Application of megastable system with 2-𝐷 strip of hidden chaotic attractors to secure communications
https://doi.org/10.22405/2226-8383-2023-24-1-89-103
Abstract
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.
About the Author
Oksana Igorevna Kuznetsova
Tula State University
Russian Federation
Russian Federation
postgraduate student
References
1. Arecchi, F. T., Meucci, R., Puccioni, G. & Tredicce, J. 1982, “Experimental evidence of
2. subharmonic bifurcations-multistability and turbulence in a Q-switched gas laser“, Phys. Rev.
3. Lett., vol. 49(17):1217.
4. Laurent, M. & Kellershohn, N. 1999, “Multistability: a major means of differentiation and
5. evolution in biological systems“, Trends Biochem Sci., vol. 24(11), pp. 418–422.
6. Komarov, A., Leblond, H. & Sanchez, F. 2005, “Multistability and hysteresis phenomena in
7. passively mode-locked fiber lasers“, Phys. Rev. A., vol. 71(5):053809.
8. Zeng, Z., Huang, T. & Zheng, W. 2010, “Multistability of recurrent neural networks with timevarying
9. delays and the piecewise linear activation function“, IEEE Trans. Neural Netw., vol.
10. (8), pp. 1371–1377
11. Ying, L., Huang, D. & Lai, Y. C. 2016, “Multistability, chaos, and random signal generation in
12. semiconductor superlattices“, Phys. Rev. E., vol. 93(6):062204.
13. Pecora, L. M. & Carroll, T. L. 1990, “Synchronization in chaotic systems“, Physical review
14. letters, vol. 64, no. 8, pp. 821-824.
15. Shoreh, A. A.-H., Kuznetsov, N. V., Mokaev, T. N. & Tavazoei, M. S. 2021, “Synchronization
16. of hidden hyperchaotic attractors in fractional Order complex-valued systems with application
17. to secure communications“, 2021 IEEE Conference of Russian Young Researchers in Electrical
18. and Electronic Engineering (ElConRus). IEEE, pp. 62—67
19. Tavazoei, M. S. & Haeri, M. 2008, “Synchronization of chaotic fractional-order systems via
20. active sliding mode controller“, Physica A: Statistical Mechanics and its Applications, vol. 387,
21. no. 1, pp. 57—70.
22. Zhang, H. & Ma, X.-K. 2004, “Synchronization of uncertain chaotic systems with parameters
23. perturbation via active control“, Chaos, Solitons & Fractals, vol. 21, no. 1, pp. 39—47.
24. Shoreh, A. A.-H., Kuznetsov, N. V. & Mokaev, T. N. 2020, “Lag synchronization for complexvalued
25. Rabinovich system with application to encryption techniques“, 2020 16th International
26. Computer Engineering Conference (ICENCO). IEEE., pp. 11—16.
27. Du, H., Zeng Q.& Lu, N. 2010, “A general method for modified function projective lag
28. synchronization in chaotic systems“, Physics Letters A., vol. 374, no. 13/14, pp. 1493—1496.
29. Mahmoud, G. M. & Mahmoud, E. E. 2012, “Lag synchronization of hyperchaotic complex
30. nonlinear systems“, Nonlinear Dynamics, vol. 67, no. 2, pp. 1613—1622.
31. Tang, Z., Park, J. H. & Feng, J. 2018.,“Novel approaches to pin cluster synchronization
32. on complex dynamical networks in Lur’e forms“, Communications in Nonlinear Science and
33. Numerical Simulation, vol. 57, pp. 422—438.
34. Mahmoud, G. M. Farghaly, A. A., Abed-Elhameed, T. M. & Darwish, M. M. 2018, “Adaptive
35. dual synchronization of chaotic (hyperchaotic) complex systems with uncertain parameters and
36. its application in image encryption“, Acta Phys. Pol. B., vol. 49, no. 11, pp. 1923-1939.
37. He, H., Tu, J. & Xiong, P. 2011, “Lr-synchronization and adaptive synchronization of a class of
38. chaotic Lurie systems under perturbations“, Journal of the Franklin Institute, vol. 348, no. 9,
39. pp. 2257—2269.
