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 Reversible Steganography Scheme of Secret Image Sharing Based on Cellular Automata and Least Significant Bits Construction

Secret image sharing schemes have been extensively studied by far. However, there are just a few schemes that can restore both the secret image and the cover image losslessly. These schemes have one or more defects in the following aspects: (1) high computation cost; (2) overflow issue existing when modulus operation is used to restore the cover image and the secret image; (3) part of the cover image being severely modified and the stego images having worse visual quality. In this paper, we combine the methods of least significant bits construction (LSBC) and dynamic embedding with one-dimensional cellular automata to propose a new lossless scheme which solves the above issues and can resist differential attack and support parallel computing. Experimental results also show that this scheme has the merit of big embedding capacity

Determining the Optimal Contrast for Secret Sharing Schemes in Visual Cryptography

This paper shows that the largest possible contrast C(k,n) in a k-out-of-n secret sharing scheme is approximately 4^(-(k-1)). More precisely, we show that 4^(-(k-1)) <= C_{k,n} <= 4^(-(k-1))}n^k/(n(n-1)...(n-(k-1))). This implies that the largest possible contrast equals 4^(-(k-1)) in the limit when n approaches infinity. For large n, the above bounds leave almost no gap. For values of n that come close to k, we will present alternative bounds (being tight for n=k). The proofs of our results proceed by revealing a central relation between the largest possible contrast in a secret sharing scheme and the smallest possible approximation error in problems occuring in Approximation Theory