A visual cryptography scheme (VCS) is a kind of secret sharing scheme which allows the encoding of a secret image into n shares distributed to n participants. The beauty of such a scheme is that a set of qualified participants is able to recover the secret image without any cryptographic knowledge and computation devices. An extended visual cryptography scheme (EVCS) is a kind of VCS which consists of meaningful shares (compared to the random shares of traditional VCS). In this paper, we propose a construction of EVCS which is realized by embedding random shares into meaningful covering shares, and we call it the embedded EVCS. Experimental results compare some of the well-known EVCSs proposed in recent years systematically, and show that the proposed embedded EVCS has competitive visual quality compared with many of the well-known EVCSs in the literature. In addition, it has many specific advantages against these well-known EVCSs, respectively.

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Embedded Extended Visual Cryptography Schemes

Image secret sharing method with two-decoding-options: Lossless recovery and previewing capability

Threshold visual secret sharing by random grids with improved contrast

Improvements of a two-in-one image secret sharing scheme based on gray mixing model

Halftone visual cryptography with minimum auxiliary black pixels and uniform image quality

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.

Colour 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.

The alignment problem of visual cryptography schemes

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.

Cheating immune visual cryptography scheme

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.

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

For visual cryptography scheme (VCS), normally, the size of the recovered secret image will be expanded by m( ≥ 1) times of the original secret image. In most cases, m is not a square number, hence the recovered secret image will be distorted. Sometimes, m is too large that will bring much inconvenience to the participants to carry the share images. In this paper, we propose two visual cryptography schemes which simulated the principle of fountains. The proposed schemes have two advantages: non-distortion and flexible (with respect to the pixel expansion). Furthermore, the proposed schemes can be applied to any VCS that is under the pixel by pixel encryption model, such as VCS for general access structure, color VCS and extended VCS, and our VCS does not restrict to any specific underlying operation. Compared with other non-distortion schemes, the proposed schemes are more general and simpler, real flexible and has competitive visual quality for the recovered secret image.

Chuan Kun Wu

Papers

Colour visual cryptography schemes

The alignment problem of visual cryptography schemes

Cheating immune visual cryptography scheme

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

Flexible Visual Cryptography Scheme and Its Application