Application of megastable system with $2$-$D$ strip of hidden chaotic attractors to secure communications

O. I. Kuznetsova

Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 89-103.

Résumé

Many real dynamical systems are characterized by the presence of a coexisting attractors set. This property of systems is called multistability. In multistable systems, a sudden transition to unwanted or unknown attractors can occur. Such a transition can lead to catastrophic events. It turned out that multistability is also associated with the emergence of unpredictable attractors, which are called hidden attractors. One of the defining reasons for studying multistable chaotic systems with different characteristics is a wide range of their potential engineering applications - synchronization of the receiver and transmitter, masking and recovery of messages, noise filtering, recovery of information signals, as well as the development of decoding and coding algorithms that allow you to present an arbitrary digital message through the symbolic dynamics of a chaotic system. This paper proposes not only a mathematical model of a secure communication scheme based on adaptive synchronization between a pair of identical megastable systems with a 2-D band of hidden chaotic attractors, but also its numerical simulation using the MATLAB Simulink environment. The use of synchronization in communication systems is of fundamental importance, since it forces systems to simultaneously output the same output data and, in turn, leads to accurate restoration of information signals. Meanwhile, on the receiver side, information can be successfully recovered using adaptive technology. The presented method is stable with respect to various levels of additive white Gaussian noise. The scheme used for synchronization made it possible to overcome the well-known difficulties presented in the works of a number of specialists that arise in the problem of synchronizing in the case of multistability and coexistence of hidden oscillations, with the wrong choice of the form of the control signal. Numerical simulations are given to verify the feasibility of proposed synchronization and better performance of image encryption technique in terms of histogram, robustness to noise and visual imperceptibility. Three types of masked messages (text, grayscale image and audio signal) are considered as test examples.

Détail

Keywords: dynamical systems, chaos, hidden attractors, countable number of coexisting attractors, secure communications.

Bibliographie

[1] Arecchi F. T., Meucci R., Puccioni G., Tredicce J., “Experimental evidence of subharmonic bifurcations-multistability and turbulence in a Q-switched gas laser”, Phys. Rev. Lett., 49:17 (1982), 1217 | DOI

[2] Laurent M., Kellershohn N., “Multistability: a major means of differentiation and evolution in biological systems”, Trends Biochem Sci, 24:11 (1999), 418–422 | DOI

[3] Komarov A., Leblond H., Sanchez F., “Multistability and hysteresis phenomena in passively mode-locked fiber lasers”, Phys. Rev. A, 71:5 (2005), 053809 | DOI

[4] Zeng Z., Huang T., Zheng W., “Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function”, IEEE Trans Neural Netw, 21:8 (2010), 1371–1377 | DOI | MR

[5] Ying L., Huang D., Lai Y. C., “Multistability, chaos, and random signal generation in semiconductor superlattices”, Phys. Rev. E, 93:6 (2016), 062204 | DOI | MR

[6] Pecora L. M., Carroll T. L., “Synchronization in chaotic systems”, Physical review letters, 64:8 (1990), 821–824 | DOI | MR | Zbl

[7] Shoreh A. A.-H., Kuznetsov N. V., Mokaev T. N., Tavazoei M. S., “Synchronization of hidden hyperchaotic attractors in fractional Order complex-valued systems with application to secure communications”, 2021 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElConRus), IEEE, 2021, 62–67 | DOI

[8] Tavazoei M. S., Haeri M., “Synchronization of chaotic fractional-order systems via active sliding mode controller”, Physica A: Statistical Mechanics and its Applications, 387:1 (2008), 57–70 | DOI

[9] Zhang H., Ma X.-K., “Synchronization of uncertain chaotic systems with parameters perturbation via active control”, Chaos, Solitons Fractals, 21:1 (2004), 39–47 | DOI | MR | Zbl

[10] Shoreh A. A.-H., Kuznetsov N. V., Mokaev T. N., “Lag synchronization for complex-valued Rabinovich system with application to encryption techniques”, 2020 16th International Computer Engineering Conference (ICENCO), IEEE, 2020, 11–16 | DOI

[11] Du H., Zeng Q., Lu N., “A general method for modified function projective lag synchronization in chaotic systems”, Physics Letters A, 374:13/14 (2010), 1493–1496 | Zbl

