Secure Communication Scheme Based on a New 3-D Jerk Chaotic System
Keywords:
Nonlinear Dynamics, Chaos, Jerk, Synchronization, Secure communication
Abstract
Chaos theory plays a significant role in the engineering fields and especially in the security of data transmission in communication systems. In this paper, a new 3-D jerk chaotic system has been suggested. The fundamental dynamical properties, including the fixed points, chaotic attractors, bifurcation diagrams, and Lyapunov exponents are investigated. In communication systems, data security and the implementation of designed transceivers of secure communication scheme can be considered the main challenge for applying such systems. In this work, a 3-D new jerk chaotic scheme has been proposed to be used in data encryption of communication systems. The proposed jerk chaotic system is used for constructing identical transceivers of communication scheme that are presented by a master (transmitter) and a slave (receiver). In the master end, a useful information beam is encrypted through a chaotic signal. On the other hand, in the slave side, the original information beam is retrieved from the mutual transmitted beam by a chaotic synchronization mechanism. The communication scheme transceivers are synchronized by an adaptive observer synchronization mechanism. Finally, the system is tested and evaluated on a stream of binary information that is encrypted in the transmitter and recovered in the receiver. The results show that our proposal cryptosystem has good performance in term of securing transmitted data.
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References
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[33] Hassan Salarieh, Aria Alasty,: Adaptive synchronization of two chaotic systems withstochastic unknown parameters, Communications in Nonlinear Science and Numerical Simulation, Vol. 14 ,2009, pp. 508–519.
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[37] Shko Ali Tahir.,”The synchronization of identical Memristors systems via Lyapunov direct method”, Applied and Computational Mathematics, Vol.2, No, 6, 2013; pp. 130-136.
[2] V.-T. Pham, S. Vaidyanathan, C. K. Volos, and S. Jafari, “Hidden attractors in a chaotic system with an exponential nonlinear term,” Eur. Phys. J. Spec. Top., vol. 224, no. 8, pp. 1507–1517, 2015.
[3] Ilia Grigorenko, Elena Grigorenko: Chaotic Dynamics of the Fractional Lorenz System, PH YSICA L R EV I EW L ET T ERS, Vol. 91, No. 3, 18 JULY 2003, pp. 1-4.
[4] Fatma Yildirim Dalkiran: Simple Chaotic Hyperjerk System, International Journal of Bifurcation and Chaos, Vol. 26, No. 11, 2016, pp.1650189(1-6).
[5] Gamal M. Mahmoud, Mansour E. Ahmed: Chaotic and Hyperchaotic Complex Jerk Equations, International Journal of Modern Nonlinear Theory and Application, Vol. 1, 2012, pp. 6-13.
[6] Arturo Buscarinoy, Luigi Fortunay, Mattia Frascay, and Antonio Gallo: Hyperjerk dynamics in hyperchaotic systems, International Symposium on Nonlinear Theory and its Applications, NOLTA2014, Luzern, Switzerland, September 2014, pp.14-18,
[7] J. C. Sprott: Some simple chaotic jerk functions, Am. J. Phys. Vol. 65, No.6, June 1997, pp. 537-543.
[8] Boubaker O, Jafari S. Recent advances in chaotic systems and synchronization: from theory to real world applications 2018.
[9] Z L. Moysis, C. Volos, V.-T. Pham, S. Goudos, I. Stouboulos, and M. K. Gupta, “Synchronization of a chaotic system with line equilibrium using a descriptor observer for secure communication,” in 2019 8th International Conference on Modern Circuits and Systems Technologies (MOCAST), 2019, pp. 1–4.
[10] Sergej Cˇ elikovsky and Guanrong Chen: Secure Synchronization of a Class of Chaotic Systems From a Nonlinear Observer Approach, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 50, NO. 1, JANUARY 2005, PP.76-82.
[11] Andrzej Stefanskin, Tomasz Kapitaniak: Synchronization of two chaotic oscillators via a negative feedback mechanism, International Journal of Solids and Structures Vol. 40, 2003, pp. 5175–5185.
[12] Zhang H, Zhang W, Zhao Y, Ji M, Huang L. Adaptive state observers for incrementally quadratic nonlinear systems with application to chaos synchronization. Circuits, Syst Signal Process 2020;39:1290–306.
[13] Martínez-Guerra R, Pérez-Pinacho CA. Advances in Synchronization of Coupled Fractional Order Systems: Fundamentals and Methods. Springer; 2018.
[14] Mou J, Li P, Zu L, Jin J, Ma X. Control of chaos observer synchronization and the application in secure communication. 2013 IEEE Int. Conf. IEEE Reg. 10 (TENCON 2013), IEEE; 2013, p. 1–4.
[15] De la Hoz MZ, Acho L, Vidal Y. A modified Chua chaotic oscillator and its application to secure communications. Appl Math Comput 2014;247:712–22.
