Secret Image Sharing Scheme with Threshold Changeable Capability

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2016, Article ID 9576074, 11 pages http://dx.doi.org/10.1155/2016/9576074 Research Article Secret Image Sharing Scheme with Threshold Changeable Capability Lifeng Yuan,1,2 Mingchu Li,1,2 Cheng Guo,1,2 Weitong Hu,3 and Xinjian Luo1,2 1 School of Software Technology, Dalian University of Technology, Dalian 116620, China Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, Dalian 116620, China 3 School of Computer and Technology, Hangzhou Dianzi University, Hangzhou 310018, China 2 Correspondence should be addressed to Cheng Guo; Received 27 January 2016; Accepted 22 May 2016 Academic Editor: Nazrul Islam Copyright © 2016 Lifeng Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In secret image sharing schemes, the threshold may have to be adjusted in case of changes in the security policy and the adversary structure before recovering the secret image. For example, if participants leave the group, their stego images are useless to them and may not be kept safely. As a result, these images can be easily stolen and utilized by intruders, which reduces the security of the scheme. To solve this problem, we propose a novel threshold changeable secret image sharing scheme with 𝑁 potential changeable thresholds 𝑡1 , 𝑡2 , . . . , 𝑡𝑁 . By preparing advance shares for thresholds 𝑡1 , 𝑡2 , . . . , 𝑡𝑁 and using the two-variable one-way function to generate the identification value, we can change the threshold when necessary. The experiments show that the quality of the stego images in our scheme is satisfactory and the secret image can be recovered without distortion. Moreover, the security analysis shows that we can change the threshold safely. 1. Introduction The rapid development of Internet has brought much more convenience to people’s daily lives, but it has also brought security risks. In the open communication networks, it is easy to intercept, modify, fabricate, and even destroy data. Modern cryptography provides an effective solution to ensure the security of information. Since the design details of most cryptography algorithms are public, the security of the encrypted information depends on the security of the key. Thus, it is important that the key be kept safely. In order to solve this secret key protecting problem, Shamir [1] and Blakley [2] proposed (𝑡, 𝑛) threshold secret sharing schemes independently. Shamir constructed his scheme based on polynomial interpolation, while Blakley provided a geometric construction. In a (𝑡, 𝑛) threshold secret sharing scheme, a dealer encodes and divides the secret into 𝑛 shares that are distributed to 𝑛 participants, and then 𝑡 or more participants can recover the secret, but less than 𝑡 participants cannot get any information about the secret. In 1994, Naor and Shamir [3] proposed a visual secret image sharing scheme. Utilizing the (𝑡, 𝑛) threshold secret sharing technique, the secret image is encoded and divided into 𝑛 random-noise-like images (called share images), and these share images are distributed to the participants, so that any 𝑡 or more participants can see the secret image by stacking their share images together. However, the random-noise-like images, which are meaningless, can easily attract malicious intruders’ attention. To solve this problem, Lin and Tsai [4] provided a (𝑡, 𝑛) threshold image sharing scheme using steganography. In their scheme, the shares are camouflaged in a cover image to form the stego images, which cannot be distinguished by the human eye, so these shares can be concealed from intruders. At the same time, their scheme embeds watermarks into the stego images for verification. In recent years, various secret image sharing techniques have been developed rapidly. In 2007, Yang et al. [5] proposed an image sharing scheme that can improve the authentication ability, but it degraded the quality of the stego images. In 2009, Lin et al. [6] utilized the modulo operation to camouflage the secret data in the cover image to overcome this drawback. Their scheme guarantees higher quality stego images, and 2 it can reconstruct the secret image and the cover image without distortion. In 2010, Lin and Chan [7] proposed an invertible secret image sharing scheme with satisfactory quality of the stego images. It can recover the secret image and the cover image without distortion, and it allows for a large capacity of secret data embedding. In reality, the single (𝑡, 𝑛) threshold access structure cannot satisfy the demand of complex applications. To solve this problem, Guo et al. [8] first proposed a hierarchical secret image sharing, based on polynomial interpolation in 2012, which divided the secret share images into different hierarchies and set different threshold values. Also in 2012, Guo et al. [9] proposed another novel hierarchical secret image sharing scheme based on monotone span programs (MSPs). In 2013, Ulutas et al. [10] proposed an invertible secret image sharing scheme using modification direction and the modulo operation. Their scheme can improve the quality of the stego images effectively when grey-scale cover image is used, and it can also obtain acceptable quality stego images when dithered cover image is used. In 2014, Pakniat et al. [11] used cellular automata and Birkhoff interpolation to propose a novel secret image sharing scheme with hierarchical threshold access structure. In this scheme, each authorized subset of participants is able to recover the secret image and the cover image without distortion, and they can also check the validity of the secret image. Before recovering the secret image, the security policies and adversary structures may change, so it may be necessary to adjust the threshold. For example, (1) the importance level of the secret image is increased or decreased; (2) some participants join or leave the group; (3) the mutual trust of participants is strengthened or weakened; (4) the adversary might have corrupted more than 𝑛 − 𝑡 participants. Currently, there is not a secret image sharing scheme that can change the threshold after distributing the stego images and before recovering the secret image. Therefore, it is necessary to set up a changeable threshold secret image sharing scheme. Currently, many researchers are interested in secret sharing schemes, especially threshold changeable secret sharing schemes. In 1991, Laih et al. [12] proposed the first threshold changeable secret sharing scheme. In recent years, some researchers have been developing threshold changeable secret sharing schemes based on various techniques, such as (1) the share redistributing technique in [13–15]; (2) the lattice basis reduction technique in [16–18]; (3) the redundant shares technique in [19, 20]; and (4) the (...truncated)