[12] Mahmoud G. M., Mahmoud E. E., “Lag synchronization of hyperchaotic complex nonlinear systems”, Nonlinear Dynamics, 67:2 (2012), 1613–1622 | DOI | MR | Zbl

[13] Tang Z., Park J. H., Feng J., “Novel approaches to pin cluster synchronization on complex dynamical networks in Lur'e forms”, Communications in Nonlinear Science and Numerical Simulation, 57 (2018), 422–438 | DOI | MR | Zbl

[14] Mahmoud G. M. Farghaly A. A., Abed-Elhameed T. M., Darwish M. M., “Adaptive dual synchronization of chaotic (hyperchaotic) complex systems with uncertain parameters and its application in image encryption”, Acta Phys. Pol. B, 49:11 (2018), 1923–1939 | DOI | MR

[15] He H., Tu J., Xiong P., “Lr-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations”, Journal of the Franklin Institute, 348:9 (2011), 2257–2269 | DOI | MR | Zbl

[16] Xu Y., Zhou W., Sun W., “Adaptive synchronization of uncertain chaotic systems with adaptive scaling function”, Journal of the Franklin Institute, 348:9 (2011), 2406–2416 | DOI | MR | Zbl

[17] Shoreh A.-H., Kuznetsov N., Mokaev T., “New adaptive synchronization algorithm for a general class of complex hyperchaotic systems with unknown parameters and its application to secure communication”, Physica A: Statistical Mechanics and its Applications, 2021 | DOI | MR

[18] Kolumban G., Kennedy M. P., Chua L. O., “The role of synchronization in digital communications using chaos. I. Fundamentals of digital communications”, IEEE Transactions on circuits and systems I: Fundamental theory and applications, 44:10 (1997), 927–936 | DOI | MR

[19] Kolumban G., Kennedy M. P., Chua L. O., “The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization”, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45:11 (1998), 1129–1140 | DOI | MR | Zbl

[20] Guan Z. H., Huang F., Guan W., “Chaos-based image encryption algorithm”, Phys. Lett. A, 346:1-3 (2005), 153–157 | DOI | Zbl

[21] Gao T., Chen Z., “A new image encryption algorithm based on hyper-chaos”, Phys. Lett. A, 372:4 (2008), 394–400 | DOI | MR | Zbl

[22] Xie E. Y., Li C., Yu S, Lü J., “On the cryptanalysis of Fridrich's chaotic image encryption scheme”, Signal processing, 132 (2017), 150–154 | DOI

[23] Wang S., Kuang J., Li J., Luo Y., Lu H., Hu G., “Chaos-based secure communications in a large community”, Phys. Rev. E, 66 (2012), 065202R

[24] Chen G. R., Mao Y. B., Chui C. K., “A symmetric image encryption scheme based on 3D chaotic cat maps”, Chaos Solitons Fractals, 21:3 (2004), 749–761 | DOI | MR | Zbl

[25] Pareek N. K., Patidar V., Sud K. K., “Image Encryption Using Chaotic Logistic Map”, Image and Vision Computing, 24 (2006), 926–934 | DOI

[26] Yen J.-I., Guo J.-C., “Efficient hierarchical chaotic image encryption algorithm and its VLSI realisation”, IEE Proc - Vision, Image, Sign Proc., 147:2 (2000), 167–175 | DOI

[27] Burkin I. M., Kuznetsova O. I., “New megastable system with 2-D strip of hidden attractors and analytical solutions”, Chebyshevskii sbornik, 22:4 (2021), 360–368 | DOI | MR

[28] Kuznetsova O. I., Programma dlya shifrovaniya informatsii s ispolzovaniem megastabilnoy sistemy s 2-D polosoy skrytyh attractorov, Svidetelstvo o gosudarstvennoy registracii programmy dlya EVM No 2022666310, TSU, 2022, 1 pp.

[29] Wang Z., Bovik A. C., Sheikh H. R., Simoncelli E. P., “Image quality assessment: from error visibility to structural similarity”, IEEE transactions on image processing, 13:4 (2004), 600–612 | DOI

[30] Wang Z., Bovik A. C., “A universal image quality index”, IEEE signal processing letters, 9:3 (2002), 81–84 | DOI