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

The extended visual cryptography scheme (EVCS) proposed by Ateniese et al. is one variation of the visual cryptography scheme such that a secret image is recovered from certain qualified collections of meaningful shares that are distributed to respective participants. In this paper, we give a new definition of the EVCS for improving visibility of the recovered secret image as well as the shares. We construct optimal basis matrices with the minimum number of pixel expansion by solving a certain integer programming problem. We also analyze security of the EVCS meeting the new definition from information-theoretic viewpoint.