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A non-degenerate chaotic bits XOR system with application in image encryption

Author

Listed:
  • Zhu, Hegui
  • Ge, Jiangxia
  • He, Jinwen
  • Zhang, Libo

Abstract

The existing chaotic systems exhibit chaos degradation phenomena because of the limited chaotic precision in the real number field. In response to this deficiency, this paper proposes a chaotic bits XOR system (CBXS) in the integer field satisfying Devaney’s chaos. That is, CBXS has the property of sensitivity of initial value, topological transitivity, and periodic point density. Then, a series of chaotic and random test results illustrate that the sequences generated by CBXS with linear feedback shift register (LFSR) in the finite field GF(2) have good random and chaotic performance. It can overcome the chaos degradation problem because it is generated in the integer field and can avoid the limited precision in the real number field. Finally, we employ the proposed CBXS to image encryption with the optimized Arnold’s transformation. The experimental results verify that even after simple encryption, the cipher image still exhibits good encryption effect and efficiency, which illustrates the effectiveness of CBXS.

Suggested Citation

  • Zhu, Hegui & Ge, Jiangxia & He, Jinwen & Zhang, Libo, 2024. "A non-degenerate chaotic bits XOR system with application in image encryption," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 231-250.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:231-250
    DOI: 10.1016/j.matcom.2023.12.023
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    References listed on IDEAS

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    1. 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.
    2. Cao, Weijia & Cai, Hang & Hua, Zhongyun, 2022. "n-Dimensional Chaotic Map with application in secure communication," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Arroyo, David & Li, Chengqing & Li, Shujun & Alvarez, Gonzalo & Halang, Wolfgang A., 2009. "Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2613-2616.
    4. Zheng, Jun & Hu, Hanping & Ming, Hao & Zhang, Yanxia, 2021. "Design of a hybrid model for construction of digital chaos and local synchronization," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Elmanfaloty, Rania A. & Abou-Bakr, Ehab, 2019. "Random property enhancement of a 1D chaotic PRNG with finite precision implementation," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 134-144.
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