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<p>Many chaotic systems suffer from limitations such as narrow chaotic ranges and dynamic degradation. To address this, this paper proposes a novel 3D Improved Logistic Embedded Sine–Cosine Map (3D-ILESCM). By introducing a dynamic, state-dependent exponential term, the map achieves controllable Lyapunov exponents (LEs), allowing for adjustable chaotic complexity. Performance analysis confirms its superior dynamical properties and extensive chaotic regimes. This map is subsequently applied to an innovative multiple-image holographic encryption schemeutilizing a modified Gerchberg–Saxton (GS) algorithm and space division multiplexing. This approach significantly increases encryption capacity by embedding up to 12 grayscale images into a single ciphertext. Moreover, it leverages holography to convert amplitude information into the secure phase domain, effectively resisting statistical analysis. The hologram is secured via block adaptive permutation and semi-tensor product (STP)-based nonlinear diffusion. Unlike traditional XOR operations, the STP diffusion employs a chaotic key matrix to introduce strong nonlinearity and complex matrix mixing, making the encryption process highly sensitive to key variations and resistant to cryptanalysis. Simulation results demonstrate that the scheme exhibits high pseudo-randomness and effectively resists various attacks, offering an efficient encryption approach.</p>

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A novel 3D chaotic map with controllable Lyapunov exponents and extensive regimes: application to multiple images holographic encryption

  • 期刊论文

  • 发表日期：

    2026年3月20日

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  • Hong Cheng,
  • Yuxiao Li,
  • Baohua Yu,
  • Xiaoyuan Wang,
  • Fen Zhang,
  • PengPeng Yuan,
  • Dawei Ding

摘要

Many chaotic systems suffer from limitations such as narrow chaotic ranges and dynamic degradation. To address this, this paper proposes a novel 3D Improved Logistic Embedded Sine–Cosine Map (3D-ILESCM). By introducing a dynamic, state-dependent exponential term, the map achieves controllable Lyapunov exponents (LEs), allowing for adjustable chaotic complexity. Performance analysis confirms its superior dynamical properties and extensive chaotic regimes. This map is subsequently applied to an innovative multiple-image holographic encryption schemeutilizing a modified Gerchberg–Saxton (GS) algorithm and space division multiplexing. This approach significantly increases encryption capacity by embedding up to 12 grayscale images into a single ciphertext. Moreover, it leverages holography to convert amplitude information into the secure phase domain, effectively resisting statistical analysis. The hologram is secured via block adaptive permutation and semi-tensor product (STP)-based nonlinear diffusion. Unlike traditional XOR operations, the STP diffusion employs a chaotic key matrix to introduce strong nonlinearity and complex matrix mixing, making the encryption process highly sensitive to key variations and resistant to cryptanalysis. Simulation results demonstrate that the scheme exhibits high pseudo-randomness and effectively resists various attacks, offering an efficient encryption approach.