On the Optimal Construction of a Visual Cryptography Scheme for Multiple Secret Images

A visual cryptography scheme (VCS) is a secret sharing scheme for digital images. In a VCS, two n × m Boolean matrices, called basis matrices, are used to generate n black-white images called shares from a black-white secret image. Usually, m is called the pixel expansion because the n shares become m times larger than a secret image. So far, minimization of the pixel expansion has been discussed by various authors. In this paper, we consider a VCS that enables the secret sharing of q multiple secret images under q distinct access structures. We give a construction of 2^q basis matrices with the minimum pixel expansion by solving a certain integer programming problem. It is also shown that 2^q basis matrices can be explicitly constructed for a certain class of q access structures.