Xor based non-monotone t-(K, n)∗-visual cryptographic schemes using linear algebra

Abstract

XOR-based visual cryptographic schemes for non-monotonic (k, n)-threshold access structures deviate from the fact that the superset of any collection of k+1 or more participants may not get the secret back while providing their shares together. In this paper, we generalize this access structure to non-monotonic t-(k, n)∗-access structure in which tessential participants along with any other (k −t) participants can reveal the secret, 0 ≤ t ≤ k and 2 ≤ k ≤ n. This notion is a generalization of the non-monotonic (k, n)-threshold access structure in the sense that if we take t = 0, we get the non-monotonic (k, n)-threshold access structure. Visual cryptographic schemes for t-(k, n)∗-threshold access structure based on Boolean “OR” operations are available in the literature. However the contrast of the reconstructed image is very poor, resulting a very bad recovery of the secret image visually. In this paper we study the same scenario for the “XOR” basedmodel which providesmuch better relative contrast for the reconstructed secret image. We provide an efficient technique, based on simple linear algebra, to construct the basis matrices realizing the XOR-based non-monotone (k, n)-VCS with t many essential parties. The contrast of the scheme is significantly better than the existing OR-based schemes. Finally, for some restricted t-(k, n)∗ non-monotonic access structures, we provide a scheme which not only achieves the optimal relative contrast but also achieves the optimal pixel expansion.