Participants colluding is an important issue of cheater detectable visual cryptography schemes. Based on a trusty third party, a co-cheating prevention visual cryptography scheme (CCPVCS) is proposed in this paper. Checking efficiency is improved by verifying the truth of several shares simultaneously, with designed special verification shares. Since the scheme idea is different from previous ones, the pixel expansion is small and the recovered secret image is good for viewing.

A Co-cheating Prevention Visual Cryptography Scheme

Visual cryptography (VC) encrypts a secret image into n shares (transparency). As such, we cannot see any information from any one share, and the original image is decrypted by stacking all of the shares. The general (k, n)-threshold secret sharing scheme (SSS) can similarly encrypt and decrypt the original image by stacking at least k (≤ n) shares. If one stack is fewer than k shares, the secret image is unrecognizable. Another subject is progressive visual secret sharing, which means that when more shares are progressively stacked, the combined share becomes clearer. In this study, we constructed an advanced scheme for (k, n)-threshold SSS that can be encrypted in VC for any positive integers n ≥ k ≥ 2 through the method of combination, and the size of each share is the same as that of the original image. That is, no pixel expansion is required. Our scheme is novel, and the results from the theoretical analysis and simulation reveal that our scheme exhibits favorable contrast to that of other related schemes.

https://www.mdpi.com/2410-387X/2/4/28/pdf

A (k, n)-Threshold Progressive Visual Secret Sharing without Expansion

A method of constructing basic matrices for XOR visual cryptography is proposed in this paper, which designs one kind of threshold scheme by constructing recursion operator and integrating application of recursive idea Experimental results show that the scheme constructed in this paper not only recovers the secret image sufficiently, but also resolves the problem of large pixel expansion upon XOR visual cryptography

http://ieeexplore.ieee.org/iel5/6175418/6181892/06181961.pdf

Optimization of XOR visual cryptography scheme

Aim: In visual cryptography, a secret image is encrypted into two meaningless random images called shares. These two shares can be stacked to recover the secret image without any calculations. However, because of the alignment problem in the decryption phase, risk of poor quality of the restored image exists. Encrypting multiple secrets on two images simultaneously can improve execution efficiency. Methods: Let 7 × 7 pixels be a unit; this paper designs a codebook for any unit in the secret images by using a random grid. Besides, this paper shows a general shifting approach that can embed N (≥ 2) secret images simultaneously with adjustable distortion. Results: This paper provides a visual multi-secret sharing scheme without pixel expansion; the proposed scheme can encrypt more than two secret images into two shares simultaneously. During decoding, aligning the shares precisely is not necessary. Conclusion: Theoretical analysis and simulation results indicate the effectiveness and practicality of the proposed scheme.

/pdf/advanced-fault-tolerant-visual-multi-secret-sharing-scheme-1hrmw2q8.pdf

Advanced fault-tolerant visual multi-secret sharing scheme

Visual cryptography encrypts the secret image into $n$ shares (transparency) so that only stacking a qualified number of shares can recover the secret image by the human visual system while no information can be revealed without a large enough number of shares. This paper investigates the $(k,n)$-threshold Visual Secret Sharing (VSS) model, where one can decrypt the original image by stacking at least $k$ shares and get nothing with less than $k$ shares. There are two main approaches in the literature: codebook-based schemes and random-grid-based schemes; the former is the case of this paper. In general, given any positive integers $k$ and $n$, it is not easy to design a valid scheme for the $(k,n)$-threshold VSS model. In this paper, we propose a simple strategy to construct an efficient scheme for the $(k,n)$-threshold VSS model for any positive integers $2\leq k\leq n$. The crucial idea is to establish a seemingly unrelated connection between the $(k,n)$-threshold VSS scheme and a mathematical structure -- the generalized Pascal's triangle. This paper improves and extends previous results in four aspects: Our construction offers a unified viewpoint and covers several known results; 
The resulting scheme has a progressive-viewing property that means the more shares being stacked together the clearer the secret image would be revealed. 
The proposed scheme can be constructed explicitly and efficiently based on the generalized Pascal's triangle without a computer. Performance of the proposed scheme is comparable with known results.

An Easy-to-implement Construction for (k, n)-threshold Progressive Visual Secret Sharing Schemes.

Visual cryptography (VC) was introduced by Naor and Shamir. In general, a (k, n)-threshold scheme shares a given secret image S among n so-called shadow images. People can "view" the secret image by simply stacking any k of these n shadows (k < n is a threshold value). In most of the reported VC schemes, the size of each shadow is greater than that of S. This paper, we use Hilbert curve and two queues to present a VC scheme with the following properties: (1). Each shadow image is as small as the input image S. (2). Many gracious (k, n) contrast-optimal algorithms can be directly and easily applied to our scheme. (3) Image quality is competitive.

Sen-Jen Lin

Papers

Visual Cryptography (VC) with non-expanded shadow images: Hilbert-curve approach