A novel secret sharing scheme using multiple share images

Xiaoping Li; Yanjun Liu; Hefeng Chen; Chin-Chen Chang; Xiaoping Li; Yanjun Liu; Hefeng Chen; Chin-Chen Chang

doi:10.3934/mbe.2019317

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 6350-6366. doi: 10.3934/mbe.2019317

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Research article Special Issues

A novel secret sharing scheme using multiple share images

1.
School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 611731, China.
2.
Department of Information Engineering and Computer Science, Feng Chia University, Taichung 407, Taiwan.
3.
Computer Engineering College, Jimei University, Xiamen 361021, China

Received: 18 March 2019 Accepted: 02 July 2019 Published: 09 July 2019

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.
- secret image sharing,
- Chinese remainder theorem (CRT),
- generalized CRT,
- share image,
- reconstruction
Citation: Xiaoping Li, Yanjun Liu, Hefeng Chen, Chin-Chen Chang. A novel secret sharing scheme using multiple share images[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6350-6366. doi: 10.3934/mbe.2019317

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Abstract

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.

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