40. Xu, Y., Zhou, W. & Sun, W. 2011, “Adaptive synchronization of uncertain chaotic systems with
41. adaptive scaling function“, Journal of the Franklin Institute, vol. 348, no. 9, pp. 2406—2416.
42. Shoreh, A.-H., Kuznetsov, N. & Mokaev, T. 2021, “New adaptive synchronization algorithm
43. for a general class of complex hyperchaotic systems with unknown parameters and its
44. application to secure communication“, Physica A: Statistical Mechanics and its Applications,
45. DOI:10.1016/j.physa.2021.126466.
46. Kolumban, G., Kennedy, M. P. & Chua, L. O. 1997, “The role of synchronization in digital
47. communications using chaos. I. Fundamentals of digital communications“, IEEE Transactions
48. on circuits and systems I: Fundamental theory and applications, vol. 44, no. 10, pp. 927—936.
49. Kolumban, G., Kennedy, M. P. & Chua, L. O. 1998, “The role of synchronization in digital
50. communications using chaos. II. Chaotic modulation and chaotic synchronization“, IEEE
51. Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 45, no.
52. , pp. 1129—1140.
53. Guan, Z. H., Huang, F. & Guan, W. 2005, “Chaos-based image encryption algorithm“, Phys.
54. Lett. A., vol. 346, no. 1-3, pp.153-157.
55. Gao, T. & Chen, Z. 2008, “A new image encryption algorithm based on hyper-chaos“, Phys.
56. Lett. A., vol. 372, no. 4, pp. 394-400.
57. Xie, E. Y., Li, C., Yu, S. & L¨u, J. 2017, “On the cryptanalysis of Fridrich’s chaotic image
58. encryption scheme“, Signal processing, vol.132, pp.150-154.
59. Wang, S., Kuang, J., Li, J., Luo, Y., Lu, H. & Hu, G. 2012, “Chaos-based secure communications
60. in a large community“, Phys. Rev. E., vol. 66, Art. no. 065202R.
61. Chen, G. R., Mao, Y. B. & Chui, C. K. 2004, “A symmetric image encryption scheme based on
62. D chaotic cat maps“, Chaos Solitons & Fractals, vol. 21, no. 3. pp. 749–761.
63. Pareek, N.K., Patidar, V. & Sud, K. K. 2006, “Image Encryption Using Chaotic Logistic Map“,
64. Image and Vision Computing, vol. 24, pp. 926-934.
65. Yen, J.-I. & Guo, J.-C. 2000, “Efficient hierarchical chaotic image encryption algorithm and its
66. VLSI realisation“, IEE Proc - Vision, Image, Sign Proc, vol. 147, no. 2, pp. 167-175.
67. Burkin, I. M. & Kuznetsova, O. I. 2021, “New megastable system with 2-D strip of hidden
68. attractors and analytical solutions“ , Chebyshevskii sbornik, vol. 22, no. 4, pp. 360-368.
69. Kuznetsova, O. I., TSU, 2022, “Programma dlya shifrovaniya informatsii s ispolzovaniem
70. megastabilnoy sistemy s 2-D polosoy skrytyh attractorov“, Svidetelstvo o gosudarstvennoy
71. registracii programmy dlya EVM no. 2022666310, 1 p.
72. Wang, Z., Bovik, A. C. Sheikh, H. R. & Simoncelli, E. P. 2004, “Image quality assessment: from
73. error visibility to structural similarity“, IEEE transactions on image processing, vol. 13, no. 4,
74. pp. 600—612.
75. Wang, Z. & Bovik, A. C. 2002, “A universal image quality index“, IEEE signal processing letters,
76. vol. 9, no. 3, pp. 81—84.
Review
For citations:
Kuznetsova O.I. Application of megastable system with 2-𝐷 strip of hidden chaotic attractors to secure communications. Chebyshevskii Sbornik. 2023;24(1):89-103. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-1-89-103
Views:
327
Email this article 