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Image Encryption Algorithm Based on a Novel Wide-Range Discrete Hyperchaotic Map

Author

Listed:
  • Huiyan Zhong

    (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China)

  • Guodong Li

    (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China)

  • Xiangliang Xu

    (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
    School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China)

  • Xiaoming Song

    (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China)

Abstract

Existing hyperchaotic systems suffer from a small parameter range and small key space. Therefore, we propose herein a novel wide-range discrete hyperchaotic map(3D-SCC) based on the mathematical model of the Sine map. Dynamic numerical analysis shows that this map has a wide-range of parameters, high sensitive, high sensitivity of sequences and good ergodicity, which proves that the system is well suited to the field of communication encryption. Moreover, this paper proposes an image encryption algorithm based on a dynamic cycle shift scramble algorithm and image-sensitive function. First, the image feature is extracted by the image-sensitive function to input into the chaos map. Then, the plaintext image is decomposed by an integer wavelet, and the low-frequency part is scrambled by a dynamic cyclic shifting algorithm. The shuffled low-frequency part and high-frequency parts are reconstructed by wavelet, and the chaotic matrix image is bitwise XOR with it to obtain the final ciphertext. The experimental results show that the average NPCR is 99.6024%, the average UACI is 33.4630%, and the average local Shannon entropy is 7.9029, indicating that the statistical properties of the ciphertext are closer to the ideal value. The anti-attack test shows that the algorithm can effectively resist cutting attacks and noise attacks. Therefore, the algorithm has great application value in the field of image encryption.

Suggested Citation

  • Huiyan Zhong & Guodong Li & Xiangliang Xu & Xiaoming Song, 2022. "Image Encryption Algorithm Based on a Novel Wide-Range Discrete Hyperchaotic Map," Mathematics, MDPI, vol. 10(15), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2583-:d:871191
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    References listed on IDEAS

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    1. Fan, Chunlei & Ding, Qun, 2022. "A universal method for constructing non-degenerate hyperchaotic systems with any desired number of positive Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
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    Cited by:

    1. Hemalatha Mahalingam & Padmapriya Velupillai Meikandan & Karuppuswamy Thenmozhi & Kawthar Mostafa Moria & Chandrasekaran Lakshmi & Nithya Chidambaram & Rengarajan Amirtharajan, 2023. "Neural Attractor-Based Adaptive Key Generator with DNA-Coded Security and Privacy Framework for Multimedia Data in Cloud Environments," Mathematics, MDPI, vol. 11(8), pages 1-23, April.
    2. Xiaoqiang Zhang & Mi Liu & Xiaochang Yang, 2023. "Color Image Encryption Algorithm Based on Cross-Spiral Transformation and Zone Diffusion," Mathematics, MDPI, vol. 11(14), pages 1-28, July.

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