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<p>To ensure the high performance for an encryption method, the multiple iterations or additional diffusion layers are applied in the processes of encryption. However, it will lead to huge computation and complex operations. Therefore, an encryption method with considerable computation costs and operations will be considered in this paper. Firstly, a discrete cosine memristor is constructed. The characteristic of the memristor hysteresis loop is tight at the origin. Then, a memristive noninvertible map is proposed through introducing a cosine memristor to a noninvertible map. For the memristive map, bifurcation diagrams, Lyapunov exponents, sensitivity analysis of initial value and entropy complexity measure are obtained via numerical simulations. Secondly, the circuit models for the discrete cosine memristor and the discrete memristive system are designed by performing simulations with PSIM, which are also confirmed by MATLAB. Finally, an image encryption method is proposed based on the memristive map. By using the method, a color image is partitioned into multiple sub-blocks with varying sizes. Numerical simulations are used to confirm the practicability of the algorithm. The results indicate that the change rate of pixel values, unified average changing intensity and information entropy are all close to theoretical values. It implies that the algorithm has high security and efficiency. The primary advantage of the proposed method is that only a single round of scrambling and diffusion is required and achieves&#xa0;a robust encryption performance with considerable computation cost.</p>

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Dynamics and image encryption of a memristive noninvertible map

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Xiaojun Liu,
  • Jing Xu,
  • Pu Wang,
  • Cheng Lei

摘要

To ensure the high performance for an encryption method, the multiple iterations or additional diffusion layers are applied in the processes of encryption. However, it will lead to huge computation and complex operations. Therefore, an encryption method with considerable computation costs and operations will be considered in this paper. Firstly, a discrete cosine memristor is constructed. The characteristic of the memristor hysteresis loop is tight at the origin. Then, a memristive noninvertible map is proposed through introducing a cosine memristor to a noninvertible map. For the memristive map, bifurcation diagrams, Lyapunov exponents, sensitivity analysis of initial value and entropy complexity measure are obtained via numerical simulations. Secondly, the circuit models for the discrete cosine memristor and the discrete memristive system are designed by performing simulations with PSIM, which are also confirmed by MATLAB. Finally, an image encryption method is proposed based on the memristive map. By using the method, a color image is partitioned into multiple sub-blocks with varying sizes. Numerical simulations are used to confirm the practicability of the algorithm. The results indicate that the change rate of pixel values, unified average changing intensity and information entropy are all close to theoretical values. It implies that the algorithm has high security and efficiency. The primary advantage of the proposed method is that only a single round of scrambling and diffusion is required and achieves a robust encryption performance with considerable computation cost.