Generalized Random Grid-Based Visual Secret Sharing for General Access Structures

摘要

A conventional matrix-based visual secret sharing scheme has the drawbacks of pixel expansion and the requirement of predetermined sophisticated codebooks. A random grid-based visual secret sharing (RGVSS) scheme is an effective approach to solving these two problems. However, up to now, most of the existing publications about the RGVSS scheme deal with the threshold access structures, while there is hardly any appropriate method to construct the RGVSS scheme for general access structures (GASs). In this paper, a novel method to construct a generalized RGVSS (GRGVSS) scheme for GASs is proposed. The construction algorithm consists of two parts. In the first part, a more general (n, n)-GRGVSS scheme is proposed; in addition, the visual quality of the reconstructed secret image for this GRGVSS scheme is formally analyzed. In the second part, we utilize this (n,n)-GRGVSS to construct the GRGVSS scheme for given GASs by treating the procedure as a nonlinear 0-1 programming model. In the experimental phase, by changing the given preconditions, we analyze the security of the proposed scheme and assess the visual quality of the recovered secret images for the proposed scheme under different situations. The simulation results show that the proposed GRGVSS scheme for GASs is feasible and efficient.