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<p>Aiming at the issue of image privacy protection for distributed storage in the resource-constrained environment, an image encryption algorithm combining two-dimensional parametric polynomial hyperchaotic map (2D-PPHM) and sharing matrix is proposed. To enhance cryptographic security and efficiency, a 2D-PPHM is first designed to generate chaotic sequences for measurement matrix construction, data confusion and diffusion. Subsequently, the plain image is sparsely represented and encrypted via compressed sensing (CS) followed by index confusion and bidirectional diffusion, significantly reducing image size while ensuring confidentiality. To achieve distributed storage, a sharing matrix method is employed to decompose the secret image into multiple shadow images. This mechanism ensures that the plain image can be reconstructed even if certain shadows are corrupted or lost. Simulation results and performance analyses demonstrate that the proposed algorithm provides high security and robustness with low computational overhead, making it well-suited for resource-constrained applications.</p>

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Image Encryption Algorithm Combining Two-Dimensional Parametric Polynomial Hyperchaotic Map and Sharing Matrix

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Yuliang Xu,
  • Jiangtao Guo

摘要

Aiming at the issue of image privacy protection for distributed storage in the resource-constrained environment, an image encryption algorithm combining two-dimensional parametric polynomial hyperchaotic map (2D-PPHM) and sharing matrix is proposed. To enhance cryptographic security and efficiency, a 2D-PPHM is first designed to generate chaotic sequences for measurement matrix construction, data confusion and diffusion. Subsequently, the plain image is sparsely represented and encrypted via compressed sensing (CS) followed by index confusion and bidirectional diffusion, significantly reducing image size while ensuring confidentiality. To achieve distributed storage, a sharing matrix method is employed to decompose the secret image into multiple shadow images. This mechanism ensures that the plain image can be reconstructed even if certain shadows are corrupted or lost. Simulation results and performance analyses demonstrate that the proposed algorithm provides high security and robustness with low computational overhead, making it well-suited for resource-constrained applications.