Paper 2017/779

Efficient Constructions for $t$-$ (k,n)^{*}$-Random Grid Visual Cryptographic Schemes

Bibhas Chandra Das and Md Kutubuddin Sardar and Avishek Adhikari

Abstract

In this paper we consider both ``OR" and ``XOR" based monochrome random grid visual cryptographic schemes (RGVCS) for $t$-$(k,n)^*$ access structure which is a generalization of the threshold $(k,n)$ access structure in the sense that in all the successful attempts to recover the secret image, the $t$ essential participants must always be present, i.e., a group of $k$ or more participants can get back the secret if these $t$ essential participants are among them. Up to the best of our knowledge, the current proposed work is the first in the literature of RGVCS which provides efficient direct constructions for the $t$-$(k,n)^*$-RGVCS for both ``OR" and ``XOR" model. Finding the closed form of light contrast is a challenging work. However, in this paper we come up with the closed forms of the light contrasts for the ``OR" as well as for the ``XOR" model. As our proposed schemes are the first proposed schemes for $t$-$(k,n)^*$-RGVCS, it is not possible for us to compare our schemes directly with the existing schemes. However, we have constructed $t$-$(k,n)^*$-RGVCS, as a particular case, from the random grid based schemes for general access structures. Theoretical as well as simulation based data show that our proposed schemes work much efficiently than all these customized schemes.