Efficient Construction of Visual Cryptographic Scheme for Compartmented Access Structures

In this paper, we consider a special type of secret sharing scheme known as Visual Cryptographic Scheme (VCS) in which the secret reconstruction is done visually without any mathematical computation unlike other secret sharing schemes. We put forward an efficient direct construction of a visual cryptographic scheme for compartmented access structure which generalizes the access structure for threshold as well as for threshold with certain essential participants. Up to the best of our knowledge, the scheme is the first proposed scheme for compartmented access structure in the literature of visual cryptography. Finding the closed form of relative contrast of a scheme is, in general, a combinatorially hard problem. We come up with a closed form of both pixel expansion as well as relative contrast. Numerical evidence shows that our scheme performs better in terms of both relative contrast as well as pixel expansion than the cumulative array based construction obtained as a particular case of general access structure. keywords: Compartmented access structure, monotone access structure, probabilistic VCS, basis matrices.