A Novel Pixel Merging-Based Lossless Recovery Algorithm for Basic Matrix VSS

Introduction

One of efficient secure methods for secret image protection is the visual secret sharing (VSS), also called visual cryptography scheme (VCS) (Wang, Zhang, Ma, & Li, 2007) (Naor, & Shamir, 1999). The original secret image is divided into different meaningless or meaningful shadows (shares) in VSS generating phase. The generated shares are distributed to a group of participants (Yang, 2004) (Cimato, Prisco & Santis, 2006) (Kafri, & Keren, 1987). If enough shadows collected, the secret image is performed by superposing all or some of shares. Based on human visual system (HVS) we can easily obtain the original secret image. However, less than th threshold coefficient^(k) participants give nothing about the secret image.

Literature on VSS is quite rich (Liu, Guo, Wu, & Qian, 2012) (Shyu, 2009) (Li, El-Latif, & Niu, 2012) (Chen, & Tsao, 2011) (Yan, Jin, & Kankanhalli, 2004) (Li, Ma, Su, & Yang, 2012). The concept of the VSS is first introduced by Naor and Shamir (Naor, & Shamir, 1999), the shadow images are generated according to the basic matrixes and are expanded to the larger size than the secret image. Following Naor and Shamir’s work, many research works focus on VSS own physical properties and problems of the VSS mechanism. The probabilistic VSS (ProbVSS) (Yang, 2004) and Random grid (RG)-based VSS (Kafri, & Keren, 1987) (Liu, Guo, Wu, & Qian, 2012) (Shyu, 2009) (Li, El-Latif, & Niu, 2012) (Chen, & Tsao, 2011) are proposed to solve the problem of the pixel expansion. The (Blundo, D'Arco, Santis, & Stinson, 2003) (Hou, & Quan, 2011) focus on the basic matrixes, (Yan, Jin, & Kankanhalli, 2004) (Li, Ma, Su, & Yang, 2012) (Yan, Liu, & Yang, 2015) and XOR-based VSS (XVSS) (Tuyls, Hollmann, & Lint, 2005) concentrate on improving the visual quality. The basic matrix-based VSS scheme is our research object.

It is worth noting that in a lot of situations the lossless recovery of secret image is necessary such as for transmission and storage of military secret images, private medical images, and so on. It is very meaningful to research the lossless recovery scheme which only uses simple computation in the phase of decrypting (recovering).

In the following, we discuss some related works and scope of the proposed work. Lossless recovery can reconstruct the secret losslessly if the light-weight computation device is available.

Chen et al. (Chen, Wang, Yan, & Li, 2014) proposed a progressive^{(2, n)} VSS and the secret will be reconstructed losslessly by additive operation. Wu and Sun (Wu, & Sun, 2013) proposed a scheme having the abilities of OR and exclusive OR (XOR) decryptions and the secret could be recovered losslessly at the condition of collecting all n shares. Utilizing XOR operation, Yan et al. (Yan, Wang, El-Latif, & Niu, 2015) proposed a scheme which needs all n shares to reveal the distortion-less secret image. Nevertheless, none of these schemes (Chen, Wang, Yan, & Li, 2014) (Wu, & Sun, 2013) (Yan, Wang, El-Latif, & Niu, 2015) could recover the secret losslessly when the size of shadow images is expanded. The two-in-one VSS (TiOISS) (Lin, & Lin, 2007) only needs k shares to reconstruct the distortion-less secret image. However, it still requires knowing the order of shadow images and needing complicated computations, i.e., Lagrange interpolations, in the second decoding phase. In addition, in most literatures, the visual quality of the recovered image is always low and the secret image could not be losslessly recovery.