Optimal Colored Threshold Visual Cryptography Schemes

Visual cryptography schemes allow the encoding of a secret image into n shares which are distributed to the participants. The shares are such that only qualified subsets of participants can visually recover the secret image. Usually the secret image consist of black and white pixels. In colored threshold visual cryptography schemes the secret image is composed of pixels taken from a given set of c colors. The pixels expansion and the contrast of a scheme are two measures of the goodness of the scheme. In this paper, we study c-color (k,n)-threshold visual cryptography schemes and provide a characterization of contrast-optimal schemes. More specifically we prove that there exists a contrast-optimal scheme that is a member of a special set of schemes, which we call canonical schemes, and that satisfy strong symmetry properties. Then we use canonical schemes to provide a constructive proof of optimality, with respect to the pixel expansion, of c-color (n,n)-threshold visual cryptography schemes. Finally, we provide constructions of c-color (2,n)-threshold schemes whose pixels expansion improves on previously proposed schemes

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

On Real-valued Visual Cryptographic Basis Matrices

Visual cryptography (VC) encodes an image into noise-like shares, which can be stacked to reveal a reduced quality version of the original. The problem with encrypting colour images is that they must undergo heavy pre-processing to reduce them to binary, entailing significant quality loss. This paper proposes VC that works directly on intermediate grayscale values per colour channel and demonstrates real-valued basis matrices for this purpose. The resulting stacked shares produce a clearer reconstruction than in binary VC, and to the best of the authors’ knowledge, is the first method posing no restrictions on colour values while maintaining the ability to decrypt with human vision. Grayscale and colour images of differing entropies are encrypted using fuzzy OR and XOR, and their PSNR and structural similarities are compared with binary VC to demonstrate improved quality. It is compared with previous research and its advantages highlighted, notably in high quality reconstructions with minimal processing

Visual Pixel Expansion of Secret Image

Two common drawbacks of the visual cryptography scheme VCS are the large pixel expansion of each share image and the small contrast of the recovered secret image In this paper we propose a step construction to construct VCSOR and VCSXOR for general access structure by applying 2 2 -VCS recursively where a participant may receive multiple share images The proposed step construction generates VCSOR and VCSXOR which have optimal pixel expansion and contrast for each qualified set in the general access structure in most cases Our scheme applies a technique to simplify the access structure which can reduce the average pixel expansion APE in most cases compared with many of the results in the literature Finally we give some experimental results and comparisons to show the effectiveness of the proposed schem

Two Step Share Visual Cryptography Algorithm for Secure Visual Sharing

This paper re - examines the problem of visual secret sharing for general access structures by using visual cryptograms of random grids (VCRG). Given a binary or color secret image shared by a set of n participants with a strong access structure, we devise t wo effective algorithms to produce a set of VCRG so that the members in each qualified set can reconstruct the secret image by superimposing their sh ares, while those in any forbidden set cannot. The basic 2 out of 2 visual cryptography model consists of a secret message encoded into two transparencies, one transparency representing the cipher text and the other acting as a secret key. Both transparencies appear to be random dots when inspected individually and provide no information about the original clea r text. However, by carefully aligning the transparencies, the original secret message is reproduced. The actual decoding is accomplished by the human visual system. Our algorithms do not require any extr a pixel expansion, which is indispensable and grows exponentially as n increases in conventional visual cryptographic schemes