[16] Durdu A, Uyaroğlu Y, Özcerit AT. A novel chaotic system for secure communication applications. Inf Technol Control 2015;44:271–8.
[17] Vaidyanathan S. A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control. Arch Control Sci 2017;27.
[18] Vaidyanathan S, Sambas A, Kacar S, Çavuşoğlu Ü. A new three-dimensional chaotic system with a cloud-shaped curve of equilibrium points, its circuit implementation and sound encryption. Int J Model Identif Control 2018;30:184–96.
[19] Azar AT, Vaidyanathan S, Ouannas A. Fractional order control and synchronization of chaotic systems. vol. 688. Springer; 2017.
[20] Liu T, Yan H, Banerjee S, Mou J. A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation. Chaos, Solitons & Fractals 2021;145:110791.
[21] Gong L, Wu R, Zhou N. A New 4D Chaotic system with coexisting hidden chaotic attractors. Int J Bifurc Chaos 2020;30:2050142.
[22] Zhou C, Yang C, Xu D, Chen C. Dynamic analysis and synchronisation control of a novel chaotic system with coexisting attractors. Pramana 2020;94:1–10.
[23] Lai Q, Wan Z, Kuate PDK, Fotsin H. Coexisting attractors, circuit implementation and synchronization control of a new chaotic system evolved from the simplest memristor chaotic circuit. Commun Nonlinear Sci Numer Simul 2020;89:105341.
[24] Hadjabi F, Ouannas A, Shawagfeh N, Khennaoui A-A, Grassi G. On two-dimensional fractional chaotic maps with symmetries. Symmetry (Basel) 2020;12:756.
[25] RenatoCandido, DiogoC.Soriano, MagnoT.M.Silva, MarcioEisencraft, : Do chaos-based communication systems really transmit chaotic signals?, SignalProcessing, Vol. 108, 2015, pp. 412–420.
[26] Gong L, Wu R, Zhou N. A New 4D Chaotic system with coexisting hidden chaotic attractors. Int J Bifurc Chaos 2020;30:2050142.
[27] F. N. Ayoob, F. R. Tahir, and K. M. Abdul-Hassan, “Bifurcations and Chaos in Current-Driven Induction Motor,” Iraqi J. Electr. Electron. Eng., vol. 15, no. 2–2019, 2019.
[28] Jasim BH, Rashid MT, Omran KM. Synchronization and tracking control of a novel 3-dimensional chaotic system. Iraqi J Electr Electron Eng 2020.
[29] Çiçek S, Ferikoğlu A, Pehlivan İ. A new 3D chaotic system: dynamical analysis, electronic circuit design, active control synchronization and chaotic masking communication application. Optik (Stuttg) 2016;127:4024–30.
[30] T. Ma, W. Luo, Z. Zhang, and Z. Gu, “Impulsive synchronization of fractional-order chaotic systems with actuator saturation and control gain error,” IEEE Access, vol. 8, pp. 36113–36119, 2020.
[31] Hashemi S, Pourmina MA, Mobayen S, Alagheband MR. Design of a secure communication system between base transmitter station and mobile equipment based on finite-time chaos synchronisation. Int J Syst Sci 2020;51:1969–86.
[32] Changchun Hua, Xinping Guan, Xiaoli Li a, Peng Shi: Adaptive observer-based control for a class of chaotic systems, Chaos, Solitons and Fractals, Vol. 22, 2004, pp.103–110.
[33] Hassan Salarieh, Aria Alasty,: Adaptive synchronization of two chaotic systems withstochastic unknown parameters, Communications in Nonlinear Science and Numerical Simulation, Vol. 14 ,2009, pp. 508–519.
[34] Shko Ali Tahir.,”The synchronization of identical Memristors systems via Lyapunov direct method”, Applied and Computational Mathematics, Vol.2, No, 6, 2013; pp. 130-136.
[35] H. Jahanshahi, A. Yousefpour, J. M. Munoz-Pacheco, S. Kacar, V.-T. Pham, and F. E. Alsaadi, “A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption,” Appl. Math. Comput., vol. 383, p. 125310, 2020.
[36] Hashemi S, Pourmina MA, Mobayen S, Alagheband MR. Design of a secure communication system between base transmitter station and mobile equipment based on finite-time chaos synchronisation. Int J Syst Sci 2020;51:1969–86.
[37] Shko Ali Tahir.,”The synchronization of identical Memristors systems via Lyapunov direct method”, Applied and Computational Mathematics, Vol.2, No, 6, 2013; pp. 130-136.
Published
2022-05-04
How to Cite
A. Rahman, Z.-A. S., Basil H. Jasim, & Ehsan Alhamdawee. (2022). Secure Communication Scheme Based on a New 3-D Jerk Chaotic System. Al-Qadisiyah Journal of Pure Science, 27(1), comp 33-47. https://doi.org/10.29350/qjps.2022.27.2.1453
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Section
Computer
Copyright (c) 2022 Zain-Aldeen S. A. Rahman
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