Contrast optimal colored visual cryptography schemes

Visual cryptography schemes allow the encoding of a secret image into n shares which are distributed to the participants, such that only qualified subsets of participants can "visually" recover the secret image. In colored threshold visual cryptography schemes, the secret image is composed of pixels taken from a given set of c colors. We study c-color (k, n)-threshold visual cryptography schemes and provide a characterization of contrast optimal schemes. More specifically, we prove that there exists a contrast optimal scheme that is a member of a special set of schemes, which we call canonical schemes, and that satisfy strong symmetry properties. Then we use canonical schemes to provide a constructive proof of optimality, with respect to the pixel expansion, of c-color (n, n)-threshold visual cryptography schemes.