Bounds for Visual Cryptography Schemes

In this paper, we investigate the best pixel expansion of the various models of visual cryptography schemes. In this regard, we consider visual cryptography schemes introduced by Tzeng and Hu [13]. In such a model, only minimal qualified sets can recover the secret image and that the recovered secret image can be darker or lighter than the background. Blundo et al. [4] introduced a lower bound for the best pixel expansion of this scheme in terms of minimal qualified sets. We present another lower bound for the best pixel expansion of the scheme. As a corollary, we introduce a lower bound, based on an induced matching of hypergraph of qualified sets, for the best pixel expansion of the aforementioned model and the traditional model of visual cryptography realized by basis matrices. Finally, we study access structures based on graphs and we present an upper bound for the smallest pixel expansion in terms of strong chromatic index

A Recursive Threshold Visual Cryptography Scheme

This paper presents a recursive hiding scheme for 2 out of 3 secret sharing. In recursive hiding of secrets, the user encodes additional information about smaller secrets in the shares of a larger secret without an expansion in the size of the latter, thereby increasing the efficiency of secret sharing. We present applications of our proposed protocol to images as well as text.Comment: 8 page