基于二次剩余的灰度图像（k，n）秘密共享方案
A Novel (k,n) Secret Sharing Scheme from Quadratic Residues for Grayscale Images
摘要：
提出了一种新的基于$(k,n)$门限秘密共享的灰度图像加密算法。该方案允许秘密图像被转换成$n$份额，其中任何$k \le n$份额都可以用于重建秘密图像，而$k-1$或更少份额的知识没有留下关于秘密图像的足够信息，并且难以解密传输的图像。在该方案中，秘密图像的像素首先置换，然后使用二次剩余加密。在最后阶段，加密图像被共享成n个影子图像使用多项式的Shamir计划。该方案是可证明安全的，实验结果表明，该方案表现良好，同时保持高水平的重建图像的质量。
英文摘要：
A new grayscale image encryption algorithm based on $(k,n)$ threshold secret sharing is proposed. The scheme allows a secret image to be transformed into $n$ shares, where any $k \le n$ shares can be used to reconstruct the secret image, while the knowledge of $k-1$ or fewer shares leaves no sufficient information about the secret image and it becomes hard to decrypt the transmitted image. In the proposed scheme, the pixels of the secret image are first permuted and then encrypted by using quadratic residues. In the final stage, the encrypted image is shared into n shadow images using polynomials of Shamir scheme. The proposed scheme is provably secure and the experimental results shows that the scheme performs well while maintaining high levels of quality in the reconstructed image.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
