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An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption

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  • Ding, Dawei
  • Wang, Wei
  • Yang, Zongli
  • Hu, Yongbing
  • Wang, Jin
  • Wang, Mouyuan
  • Niu, Yan
  • Zhu, Haifei

Abstract

One-dimensional (1D) chaotic maps have many shortcomings, including simple structures, uncomplicated chaotic behaviors, and narrow chaotic ranges. Multi-dimensional (MD) chaotic maps certainly have more complex constructions and more abundant chaotic phenomena. However, it is still challenging to artificially customize its Lyapunov exponents (LEs), which are characterization indicators of the chaotic state. This paper proposed a novel n-dimensional (nD) modulo chaotic system (nD-MCS) based on preceding works that can generate nD chaotic maps by using existing 1D chaotic maps as seed chaotic maps. The proposed nD-MCS can customize its LEs by setting system parameters. Three 2D and three 3D chaotic maps are presented as examples. Performance evaluations demonstrated that they both exhibit hyperchaotic behaviors, broad chaotic ranges, and large complexities. We present an encryption scheme to confirm the application of the developed chaotic maps to image encryption. Finally, a hardware experiment utilizing the field-programmable gate array (FPGA) is adapted to verify the proposed cryptosystem.

Suggested Citation

  • Ding, Dawei & Wang, Wei & Yang, Zongli & Hu, Yongbing & Wang, Jin & Wang, Mouyuan & Niu, Yan & Zhu, Haifei, 2023. "An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007427
    DOI: 10.1016/j.chaos.2023.113841
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    References listed on IDEAS

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    1. Moreira Bezerra, João Inácio & Valduga de Almeida Camargo, Vinícius & Molter, Alexandre, 2021. "A new efficient permutation-diffusion encryption algorithm based on a chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Lai, Qiang & Lai, Cong & Zhang, Hui & Li, Chunbiao, 2022. "Hidden coexisting hyperchaos of new memristive neuron model and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. 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).
    4. Lai, Qiang & Hu, Genwen & Erkan, Uǧur & Toktas, Abdurrahim, 2023. "High-efficiency medical image encryption method based on 2D Logistic-Gaussian hyperchaotic map," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    5. Li, Ming & Wang, Mengdie & Fan, Haiju & An, Kang & Liu, Guoqi, 2022. "A novel plaintext-related chaotic image encryption scheme with no additional plaintext information," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    6. Peng, Xuenan & Zeng, Yicheng, 2020. "Image encryption application in a system for compounding self-excited and hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Cao, Weijia & Cai, Hang & Hua, Zhongyun, 2022. "n-Dimensional Chaotic Map with application in secure communication," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    8. Yildirim, Melih, 2022. "Optical color image encryption scheme with a novel DNA encoding algorithm based on a chaotic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    9. Zhao, Hongyu & Wang, Shengsheng & Wang, Xingyuan, 2022. "Fast image encryption algorithm based on multi-parameter fractal matrix and MPMCML system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Wu, Rui & Gao, Suo & Wang, Xingyuan & Liu, Songbo & Li, Qi & Erkan, Uğur & Tang, Xianglong, 2022. "AEA-NCS: An audio encryption algorithm based on a nested chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
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    1. Fan, Zhenyi & Zhang, Chenkai & Wang, Yiming & Du, Baoxiang, 2023. "Construction, dynamic analysis and DSP implementation of a novel 3D discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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