Design of a new chaotic system by a non-smooth controller and its application

• Autorzy: He Jianbin , Zhao Kun , Wang Shiya

Identyfikatory

DOI

10.61822/amcs-2025-0029

• Języki publikacji: EN

Abstrakty

EN

Chaos theory constitutes a fundamental discipline within nonlinear science. Chaotic systems, leveraging their sensitive dependence on initial conditions, have found extensive applications in information security. While numerous chaotic systems have been developed via continuous control methodologies in recent years, the design of such systems under non-smooth control regimes remains challenging due to the lack of systematic theoretical frameworks. Under what conditions can non-smooth control schemes induce deterministic chaos in nonlinear systems? What systematic methodology enables the construction of non-smooth controllers that guarantee chaotic dynamics generation while maintaining system stabilizability? Building upon the principles of chaos theory, this study introduces a novel chaotic system developed via a non-smooth control design methodology. The newly developed chaotic system is analyzed through its complex attractors and equilibrium points. Additionally, an image encryption algorithm based on this system is investigated, combining block scrambling and diffusion techniques in its design. The feasibility of the proposed encryption algorithm is validated through numerical simulations, demonstrating an expansive key space and robust security characteristics as evidenced by comprehensive security analyses.

Słowa kluczowe

EN

chaotic system; nonsmooth control; pseudorandom sequence; image encryption

PL

układ chaotyczny; ciąg pseudolosowy; szyfrowanie obrazu

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2025
• Tom: Vol. 35, no. 3
• Strony: 417--428
• Opis fizyczny: Bibliogr. 38 poz., rys., tab., wykr.

