Extended Schemes for Visual Cryptography

An extended visual cryptography scheme, (? Qual ; ? Forb ; m)-EVCS for short, with pixel \expansion" m, for an access structure (? Qual ; ? Forb) on a set of n participants, is a technique to encode n innocent looking images in such a way that when we stack together the transparencies associated to participants in any set X 2 ? Qual we get the secret message with no trace of the original images, but any X 2 ? Forb has no information on the shared image. Moreover, after the original innocent looking images are encoded they are still meaningful, that is, any user will recognize the image on his transparency. In this paper we rst present a general technique to implement extended visual cryptography schemes, which uses hypergraph colourings. Then we discuss some applications of this technique to various interesting classes of access structures by using relevant results from the theory of hypergraph colourings.