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Dynamic analysis and image encryption application of a sinusoidal-polynomial composite chaotic system

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  • Zhu, Hegui
  • Ge, Jiangxia
  • Qi, Wentao
  • Zhang, Xiangde
  • Lu, Xiaoxiong

Abstract

Due to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal-polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney’s definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation and pixel diffusion operation with the proposed SPCCS. The detailed simulation results verify superiority and effectiveness of the proposed image encryption algorithm.

Suggested Citation

  • Zhu, Hegui & Ge, Jiangxia & Qi, Wentao & Zhang, Xiangde & Lu, Xiaoxiong, 2022. "Dynamic analysis and image encryption application of a sinusoidal-polynomial composite chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 188-210.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:188-210
    DOI: 10.1016/j.matcom.2022.02.029
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    References listed on IDEAS

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    3. Xiuli Chai & Zhihua Gan & Yang Lu & Yiran Chen & Daojun Han, 2017. "A novel image encryption algorithm based on the chaotic system and DNA computing," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(05), pages 1-24, May.
    4. Castro, Julio Cesar Hernandez & Sierra, José María & Seznec, Andre & Izquierdo, Antonio & Ribagorda, Arturo, 2005. "The strict avalanche criterion randomness test," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(1), pages 1-7.
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    Cited by:

    1. Zhu, Shenli & Deng, Xiaoheng & Zhang, Wendong & Zhu, Congxu, 2023. "Secure image encryption scheme based on a new robust chaotic map and strong S-box," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 322-346.
    2. Shenli Zhu & Xiaoheng Deng & Wendong Zhang & Congxu Zhu, 2023. "Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA Coding," Mathematics, MDPI, vol. 11(1), pages 1-22, January.
    3. Yang, Zhen & Liu, Yinzhe & Wu, Yuqi & Qi, Yunliang & Ren, Fengyuan & Li, Shouliang, 2023. "A high speed pseudo-random bit generator driven by 2D-discrete hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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