Abstract:
A visual cryptography scheme for a set $\cal P $ of $n$ participants is a method to encode a secret image $SI$ into $n$ shadow images called shares, where each participant in $\cal P$ receives one share. Certain qualified subsets of participants can ``visually'' recover the secret image, but other, forbidden, sets of participants have no information (in an information-theoretic sense) on $SI$. A ``visual'' recovery for a set $X\subseteq{\cal P}$ consists of xeroxing the shares given to the participants in $X$ onto transparencies, and then stacking them. The participants in a qualified set $X$ will be able to see the secret image without any knowledge of cryptography and without performing any cryptographic computation. This cryptographic paradigm has been introduced by Naor and Shamir \cite{NaSh}. In this paper we propose two techniques to construct visual cryptography schemes for general access structures. We analyze the structure of visual cryptography schemes and we prove bounds on the size of the shares distributed to the participants in the scheme. We provide a novel technique to realize $k$ out of $n$ threshold visual cryptography schemes. Finally, we consider graph-based access structures, i.e., access structures in which any qualified set of participants contains at least an edge of a given graph whose vertices represent the participants of the scheme.