). Novel encryption method based on optical time-delay chaotic system and a wavelet for data transmission. Optics & Laser Technology, 108, 162–169.

    Article  Google Scholar 

  8. Halimi, M., Kemih, K., & Ghanes, M. (2014). Circuit simulation of an analog secure communication based on synchronized chaotic Chua’s system. Applied Mathematics & Information Sciences, 8(4), 1509.

    Article  Google Scholar 

  9. Kemih, K., Ghanes, M., Remmouche, R., et al. (2015). A novel 5D-dimentional hyperchaotic system and its circuit simulation by EWB. Mathematical Sciences Letters, 4(1), 1–4.

    Google Scholar 

  10. Zambrano-Serrano, E., Muñoz-Pacheco, J. M., & Campos-Cantón, E. (2017). Chaos generation in fractional-order switched systems and its digital implementation. AEU-International Journal of Electronics and Communications, 79, 43–52.

    Article  Google Scholar 

  11. Chao, L. (2015). Asynchronous error-correcting secure communication scheme based on fractional-order shifting chaotic system. International Journal of Modern Physics C, 26(06), 1550065.

    Article  Google Scholar 

  12. Hamiche, H., Guermah, S., Kassim, S., et al. (2015). Secure data transmission scheme based on fractional-order discrete chaotic system. In 2015 3rd international conference on control, engineering & information technology (CEIT) (pp. 1–6). IEEE.

  13. Shah, D. K., Chaurasiya, R. B., Vyawahare, V. A., et al. (2017). FPGA implementation of fractional-order chaotic systems. AEU-International Journal of Electronics and Communications, 78, 245–257.

    Article  Google Scholar 

  14. Borah, M., Singh, P. P., & Roy, B. K. (2016). Improved chaotic dynamics of a fractional-order system, its chaos-suppressed synchronisation and circuit implementation. Circuits, Systems, and Signal Processing, 35(6), 1871–1907.

    Article  MathSciNet  MATH  Google Scholar 

  15. Megherbi, O., Hamiche, H., Djennoune, S., & Bettayeb, M. (2017). A new contribution for the impulsive synchronization of fractional-order discrete-time chaotic systems. Nonlinear Dynamics, 90(3), 1519–1533.

    Article  MathSciNet  MATH  Google Scholar 

  16. Das, S. (2011). Functional fractional calculus. Berlin: Springer.

    Book  MATH  Google Scholar 

  17. Mittag-Leffler, G. M. (1903). Sur la nouvelle fonction Eα (x). Comptes Rendus de l’Academie des Sciences de Paris, 137(2), 554–558.

    MATH  Google Scholar 

  18. Mittag-Leffler, G. M. (1905). Sur la representation analytique d unefunction branche uniforme dune fonction. Acta Mathematica, 239, 101–181.

    Article  MATH  Google Scholar 

  19. Loverro, A. (2004). Fractional calculus: history, definitions and applications for the engineer. Rapport technique, Univeristy of Notre Dame: Department of Aerospace and Mechanical Engineering (pp. 1–28).

  20. Kilbas, A., Srivastava, H. M., Trujillo, J. J. (2006). Theory and applications of fractional differential equations. Elsevier, North-Holland Mathematics Studies, 204. Fractional calculus and applied analysis (Vol. 9, No. 1, p. 71).

  21. Ishteva, M. (2005). Properties and applications of the Caputo fractional operator. M.Sc., Thesis.

  22. Podlubny, I. (1998). Fractional differential equations, volume 198: An introduction to fractional derivatives, fractional differential equations, to methods of their…(mathematics in science and engineering).

  23. Efe, M. Ö. (2008). Fractional fuzzy adaptive sliding-mode control of a 2-DOF direct-drive robot arm. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38(6), 1561–1570.

    Article  Google Scholar 

  24. Boroujeni, E. A., & Momeni, H. R. (2012). Observer based control of a class of nonlinear fractional-order systems using LMI. International Journal of Science and Engineering Investigations, 1(1), 48–52.

    Google Scholar 

  25. Tang, J. (2014). Synchronization of different fractional order time-delay chaotic systems using active control. Mathematical Problems in Engineering. https://doi.org/10.1155/2014/262151.

    MathSciNet  MATH  Google Scholar 

  26. Cheng, C.-K., Kuo, H.-H., Hou, Y.-Y., et al. (2008). Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays. Physica A: Statistical Mechanics and its Applications, 387(13), 3093–3102.

    Article  MathSciNet  Google Scholar 

  27. Wang, X. F., & Wang, Z. Q. (2003). A robust demodulation approach to communications using chaotic signals. International Journal of Bifurcation and Chaos, 13(01), 227–231.

    Article  MATH  Google Scholar 

  28. Boukal, Y., Darouach, M., Zasadzinski, M., et al. (2014). Design of functional fractional-order observers for linear time-delay fractional-order systems in the time domain. In 2014 International conference on fractional differentiation and its applications (ICFDA) (pp. 1–6). IEEE.

  29. Pourgholi, M., & Majd, V. J. (2011). A nonlinear adaptive resilient observer design for a class of Lipschitz systems using LMI. Circuits, Systems, and Signal Processing, 30(6), 1401–1415.

    Article  MathSciNet  MATH  Google Scholar 

  30. Liu, C. X. (2011). Fractional-order chaotic circuit theory and applications. Xian Jiaotong University Press, Xian.

    Google Scholar 

  31. Jun-Jie, L., & Chong-Xin, L. (2007). Realization of fractional-order Liu chaotic system by circuit. Chinese Physics, 16(6), 1586.

    Article  Google Scholar 

  32. Biswas, D., & Banerjee, T. (2016). A simple chaotic and hyperchaotic time-delay system: design and electronic circuit implementation. Nonlinear Dynamics, 83(4), 2331–2347.

    Article  MathSciNet  Google Scholar 

  33. https://forums.ni.com/t5/Multisim-Custom-Simulation/Noise-Source-Generator/ta-p/3502584. Accessed 18 Jan 2017.

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Correspondence to Karim Kemih.

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Zouad, F., Kemih, K. & Hamiche, H. A new secure communication scheme using fractional order delayed chaotic system: design and electronics circuit simulation. Analog Integr Circ Sig Process 99, 619–632 (2019). https://doi.org/10.1007/s10470-018-01382-x

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  • DOI: https://doi.org/10.1007/s10470-018-01382-x

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