(t, k, n) XOR-based visual cryptography scheme with essential shadows

Visual cryptography is an encryption technique that decomposes secret images into multiple shares. These shares are digitally or physically overlapped to recover the original image, negating the need for complex mathematical operations or additional hardware. There have been many variations of visual cryptography proposed over the years, each addressing different problems or to fulfill different security requirements. Existing review papers on the area only cover certain types of visual cryptography or lack comparisons between the various schemes. To address this gap, this paper provides broad overview of the area to aid new researchers in identifying research problems or to select suitable visual cryptography methods for their desired applications. For more veteran researchers in the area, our paper provides the most up-to-date coverage of the state-of-the-art. We first provide an introduction to the various categories of visual cryptography techniques, including a discussion on recently proposed schemes. These schemes are then compared in terms of their features, performance metrics, advantages and disadvantages. Compared to prior work, we extend the number of comparison metrics to include signal-to-noise ratio and the type of shares. Over 40 visual cryptography schemes that have been proposed in the past two decades were analyzed and compared. Our findings indicate that existing problems such as pixel expansion, poor quality of recovered image quality, computational and memory complexities still exist, and a optimizing the trade-off between these requirements still requires further investigation. We conclude the paper with a discussion of these open problems and future research directions.

An overview of visual cryptography techniques

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.

Embedded Extended Visual Cryptography Schemes.

Hou et al. introduced a (2, n) block-based progressive visual cryptographic scheme (BPVCS). In (2, n)-BPVCS, a secret image is subdivided into n non-overlapped image blocks. When t (2 ≤ t ≤ n) participants stack their shadow images, the image blocks belonged to these t participants will be recovered. Unfortunately, Hou et al.’s (2, n)-BPVCS suffers from the cheating problem. Additionally, Hou et al.’s scheme is only suitable for 2-out-of-n case, i.e., (k, n)-BPVCS where k = 2. In this paper, we propose a cheating immune (k, n)-BPVCS for k>2. The main contribution of our paper is that the proposed (k, n)-BPVCS is not only cheating immune, but also suitable for general k-out-of-n threshold, where k and n are integers with 2 ≤ k ≤ n. Theoretical analysis demonstrates that our scheme still holds progressive recovery and security, and meantime has cheating immune capability.

Cheating immune k-out-of-n block-based progressive visual cryptography

The appearance of shares encoded by traditional visual cryptography is not easy to distinguish and meaningless. It means the shares cannot be managed efficiently nor user-friendly. A tagged visual cryptography scheme (TVCS) provides additional tag images for the shares and decodes the tag images by folding up a single tagged share. A TVCS allows users to efficiently manage shares and greatly increases the user-friendliness of the shares. Previous researches have focused on codebook-based and random-grid-based TVCS approaches, but the visual qualities of recovered secret images and tag images can still be improved. Therefore, this study aims to provide better visual quality of recovered images by improving on previous methods. Moreover, the proposed approach supports adjustable visual qualities of recovered secret images and tag images. In this study, we theoretically analyze the performances of the proposed approach and then demonstrate implementation of the approach.

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Threshold Visual Cryptography Schemes With Tagged Shares

Visual cryptography scheme (VCS) shares a binary secret image into multiple shadows, stacking qualified set of shadows will decode the secret image without computer resources. In this paper, we propose a (2, 3)-VCS, which can share one or two secret images into 3 shadows, stacking any two shadows will reveal the secret image. The shadow size is 3/2 times of the secret image. The contrasts of the revealed image are 1/3 and 1/2 when we share one and two secret images, respectively. We can also reveal the secret image by XOR decoding operation, and the visual quality of the revealed image can be further improved. By XOR decoding operation, the contrasts of the revealed image will be 2/3 and 1 when we share one or two secret images, respectively. In the case of sharing two secret images, the revealed two secret images have no distortion. Theoretic analysis and experimental results demonstrate the feasibility and advantages of the proposed (2, 3)-VCS.

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A Construction Method of (2, 3) Visual Cryptography Scheme

Visual cryptography scheme (VCS) shares a binary secret image into multiple shadows printed on transparencies. Stacking shadows can visually decode the secret image without computational resources. Specifically, a (k, n) threshold VCS ((k, n)-VCS) shares a secret image into n shadows, stacking any k shadows can reveal the secret image by human visual system, while any less than k shadows cannot decode any information regarding the secret image. In practice, some participants (essentials) play more important roles than others (non-essentials). In this paper, we propose a (t, s, k, n) VCS with essential participants (so called (t, s, k, n)-EVCS). The secret image is shared into n shadows with s essentials and n-s non-essentials. Any k shadows, including at least t essentials, can reveal the secret image. The proposed scheme is constructed from a monotonic (K, N)-VCS. The condition and optimal choice of (K, N)-VCS to construct (t, s, k, n)-EVCS are given by solving integer programming model. The experimental results are conducted to verify the feasibility of our scheme.

Visual Cryptography Scheme with Essential Participants

Secret image sharing will inevitably be threatened by various types of attacks in practical applications, of which cheating behavior is the most prone. In this paper, in order to prevent deceivers from threatening the security of secret image transmission process, a polynomial based cheating detection scheme is proposed. The (k, n) secret image sharing scheme must ensure that any k or more participants can restore the secret image, and less than k participants cannot get any information of the secret image. In our scheme, only one honest shareholder can detect the collusion from other k − 1 deceivers. Furthermore, our scheme reduces the size of shadow images thus saving storage space and transmission time. Theory and experiments show that our scheme is effective and feasible in cheating detection.

Cheating Detection in (k, n) Secret Image Sharing Scheme.

The invention provides an image sharing and restoring method. Two binary images with the same size can be shared and restored. According to the method, pixel blocks with the same positions are selected from two images, a corresponding basic sharing matrix group is selected according to the values of the pixel blocks, the sharing matrixes in the basic sharing matrix group are utilized to generate the pixel blocks of the shared image, the finally obtained shared image is a random image, and any original image information cannot be obtained from any shared image. The invention also provides a method for restoring an original image by using any two shared images, and provides two restoration schemes, namely an image restoration scheme based on OR operation and an image restoration scheme basedon XOR operation. Original images with different qualities can be restored through the two schemes, and image restoration means are increased.

Image sharing and restoring method

The invention provides a sharing and restoring method of a single image. When an image is shared, two pixels are shared at the same time, a sharing matrix group corresponding to a pixel value is selected, a pixel block of the shared image is generated by utilizing a sharing matrix in the sharing matrix group, the finally obtained shared image is a random image, and any original image information cannot be obtained in any shared image. The invention also provides a method for restoring an original image by using any two shared images, and provides three restoration schemes, namely a low-visual-quality image restoration scheme based on OR operation, a medium-visual-quality image restoration scheme based on XOR operation and a scheme for restoring an accurate image by using a computer. The size of the shared image obtained by the method is 1.5 times of that of the original secret image, and is the lowest level in the same kind of methods.

Jianfeng Ma

Papers

A Construction Method of (2, 3) Visual Cryptography Scheme

Visual Cryptography Scheme with Essential Participants

Cheating Detection in (k, n) Secret Image Sharing Scheme.

Image sharing and restoring method

Sharing and restoring method of single image