School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 611731, China.
Department of Information Engineering and Computer Science, Feng Chia University, Taichung 407, Taiwan.
Math Biosci Eng. 2019 Jul 9;16(6):6350-6366. doi: 10.3934/mbe.2019317.
Secret image sharing has been widely applied in numerous areas, such as military imaging systems, remote sensing, and so on. One of the problems for image sharing schemes is to efficiently recover original images from their shares preserved by the shareholders. However, most of the existing schemes are based on the assumption that the shares are distortion-free. Moreover, the correspondence between secret images and their shares is definite. To overcome these shortcomings, we propose a novel secret sharing scheme using multiple share images based on the generalized Chinese remainder theorem (CRT) in this paper, where all of the shares are needed to recover the original images. Two categories of distortions are considered. In the first category, some pairs of shares with the same moduli are exchanged, while in the second category, some of pixels in the pairs of shares with the same moduli are exchanged. Based on these two sharing methods, we propose a generalized CRT based recovery method. Compared with the existing CRT based methods as well as combinatorial based methods, the proposed approach is much more efficient and secure. Furthermore, the conditions for successful recovery of two images from the given distorted shares are obtained. Simulations are also presented to show the efficiency of the proposed scheme.
秘密图像共享已广泛应用于军事成像系统、遥感等众多领域。图像共享方案面临的一个问题是如何有效地从股东保存的共享中恢复原始图像。然而，大多数现有的方案都基于这样的假设，即共享是无失真的，并且秘密图像与其共享之间的对应关系是确定的。为了克服这些缺点，我们提出了一种新的基于广义中国剩余定理（CRT）的使用多个共享图像的秘密共享方案，其中需要所有的共享来恢复原始图像。考虑了两类失真。在第一类中，交换了具有相同模数的某些共享对，而在第二类中，交换了具有相同模数的共享对中的某些像素。基于这两种共享方法，我们提出了一种基于广义 CRT 的恢复方法。与现有的基于 CRT 的方法以及基于组合的方法相比，所提出的方法效率更高，安全性更强。此外，还获得了从给定失真共享中成功恢复两幅图像的条件。还进行了仿真，以显示所提出方案的效率。
