Extended XOR-based visual cryptography schemes by integer linear program

Abstract

XOR-based visual cryptography scheme (XVCS) is a promising branch of VCS since superior visual quality of recovered secret image is provided. To assist the shadow management, meaningful shadow is preferred. However, existing extended XVCSs (EXVCSs) that generate meaningful shadows are confined to the (n,n) threshold. They are not practical for real-world applications. In this paper, we introduce EXVCS for (k,n) threshold and general access structure (GAS) by using integer linear program (ILP) technique. First of all, an approach for implementing the (k,n)-XVCS is given. We associate the (k,n)-XVCS with a minimizing problem, where the constraints in this problem are derived from the contrast and security conditions in (k,n)-XVCS. The ILP technique is adopted to solve this problem for obtaining the best solutions for constructing the base matrices for (k,n)-XVCS. Further, the construction is extended to (k,n)-EXVCS, in which the shadows with meaningful contents are constructed. To realize complicated sharing strategies, a construction of EXVCS for GAS is described as well. The base matrices for XVCS and EXVCS are demonstrated, as well as the pixel expansion and contrast. Comparisons among related methods are illustrated to show the advantages of the proposed schemes.