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Analysis and implementation of no-equilibrium chaotic system with application in image encryption

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Abstract

The study of no-equilibrium chaotic system is one of the recent hot topics. This paper constructs a new no-equilibrium chaotic system by introducing an additional variable and a constant term to a three-dimensional chaotic system. Different from the previous no-equilibrium chaotic system, the new system has period-doubling bifurcation and performs hidden chaotic attractors for a large constant term. The analog circuit and field-programmable gate array (FPGA) implementation are given to illustrate the existence of the system. By utilizing the new system, a chaotic magic cube transformation image encryption algorithm (CMCT-IEA) is proposed, which has a classical permutation-diffusion structure. A new permutation method is designed to scramble image pixels in three-dimensional space, and a diffusion method is developed to diffuse small pixel changes of the original image to all pixels in three-dimensional space. A dynamic key is also designed to improve the security of the encryption algorithm. We also analyze the security of CMCT-IEA in terms of computational complexity, statistical properties, and the ability to defend against several common attacks. Compared with several advanced algorithms, the CMCT-IEA exhibits excellent security characteristics.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 61961019, and the Youth Key Project of Natural Science Foundation of Jiangxi Province of China under Grant 20202ACBL212003.

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Authors and Affiliations

  1. School of Electrical and Automation Engineering, East China Jiaotong University, 330013, Nanchang, China

    Qiang Lai & Hui Zhang

  2. Laboratory of Condensed Matter, Electronics and Signal Processing, Department of Physics, University of Dschang, P.O. Box 067, Dschang, Cameroon

    Paul Didier Kamdem Kuate

  3. School of Electrical and Electronics Engineering, Hubei University of Technology, 430068, Wuhan, China

    Guanghui Xu

  4. School of Mathematics, Hefei University of Technology, 230009, Hefei, China

    Xiao-Wen Zhao

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  1. Qiang Lai
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  2. Hui Zhang
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  4. Guanghui Xu
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  5. Xiao-Wen Zhao
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Correspondence to Qiang Lai.

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Lai, Q., Zhang, H., Kuate, P.D.K. et al. Analysis and implementation of no-equilibrium chaotic system with application in image encryption. Appl Intell 52, 11448–11471 (2022). https://doi.org/10.1007/s10489-021-03071-1

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