https://doi.org/10.1140/epjp/s13360-023-03904-7
Regular Article
Complex chaotic attractor via fractal process with parabolic map and triangular map
1
College of Computer and Information Science, Chongqing Normal University, 401331, Chongqing, China
2
Key Laboratory of Luminescence Analysis and Molecular Sensing (Southwest University), Ministry of Education, Chongqing, China
3
College of Artificial Intelligence, Southwest University, 400715, Chongqing, China
a
411354525@qq.com
e
ldwang@swu.edu.cn
Received:
16
January
2023
Accepted:
15
March
2023
Published online:
19
April
2023
Chaotic systems and fractal processes have recently been extensively investigated in many fields. In this paper, we propose different systems of fractal process based on Julia’s fractal process, double-scroll chaotic attractor, parabolic map, and triangular map, which can yield different multi-scroll chaotic attractors with different topologies. Furthermore, the results of the numerical simulations are well demonstrated by the micro-controller (MCU) experiments, which reveal the existence of fractal-based multi-scroll chaotic attractors and provide a new idea for the generation of multi-scroll chaotic attractors. From the perspective of engineering applications, the random performance of one of the systems of the fractal process is tested by NIST test suits, and the results confirmed that the systems of the fractal process have excellent randomness and are suitable for image encryption. Therefore, to further verify the randomness of the system of fractal processes, we introduced a new image encryption algorithm with this system of fractal processes as the core. We first replace the pixels in the plain image with the help of an S-box based on chaotic sequences, after which we propose a range-limited pixel diffusion method based on the water wave propagation principle. The simulation results and performance analysis of this algorithm demonstrate that it can effectively hide the information of the plain image, scramble the statistical features such as pixel distribution of the plain image, and at the same time achieve performance improvement compared with other algorithms.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
