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Image encryption algorithm based on butterfly module and chaos

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  • Zhang, Yong

Abstract

Image information security is a hot research area in cryptography after text encryption research. To effectively secure digital images, a practical and graceful new image encryption algorithm was proposed in this paper. Firstly, four substitution boxes (S-boxes) are constructed based on the method of generating S-box of AES. Secondly, a chaotic system with uniform probability density function is created by fusing piecewise linear map (PWLM) and Arnold cat map. The resulting system is used to produce an equivalent-key sequence of the same size as the plain image using an external secret key of length 256 bits. Thirdly, a butterfly encoding module based on the butterfly node algorithm is presented. Finally, the basic image cryptosystem based on the butterfly encoding module, the enhanced image cryptosystem with cipher-text sensitivity, and the unified image cryptosystem with identical encryption and decryption processes are sequentially studied. The performance analysis shows that the proposed image encryption systems have a time complexity of 3 and a spatial complexity of approximately 3.03, the generated cipher images are similar to noise images, and the secret key, the equivalent key, and the plain image are all extremely sensitive. Thus, the proposed cryptographies are high-speed and secure image encryption algorithms.

Suggested Citation

  • Zhang, Yong, 2025. "Image encryption algorithm based on butterfly module and chaos," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 382-407.
    • Handle: RePEc:eee:matcom:v:232:y:2025:i:c:p:382-407
    DOI: 10.1016/j.matcom.2025.01.011
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    References listed on IDEAS

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    1. Haider, Muhammad Imran & Shah, Tariq & Ali, Asif & Shah, Dawood & Khalid, Ijaz, 2023. "An Innovative approach towards image encryption by using novel PRNs and S-boxes Modeling techniques," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 153-168.
    2. 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.
    3. Zijing Gao & Zeyu Liu & Lichan Wang & Piergiulio Tempesta, 2021. "An Image Encryption Algorithm Based on the Improved Sine-Tent Map," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-16, October.
    4. Hu, Long-Long & Chen, Ming-Xuan & Wang, Meng-Meng & Zhou, Nan-Run, 2024. "A multi-image encryption scheme based on block compressive sensing and nonlinear bifurcation diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    5. Lai, Qiang & Chen, Zhijie, 2023. "Grid-scroll memristive chaotic system with application to image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    Full references (including those not matched with items on IDEAS)

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