Essential secret image sharing scheme with different importance of shadows

In (k, n) secret image sharing (SIS), a scheme encrypts a secret image into n shadow images. Any k or more shadow images can be collaborated together to reveal the secret image. Most of the previous SIS schemes don’t distinguish the importance of shadows. However, in some application environments, some participants are accorded special privileges due to their status or importance. Thus, some shadows may be more important than others. In this paper, we consider the (t, s, k, n) essential SIS (ESIS) scheme. All n shadows are classified into s essential shadows and (n–s) non-essential shadows. When reconstructing the secret image, the (t, s, k, n)-ESIS scheme needs k shadows, which should include at least t essential shadows.     

Two-layered structure for optimally essential secret image sharing scheme

This paper presents a two-layered structure for optimally sharing a secret image among s essential and n − s non-essential shared shadows using the (t, s, k, n) essential thresholds, that t essential shared shadows and totally k shared shadows are needed to recover the secret image. The presented two-layered structure includes one user-defined parameter m to determine different kinds of optimal results. m = 1 leads to minimum size of total shared shadows (ST) and size of an essential shared shadow is close to size of a non-essential shared shadow. On the other hand, m = t leads to size of an essential shared shadow being twice of size of a non-essential shared shadow to signify the importance of an essential shared shadow. Moreover, the proposed structure overcomes the threshold fulfillment problem in Chen’s scheme (Chen, 2016). Theoretical analyses and experimental results show that the proposed scheme exhibits secure with optimal sharing ratios among related works.     

Multipartite Secret Sharing by Bivariate Interpolation

Given a set of participants that is partitioned into distinct compartments, a multipartite access structure is an access structure that does not distinguish between participants belonging to the same compartment. We examine here three types of such access structures: two that were studied before, compartmented access structures and hierarchical threshold access structures, and a new type of compartmented access structures that we present herein. We design ideal perfect secret sharing schemes for these types of access structures that are based on bivariate interpolation. The secret sharing schemes for the two types of compartmented access structures are based on bivariate Lagrange interpolation with data on parallel lines. The secret sharing scheme for the hierarchical threshold access structures is based on bivariate Lagrange interpolation with data on lines in general position. The main novelty of this paper is the introduction of bivariate Lagrange interpolation and its potential power in designing schemes for multipartite settings, as different compartments may be associated with different lines or curves in the plane. In particular, we show that the introduction of a second dimension may create the same hierarchical effect as polynomial derivatives and Birkhoff interpolation were shown to do in Tassa (J. Cryptol. 20:237–264, 2007). A preliminary version of this paper appeared in The Proceedings of ICALP 2006.     

Improvements of a two-in-one image secret sharing scheme based on gray mixing model

Yang and Ciou recently proposed a two-in-one image secret sharing scheme (TiOISSS), which can easily preview a vague image by human eyes, but also provide a perfect reconstruction of the original image by computation. However, their scheme cannot recover the lossless image by computation as they claimed. In this paper, we resolve the problem of lossless reconstruction. In addition, we improve the visual quality of the previewed image. Also, we introduce a new definition of contrast to evaluate the visual quality of the previewed image. Compared with Yang and Ciou’s TiOISSS, our scheme can gain the lossless secret image and meantime enhance the contrast of previewed image.     

User-friendly secret image sharing scheme with verification ability based on block truncation coding and error diffusion

Conventional secret image sharing schemes, which are constructed based on Shamir’s method, often suffer from random-liked shares, lossy reconstruction and high computation complexity. In addition, their generated shares are generally in original image format which may lead to more storage and suspicion from invaders. In this paper, we propose a user-friendly secret image sharing scheme based on block truncation coding (BTC) and error diffusion, where meaningful shares can be directly generated without any extra process. The meaningful shares by the proposed scheme are in BTC-compressed format which can reduce the capacity of transfer and storage. In the reconstructing phase, the secret image can be losslessly reconstructed by performing XOR operations on bit planes of sufficient BTC-compressed shares. Further, the proposed scheme provides extra verification ability to identify cheaters and check false shares. Theoretical analysis and simulation results demonstrate the feasibility of the proposed scheme.