Optimal Basis Matrices of a Visual Cryptography Scheme with Meaningful Shares and Analysis of Its Security

摘要

The extended visual cryptography scheme (EVCS) proposed by Ateniese et al. is one of variations of the visual cryptography scheme such that a secret image is recovered by superimposition of certain qualified collections of shares, where cover images are visible on respective shares. In this paper, we give a new definition of the EVCS for improving visibility of the recovered secret image as well as the cover images. We formulate the problem to construct the basis matrices of the EVCS with the minimum pixel expansion as an integer programming problem. We solve the integer programming problem for general access structures with less than or equal to five participants and show that basis matrices with a smaller pixel expansion can be obtained for certain cases. We also analyze security of the EVCS meeting the new definition from an information-theoretic viewpoint. We give a condition under which any forbidden collection of shares does not reveal any additional information on not only a secret image but also the cover images that are not visible on the other shares.