Yan Xue Hu, Zhou Xuan, Lu Yu Liang, Liu Jing Ju, Yang Guo Zheng
National University of Defense Technology, Hefei 230037, China.
Math Biosci Eng. 2020 Mar 31;17(4):2950-2966. doi: 10.3934/mbe.2020166.
The polynomial-based image secret sharing (ISS) scheme encodes a secret image into n shadows assigned to n participants. The secret image with high resolution is decoded by Lagrange interpolation when collecting any k or more shadows. Thus, ISS is used in applications such as distributive storage in the cloud, digital watermarking, block chain, and access control. Meaningful shadows are significant in ISS because meaningful shadows decrease the suspicion of image encryption and increase the efficiency of shadow management. Generally, previously meaningful ISS schemes were achieved through embedding the shadows into cover images using information hiding techniques and suffer from large pixel expansion and complex decoding procedure. Digital image processing, such as inpainting (texture synthesis), is a standard technique in multimedia applications. It will be highly significant if ISS can be performed in the processing of a normal digital image processing technique. Generally, the encoding method of an ISS scheme entails the use of a mathematical function that is sensitive to any slight change in the ISS output; therefore, the development of a method for performing the ISS procedure and simultaneously achieving image processing behavior is a key challenge. In this paper, we exploit the behavior ISS (BISS) and realize an image inpainting-based BISS scheme for the (k, n) threshold. Using screening operations, a secret image is encoded into the pixels of cover images by polynomial-based ISS in the processing of inpainting shadows to obtain meaningful shadows similar to the input cover images. In addition, the secret image can be losslessly decoded by Lagrange interpolation when collecting any k or more shadows. Experiments are given to confirm the efficiency of the scheme.
基于多项式的图像秘密共享（ISS）方案将一幅秘密图像编码为分配给n个参与者的n个影子。当收集任意k个或更多影子时，通过拉格朗日插值法对高分辨率的秘密图像进行解码。因此，ISS被应用于诸如云分布式存储、数字水印、区块链和访问控制等领域。在ISS中，有意义的影子很重要，因为有意义的影子可以降低对图像加密的怀疑并提高影子管理的效率。一般来说，以前有意义的ISS方案是通过使用信息隐藏技术将影子嵌入到掩护图像中实现的，但存在像素扩展大和解码过程复杂的问题。数字图像处理，如图像修复（纹理合成），是多媒体应用中的一种标准技术。如果能在正常的数字图像处理技术过程中执行ISS，那将具有重要意义。一般来说，ISS方案的编码方法需要使用对ISS输出的任何微小变化都敏感的数学函数；因此，开发一种执行ISS过程并同时实现图像处理行为的方法是一个关键挑战。在本文中，我们利用行为ISS（BISS），实现了一种基于图像修复的（k，n）门限BISS方案。通过筛选操作，在修复影子的过程中，利用基于多项式的ISS将秘密图像编码到掩护图像的像素中，以获得与输入掩护图像相似的有意义的影子。此外，当收集任意k个或更多影子时，秘密图像可以通过拉格朗日插值法无损解码。通过实验验证了该方案的有效性。