Twórcy

autor

He Jianbin

• School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China

autor

Zhao Kun

• School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China

autor

Wang Shiya

• School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China

Bibliografia

• [1] Akkasaligar, P.T. and Biradar, S. (2020). Selective medical image encryption using DNA cryptography, Information Security Journal: A Global Perspective 29(2): 91-101.
• [2] Al Solami, E., Ahmad, M., Volos, C., Doja, M.N. and Beg, M.M.S. (2018). A new hyperchaotic system-based design for efficient bijective substitution-boxes, Entropy 20(7): 525.
• [3] Alli, P. and Dinesh Peter, J. (2021). A novel auto-encoder induced chaos based image encryption framework aiding DNA computing sequence, Journal of Intelligent & Fuzzy Systems 41(1): 181-198.
• [4] Banu S, A. and Amirtharajan, R. (2020). A robust medical image encryption in dual domain: Chaos-DNA-IWT combined approach, Medical & Biological Engineering & Computing 58(7): 1445-1458.
• [5] Chen, L., Yin, H., Huang, T., Yuan, L., Zheng, S. and Yin, L. (2020). Chaos in fractional-order discrete neural networks with application to image encryption, Neural Networks 125: 174-184.
• [6] Folifack Signing, V., Fozin Fonzin, T., Kountchou, M., Kengne, J. and Njitacke, Z.T. (2021). Chaotic jerk system with hump structure for text and image encryption using DNA coding, Circuits, Systems, and Signal Processing 40(9): 4370-4406.
• [7] Fu, X.-Q., Liu, B.-C., Xie, Y.-Y., Li, W. and Liu, Y. (2018). Image encryption-then-transmission using DNA encryption algorithm and the double chaos, IEEE Photonics Journal 10(3): 1-15.
• [8] Gao, H. and Gao, T. (2019). Double verifiable image encryption based on chaos and reversible watermarking algorithm, Multimedia Tools and Applications 78(6): 7267-7288.
• [9] He, J., Qiu, W. and Cai, J. (2023). Synchronization of hyperchaotic systems based on intermittent control and its application in secure communication, Journal of Advanced Computational Intelligence and Intelligent Informatics 27(2): 292-303.
• [10] He, J. and Yu, S. (2019). Construction of higher-dimensional hyperchaotic systems with a maximum number of positive Lyapunov exponents under average eigenvalue criteria, Journal of Circuits, Systems and Computers 28(09): 1950151.
• [11] Huang, H., Chen, Y. and Cheng, D. (2022). Plaintext-related image encryption scheme based on chaos and game of life, Journal of Electronic Imaging 31(1): 013031.
• [12] Kaur, G., Agarwal, R. and Patidar, V. (2022). Color image encryption scheme based on fractional Hartley transform and chaotic substitution-permutation, The Visual Computer 38(3): 1027-1050.
• [13] Khaitan, S., Sagar, S. and Agarwal, R. (2020). Public key cryptosystem based on optimized chaos-based image encryption, Journal of Computational and Theoretical Nanoscience 17(12): 5217-5223.
• [14] Kumar, V., Rayappan, J.B.B., Amirtharajan, R. and Praveenkumar, P. (2022). Quantum true random number generation on IBM’s cloud platform, Journal of King Saud University-Computer and Information Sciences 34(8): 6453-6465.
• [15] Li, G. and Han, X. (2021). A color image encryption algorithm with cat map and chaos map embedded, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 29(Supp01): 73-87.
• [16] Lone, P.N., Singh, D. and Mir, U.H. (2021). A novel image encryption using random matrix affine cipher and the chaotic maps, Journal of Modern Optics 68(10): 507-521.
• [17] Mondal, B. and Singh, J.P. (2022). A lightweight image encryption scheme based on chaos and diffusion circuit, Multimedia Tools and Applications 81(24): 34547-34571.
• [18] Musanna, F., Dangwal, D., Kumar, S. and Malik, V. (2020). A chaos-based image encryption algorithm based on multiresolution singular value decomposition and a symmetric attractor, Imaging Science Journal 68(1): 24-40.
• [19] Peechara, R.R. and Sucharita, V. (2021). A chaos theory inspired, asynchronous two-way encryption mechanism for cloud computing, PeerJ Computer Science 59(3): e628.
• [20] Rajakumaran, C. and Kavitha, R. (2020). Chaos based encryption of quantum images, Multimedia Tools and Applications 79(33): 23849-23860.
• [21] Ramakrishnan, A., Ramalingam, R., Ramalingam, P., Ravi, V., Alahmadi, T.J. and Maidin, S.S. (2024). A novel chaotic binary butterfly optimization algorithm based feature selection model for classification of autism spectrum disorder, International Journal of Applied Mathematics and Computer Science 34(4): 647-660, DOI: 10.61822/amcs-2024-0043.
• [22] Ravichandran, D., Banu S, A., Murthy, B., Balasubramanian, V., Fathima, S. and Amirtharajan, R. (2021). An efficient medical image encryption using hybrid DNA computing and chaos in transform domain, Medical & Biological Engineering & Computing 59(3): 589-605.
• [23] Riyahi, M., Kuchaki Rafsanjani, M. and Motevalli, R. (2021). A novel image encryption scheme based on multi-directional diffusion technique and integrated chaotic map, Neural Computing and Applications 33(21): 14311-14326.
• [24] Sethi, J., Bhaumik, J. and Chowdhury, A.S. (2022). Chaos-based uncompressed frame level video encryption, Proceedings of the 7th International Conference on Mathematics and Computing: ICMC 2021, Shibpur, India, pp. 201-217.
• [25] Singh, R.K., Kumar, B., Shaw, D.K. and Khan, D.A. (2021). Level by level image compression-encryption algorithm based on quantum chaos map, Journal of King Saud University-Computer and Information Sciences 33(7): 844-851.
• [26] Song, Y., Zhu, Z., Zhang, W., Guo, L., Yang, X. and Yu, H. (2019). Joint image compression-encryption scheme using entropy coding and compressive sensing, Nonlinear Dynamics 95(3): 2235-2261.
• [27] Sun, Y., Zhang, H., Wang, X. and Wang, M. (2021). Bit-level color image encryption algorithm based on coarse-grained logistic map and fractional chaos, Multimedia Tools and Applications 80(8): 12155-12173.
• [28] ul Haq, T. and Shah, T. (2020). Algebra-chaos amalgam and DNA transform based multiple digital image encryption, Journal of Information Security and Applications 54: 102592.
• [29] Wang, M., Wang, X., Wang, C., Xia, Z., Zhao, H., Gao, S., Zhou, S. and Yao, N. (2020). Spatiotemporal chaos in cross coupled map lattice with dynamic coupling coefficient and its application in bit-level color image encryption, Chaos, Solitons & Fractals 139: 110028.
• [30] Wang, M., Wang, X., Zhao, T., Zhang, C., Xia, Z. and Yao, N. (2021). Spatiotemporal chaos in improved cross coupled map lattice and its application in a bit-level image encryption scheme, Information Sciences 544: 1-24.
• [31] Wang, S. and He, J. (2024). Design of chaotic systems with multiple scrolls via anti-control method and its encryption application, IAENG International Journal of Applied Mathematics 54(12): 2636-2644.
• [32] Wu, J., Wang, L., Chen, G. and Duan, S. (2016). A memristive chaotic system with heart-shaped attractors and its implementation, Chaos, Solitons & Fractals 92: 20-29.
• [33] Xiao, Y., Cao, J., Wang, Z., Long, C., Liu, Y. and He, J. (2019). Polar coded optical OFDM system with chaotic encryption for physical-layer security, Optics Communications 433: 231-235.
• [34] Xiao, Y., Tong, X., Zhang, M. and Wang, Z. (2022). Image lossless encoding and encryption method of EBCOT Tier1 based on 4D hyperchaos, Multimedia Systems 28(3): 727-748.
• [35] Zhang, Y. (2021). A new unified image encryption algorithm based on a lifting transformation and chaos, Information Sciences 547: 307-327.
• [36] Zhang, Y., He, Y., Zhang, J. and Liu, X. (2022). Multiple digital image encryption algorithm based on chaos algorithm, Mobile Networks and Applications 27(4): 1349-1358.
• [37] Zhao, K. and He, J. (2022). Design of higher-dimensional hyperchaotic system based on combined control and its encryption application, International Journal of Advanced Computer Science and Applications 13(7): 869-879.
• [38] Zhu, S., Zhu, C. and Wang, W. (2018). A new image encryption algorithm based on chaos and secure hash SHA-256, Entropy 20(9): 716.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).