Visual Secret Sharing Schemes Encrypting Multiple Images

The aim of this paper is to maximize the range of the access control of visual secret sharing (VSS) schemes encrypting multiple images. First, the formulation of access structures for a single secret is generalized to that for multiple secrets. This generalization is maximal in the sense that the generalized formulation makes no restrictions on access structures; in particular, it includes the existing ones as special cases. Next, a sufficient condition to be satisfied by the encryption of VSS schemes realizing an access structure for multiple secrets of the most general form is introduced, and two constructions of VSS schemes with encryption satisfying this condition are provided. Each of the two constructions has its advantage against the other; one is more general and can generate VSS schemes with strictly better contrast and pixel expansion than the other, while the other has a straightforward implementation. Moreover, for threshold access structures, the pixel expansions of VSS schemes generated by the latter construction are estimated and turn out to be the same as those of the existing schemes called the threshold multiple-secret visual cryptographic schemes. Finally, the optimality of the former construction is examined, giving that there exist access structures for which it generates no optimal VSS schemes.