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Novel 1-D enhanced Log-logistic chaotic map and asymmetric generalized Gaussian apertured FrFT for image encryption

Author

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  • Wang, Meng-meng
  • Song, Xin-guang
  • Zhou, Nan-run
  • Liu, Si-hang

Abstract

This paper proposes a 1-D enhanced Log-logistic chaotic map (1-DELLCM) and an asymmetric generalized Gaussian apertured fractional Fourier transform (AGGAFrFT). The 1-DELLCM is a new chaotic map that introduces the nonlinear function log2(1 + x) into the traditional logistic map. This modification leads to a more intricate behavior and an expanded spectrum of chaos. On the other hand, the AGGAFrFT utilizes the asymmetric generalized Gaussian distribution with three shaping parameters as the soft aperture in the fractional Fourier optical system. This design choice enables the AGGAFrFT to exhibit a low-pass filtering performance, which helps to resist noise attacks to some extent. To bolster the sensitivity of the three shaping parameters, an iterative image encryption algorithm has been devised to create an apertured phase mask utilized for encrypting images. Based on the experimental outcomes, the sensitivities of the three shaping parameters, fractional order, and wavelength for AGGAFrFT are found to be at least up to 10−15. Additionally, experimental findings demonstrate that incorporating 1-DELLCM and AGGAFrFT into the proposed algorithm significantly bolsters the encryption process's security, rendering it resilient against diverse attacks, particularly noise attacks.

Suggested Citation

  • Wang, Meng-meng & Song, Xin-guang & Zhou, Nan-run & Liu, Si-hang, 2024. "Novel 1-D enhanced Log-logistic chaotic map and asymmetric generalized Gaussian apertured FrFT for image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009950
    DOI: 10.1016/j.chaos.2024.115443
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    References listed on IDEAS

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    1. Long, Guoqiang & Chai, Xiuli & Gan, Zhihua & Jiang, Donghua & He, Xin & Sun, Mengge, 2023. "Exploiting one-dimensional exponential Chebyshev chaotic map and matching embedding for visually meaningful image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Çavuşoğlu, Ünal & Kaçar, Sezgin & Pehlivan, Ihsan & Zengin, Ahmet, 2017. "Secure image encryption algorithm design using a novel chaos based S-Box," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 92-101.
    3. 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.
    4. Wang, Xingyuan & Du, Xiaohui, 2022. "Pixel-level and bit-level image encryption method based on Logistic-Chebyshev dynamic coupled map lattices," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. Liu, Lingfeng & Wang, Jie, 2023. "A cluster of 1D quadratic chaotic map and its applications in image encryption," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 89-114.
    Full references (including those not matched with items on IDEAS)

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