Chuan Kun Wu

Colour visual cryptography schemes

Visual cryptography scheme (VCS) is a kind of secret-sharing scheme which allows the encryption of a secret image into n shares that are distributed to n participants. The beauty of such a scheme is that, the decryption of the secret image requires neither the knowledge of cryptography nor complex computation. Colour visual cryptography becomes an interesting research topic after the formal introduction of visual cryptography by Naor and Shamir in 1995. The authors propose a colour (k, n)-VCS under the visual cryptography model of Naor and Shamir with no pixel expansion, and a colour (k, n)-extended visual cryptography scheme ((k, n)-EVCS) under the visual cryptography model of Naor and Shamir with pixel expansion the same as that of its corresponding black and white (k, n)-EVCS. Furthermore, the authors propose a black and white (k, n)-VCS and a black and white (k, n)-EVCS under the visual cryptography model of Tuyls. Based on the black and white schemes, the authors propose a colour (k, n)-VCS and a colour (k, n)-EVCS under the same visual cryptography model, of which the pixel expansions are the same as that of their corresponding black and white (k, n)-VCS and (k, n)-EVCS, respectively. The authors also give the experimental results of the proposed schemes, and compare the proposed scheme with known schemes in the literature.

Step Construction of Visual Cryptography Schemes

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 scheme.

Threshold visual secret sharing by random grids with improved contrast

A (k, n) visual cryptographic scheme (VCS) is a secret sharing method, which encodes a secret image S into n share images in such a way that the stacking of any more than or equal to k share images will reveal S, while any less than k share images provide no information about S. Kafri and Keren (1987) firstly implements (2,2)-VCS by random grids (RG-based VCS). Compared to conventional solutions of VCS, RG-based VCSs need neither extra pixel expansion nor complex codebook design. However, for a long period, RG-based VCSs are confined to (2,2) access structure. Until recently, Chen and Tsao (2011) proposed the first (k, n) RG-based VCS. In this paper, we improve the contrast of Chen and Tsao (2011)s threshold scheme. The experimental results show that the proposed scheme outperforms Chen and Tsao (2011)s scheme significantly in visual quality.

k out of k extended visual cryptography scheme by random grids

This paper first gives a formal definition of k out of k extended visual cryptography scheme by random grids ((k, k) RG-based EVCS), in which a secret image and k cover images are encoded into k share images in such a way that the k share images show the k cover images individually and the stacking of any k share images will reveal the secret image while from any less than k share images, we can deduce no information about the secret image. Then we present a (k, k) RG-based EVCS that needs neither extra pixel expansion nor any basis matrices (codebook), which are inevitable in conventional solutions of EVCS. In addition, the proposed scheme can easily trade the visual quality of the decoded image with the visual quality of share images by setting a certain parameter in the scheme from small to large. The correctness of the proposed scheme is validated by formal proofs, and its feasibility is demonstrated by computer simulations.

Improving the visual quality of size invariant visual cryptography scheme

In order to reduce the pixel expansion of visual cryptography scheme (VCS), many size invariant visual cryptography schemes (SIVCSs) were proposed. However, most of the known SIVCSs have bad visual quality and thin line problems, hence the known SIVCSs are only suitable to encrypt coarse secret images. In this paper, we notice that the variance of the darkness levels of the pixels also reflects the visual quality of the recovered secret image, as well as the average contrast. We verify, analytically and experimentally, the effectiveness of the variance to be a criterion for evaluating the visual quality of the recovered secret image. Furthermore, we propose two multi-pixel encryption size invariant visual cryptography schemes (ME-SIVCSs) which improve the visual quality of the recovered secret image by reducing the variance of the darkness levels. In addition, the proposed ME-SIVCSs can be used to encrypt fine secret images since they avoid some known thin line problems. Experimental results and comparisons are also given to show the effectiveness of the proposed ME-SIVCSs. Finally, we give suggestions on obtaining good visual quality for the recovered secret image.

The alignment problem of visual cryptography schemes

Pixel expansion is an important parameter for Visual Cryptography Schemes (VCS). However, most papers in the literature are dedicated to reduce pixel expansion on the pixel level, i.e. to reduce the number of subpixels that represent a pixel in the original secret image. It is quite insufficient since the final size of the transparencies of the VCS is affected not only by the number of the subpixels, but also by the size of the subpixels in the transparencies. However, reducing the size of the subpixels in the transparencies results in difficulties of alignment of the transparencies. In this paper, we consider the alignment problem in VCS, and prove that in order to visually recover the original secret image, it is not necessary to align the transparencies precisely. This study is restricted to the case when only one transparency is shifted.

Cheating immune visual cryptography scheme

Most cheating immune visual cryptography schemes (CIVCS) are based on a traditional visual cryptography scheme (VCS) and are designed to avoid cheating when the secret image of the original VCS is to be recovered. However, all the known CIVCS have some drawbacks. Most usual drawbacks include the following: the scheme needs an online trusted authority, or it requires additional shares for the purpose of verification, or it has to sacrifice the properties by means of pixel expansion and contrast reduction of the original VCS or it can only be based on such VCS with specific access structures. In this study, the authors propose a new CIVCS that can be based on any VCS, including those with a general access structure, and show that their CIVCS can avoid all the above drawbacks. Moreover, their CIVCS does not care about whether the underlying operation is OR or XOR.

A new definition of the contrast of visual cryptography scheme

In this paper, some of the known definitions of the contrast of the Visual Cryptography Scheme (VCS) are shown to be inappropriate, and a new definition of the contrast based on our observations is proposed. It is also shown how our new definition of the contrast agreed with our observations.

Some Extensions on Threshold Visual Cryptography Schemes

Droste [CRYPTO’96] proposed a construction of threshold visual cryptography scheme (TVCS) under the visual cryptography model of Naor and Shamir, i.e. the visual cryptography model with the underlying operation OR. In this article, we give three extensions of TVCS. First, we prove that the TVCS proposed by Droste which was based on the OR operation is still a valid TVCS under the XOR operation, and then we propose a method to further reduce its pixel expansion. We then propose an interesting construction of TVCS with all shares being concolorous. Finally, we give a construction of threshold extended visual cryptography scheme (TEVCS) with the underlying operation OR or XOR. All of our schemes can be applied to the visual cryptography model introduced by Tuyls et al. (First Int. Conf. Security in Pervasive Computing 2004, International Patent with Application No.: PCT/IB2003/000261).

On (k, n) Visual Cryptography Scheme with t Essential Parties

In visual cryptography schemes (VCS), we often denote the set of all parties by \(P=\{1,2,\cdots ,n\}\). Arumugam et al. proposed a \((k,n)\)-VCS with one essential party recently, in which only subset \(S\) of parties satisfying \(S\subseteq P\) and \(|S|\ge k\) and \(1\in S\) can recover the secret. In this paper, we extend Arumugam et al.’s idea and propose a \((k,n)\)-VCS with \(t\) essential parties, say \((k,n,t)\)-VCS for brevity, in which only subset \(S\) of parties satisfying \(S\subseteq P\) and \(|S|\ge k\) and \(\{1,2,\ldots ,t\}\in S\) can recover the secret. Furthermore, some bounds for the optimal pixel expansion and optimal relative contrast of \((k,n,t)\)-VCS are derived.