Image Secret Sharing Construction for General Access Structure with Meaningful Share

Image Secret Sharing Construction for General Access Structure with Meaningful Share

Xuehu Yan (National University of Defense Technology, China), Yuliang Lu (National University of Defense Technology, China), Lintao Liu (National University of Defense Technology, China) and Duohe Ma (Institute of Information Engineering, Chinese Academy of Sciences, China)
Copyright: © 2018 |Pages: 12
DOI: 10.4018/IJDCF.2018070106

Abstract

This article describes how the (k, n) threshold image secret sharing technology can recover the secret image even n − k shares are lost, or n−k servers do not work, which is useful for cloud storage, etc. Image secret sharing for general access structure (GAS) is more general than (k, n) threshold. Image secret sharing with a meaningful share will decrease encryption suspicion so that the security can be enhanced. However, traditional studies have no image secret sharing construction approach for GAS with a meaningful share. In the article, they first exploit an image secret sharing construction approach for GAS with meaningful share. Following their construction approach, the authors develop a random grid (RG)-based visual secret sharing (VSS) algorithm for GAS with meaningful share as well as polynomial-based image secret sharing for GAS with meaningful share. The experiments with this concept exhibit the effectiveness of the algorithms and further their construction approach.
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1. Introduction

Image data occupies a large proportion of multimedia big data. Secure storage and calculation of cloud computing means a lot to image. A secret image is split into n shares, i.e., shadows or shadow images, by (k, n) threshold image secret sharing technology. The n shares are then stored in n corresponding cloud servers, respectively. However, some servers may be useless due to the dynamic communication environment, the random network establishment and server failure. Thus, some shares may be useless as well. (k, n) threshold image secret sharing technology can recover the secret image even n − k shares are lost or n − k servers do not work. Since image secret sharing for (k, n) threshold is loss-tolerant, i.e., the secret can be restored even n − k shares are lost. Besides, image secret sharing is useful for some applications, such as, key management, authentication, watermarking, access control, passwords transmitting, information hiding, distributed storage in cloud computing, etc. (Yan, Lu, Liu, Wan, Ding & Liu, 2017; Belazi & ElLatif, 2017). Furthermore, due to image is a special form of data and each grayscale pixel is combined of 8 bits, i.e., 1 byte, image secret sharing will be easily suitable for data secret sharing. In image secret sharing, we mainly have polynomial-based method (Shamir, 1979) and visual secret sharing (VSS) (Naor & Shamir, 1995; Wang, Liu & Yan, 2016) (also called visual cryptography (VC)).

Shamir’s first polynomial-based image secret sharing (Shamir, 1979) for (k, n) threshold encodes an image secret pixel into the constant coefficient of a random (k − 1)-degree polynomial to output n shares assigned to n owners. The secret image is restored with high-resolution by Lagrange interpolation when getting any k or more shares. Inspired by Shamir’s first method, some other studies (Yang & Ciou, 2010) proposed more polynomial-based schemes to get more features. The merit of polynomial-based image secret sharing is that the secret is restored with high quality. Although polynomial-based image secret sharing only employs k shares for restoring the distortion-less image, it has no general access structure (GAS). In image secret sharing for GAS (Wu& Sun, 2012; Yan & Lu, 2017), the user can appoint the qualified owners’ combinations which are able to restore the secret, i.e., the user will allocate a specification of all qualified subsets of owners. Hence GAS is more general than (k, n) threshold or (k, k) threshold.

In VSS (Weir & Yan, 2010) for (k, n) threshold, the outputted n shares are printed onto transparencies first and then assigned to n owners. The key merit of VSS is that the secret image is restored through superposing any k or more shares and human eyes with no cryptographic computation. Getting less than k shares will in general restore nothing of the secret image even an attacker deduces infinite computation power. Unfortunately, the conventional VSS schemes suffer from no GAS, pixel expansion, codebook design and “all-or-nothing”, which are further discussed by other works (Yang, Wu & Wang, 2014; Fu & Yu, 2014; Guo, Liu & Wu, 2013; Yan, Liu & Yang, 2015a; Wu & Sun, 2012; Yan & Lu, 2017).

On one hand, image secret sharing for GAS is more extensive than (k, n) threshold or (k, k) threshold. Although some VSS schemes for GAS (Ateniese, Blundo, De Santis & Stinson, 1996; Wu & Sun,2012; Yan & Lu, 2017) were given, most of VSS schemes still have no GAS.

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