Polynomial-Based Secret Image Sharing Scheme with Fully Lossless Recovery

Polynomial-Based Secret Image Sharing Scheme with Fully Lossless Recovery

Wanmeng Ding (National University of Defense Technology,Hefei,China), Kesheng Liu (National University of Defense Technology,Hefei,China), Xuehu Yan (National University of Defense Technology,Hefei,China) and Lintao Liu (National University of Defense Technology,Hefei,China)
Copyright: © 2018 |Pages: 17
DOI: 10.4018/IJDCF.2018040107

Abstract

Lossless recovery is important for the transmission and storage of image data. In polynomial-based secret image sharing, despite many previous researchers attempted to achieve lossless recovery, none of the proposed work can simultaneously satisfy an efficiency execution and at no cost of some storage capacity. This article proposes a secret sharing scheme with fully lossless recovery based on polynomial-based scheme and modular algebraic recovery. The major difference between the proposed method and polynomial-based scheme is that, instead of only using the first coefficient of sharing polynomial, this article uses the first two coefficients of sharing polynomial to embed the pixels as well as guarantee security. Both theoretical proof and experimental results are given to demonstrate the effectiveness of the proposed scheme.
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Introduction

Security is a big concern when considering the storage and transmission of image information. Traditional cryptography (Assad & Farajallah, 2016; Li, El-Latif, Shi, & Niu, 2012; Zhang & Xiao, 2014) method cannot prevent the data from being lost or corrupted during the transmission. Instead of cryptography, secret sharing is a way to ensure security since it has a property of loss-tolerant. Secret sharing, which comes from key management, was introduced by Shamir (1979) and Blakley (1979) independently. A (k, n) threshold secret sharing encrypts the secret into shares, and distributes the shares among n participants(kn). When any k or more participants collect together, the secret can be revealed. With this property of loss-tolerant, the secret can be decoded under the case even some shares are lost. Furthermore, secret sharing can be applied in many scenarios (Belazi & El-Latif, 2016; Yan et al., 2017). For example, in distributed storage and transmission, an image can be shared into n shares by a (k, n) threshold secret sharing scheme and be stored in n severs, the secret can be decoded under the case even n-k or less servers are broken.

Shamir's polynomial-based scheme (Li, Ma, Su, & Yang, 2012; Li, Yang, Wu, Kong, & Ma, 2013; Lin, S. J., & Lin, J. C., 2007; Shamir, 1979; Thien & Lin, 2002; Yang & Ciou, 2010) encrypts the secret into n shares using a polynomial and distributes the n shares to n participants separately. When any k or more participants with their shares get together, the secret can be reconstructed by Lagrange interpolation (Bleichenbacher & Nguyen, 2000; Chen, Liu, & Wang, 2008; Werner, 1984). Noar and Shamir (1994) extended the concept of secret sharing from number to image. In 2002, Thien and Lin (2002) used Shamir's scheme to share secret images in domain [0,250]. The scheme embedded the secret pixels in all the coefficients of the sharing polynomial, thus reducing the size of shadow images to 1/k times that of the original secret image. However, the scheme in Thien and Lin’s work truncated all gray values larger than 250 to 250 so that the method cannot actually get a lossless secret image (2002).

In terms of actual applications, the ability to recover image losslessly can be useful in a number of scenarios (Devaki & Rao, 2012; Hu & Jeon, 2006; Li, El-Latif, Yan, & Wang, 2012; Tso, Lou, Wang, & Liu, 2008; Yan & Lu, 2017). In real-world applications, like in area of medicine and military (Cheddad, Condell, Curran, & McKevitt, 2010), images details are significant and lossless images are important for the transmission and storage of image data.

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