Step Construction of Visual Cryptography Schemes

Visual cryptography (VC) schemes provide a distinguished image encryption technique to protect image security since it can visually decrypt the secret image by superimposing the encrypted shadows. VC schemes for both threshold access structures and general access structures are generally constructed based on the OR operation to minimize the pixel expansion. However, VC schemes with optimal pixel expansion typically have low contrast. Stacking operation OR frequently produces recovered images with poor visual quality and are never able to deliver flawless recovery for secret images. Therefore, we studied XOR-based VC (XVC) schemes that employ linear programming to maximize their contrast. Three schemes for general access structures and three schemes for threshold access structures are designed to maximize their contrast. The proposed schemes’ construction is reduced to a linear programming to maximize the contrast by determining the ideal combinations of basis matrices in terms of primary column matrices and unit matrices, respectively. The comparison study and experimental results demonstrate that the contrast of the previous VC and XVC schemes can be further improved.

A (k, n)-conventional visual cryptography (VC) scheme is designed to share one secret and each participant takes one share. When some common participants are involved in multiple VC schemes for multiple secrets, each needs to take multiple shares. This procedure needs more shares, which is inconvenient. It is desirable that the collaboration between the VC schemes can allow each common participant to keep only one share. Simply merging or gluing together two traditional (k(1), n(1))- and (k(2), n(2))-VC schemes, after making their pixel expansions the same, might be able to facilitate the collaboration and allow each common participant to keep only one share. But there is a security risk that when a subset of k(1) participants are from the collection of noncommon participants, some from scheme 1 and some from scheme 2, they can reconstruct secret 1, which is inconsistent with the intention of the original scheme. Similarly, k(2) noncommon participants could reconstruct secret 2. This shortcoming is inherited from the brute-force combination of traditional schemes. Therefore, a more sophisticated mechanism is required; this is the main task of this paper. In this paper, we first transform collaborative VC (CVC) schemes into the multiple secrets VC scheme with a general access structure. The construction of the basis matrices in CVC scheme between two VC schemes is formulated into an integer linear programming problem that minimizes the pixel expansion under the corresponding security and contrast constraints. Also the collaboration among more VC schemes is constructed. Finally, the experimental results illustrate the construction procedure of the CVC scheme and demonstrate the effectiveness of the CVC scheme.

Constructing visual cryptography scheme by hypergraph decomposition

Compared with the visual-cryptography-based visual secret sharing, the random-grid-based visual secret sharing (RGVSS) has some technical advantages, such as no pixel expansion and no need of codebooks. Designed based on RGVSS, the user-friendly random-grid-based visual secret sharing (UFRGVSS) not only inherits the advantages of RGVSS but also overcomes the data management problem in RGVSS by taking meaningful images as shares. Unfortunately, up to now, the existing threshold UFRGVSS schemes are only (2, 2) ones, which should use two meaningful images with complementary colors as shares. What's more, there is no feasible method to construct UFRGVSS schemes for more general threshold access structures excluding (2, 2) threshold, let alone for general access structures (GASs). Motivated by these concerns, in this paper, by stamping the gray-scale images with the shares generated from the traditional RGVSS, a novel method was proposed to design the UFRGVSS scheme for GASs, in which the resulting shares can be any meaningful gray-scale images. Experimental results show the feasibility of the proposed method by assessing its performance under different situations. Literature retrieval shows that our work may be the first attempt to construct the UFRGVSS scheme for GASs. Copyright © 2015 John Wiley & Sons, Ltd.

Visual Cryptography for General Access Structures

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.

(k, n) threshold is a special case of the general access structure (GAS) in secret image sharing (SIS), therefore GAS is more extensive than (k, n) threshold. Most of conventional SIS, including visual secret sharing (VSS), polynomial-based SIS, linear congruence (LC)-based SIS, etc., were proposed with only (k, k) threshold or (k, n) threshold other than GAS. This article introduces a common GAS construction approach in SIS with on pixel expansion from existing (k, k) threshold or (k, n) threshold SIS. The authors input classic SIS methods to test the efficiency and feasibility of the proposed common GAS construction approach. Experiments are presented to indicate the efficiency of the approach by illustrations and analysis.

Since visual cryptography scheme (VCS) was introduced by Naor and Shamir, contrast has been always regarded as an evaluation standard of visual quality of the revealed secret image. However, its original definition only reflects the relative difference between white area and black area of the revealed secret image so that it is incapable to access actual visual quality. Although other definitions of contrast were also proposed, researchers have not reached consensus on the definition of contrast until now. In this paper, a novel method is proposed to obtain recognition result of the revealed character secret image through simulating the recognition procedure of our human eyes. Recognition rate is adopted to evaluate the clearness of the revealed secret image. Experimental results and comparisons demonstrate that recognition rate can be regarded as a new visual evaluation criterion of VCS for character secret image. Finally, a construction of VCS with optimized overall pixel expansion is provided, in which the pixel expansion is thoroughly determined by recognition rate, rather than contrast.

In this paper, we first follow Ateniese et al.'s work that provides upper bounds of the pixel expansion of visual cryptography schemes(VCSs) for more kinds of graph access structures, in which we require that a subset of parties can determine the secret if they contain an edge of the graph G. The constructive upper bounds are derived by the graph decomposition technique. Then we generalize Ateniese et al.'s method of comparing the optimal pixel expansion of VCSs with two different access structures.

Journal Article Probabilistic Visual Cryptography Schemes Get access S. Cimato, S. Cimato *Corresponding author: robdep@dia.unisa.it Search for other works by this author on: Oxford Academic Google Scholar R. De Prisco, R. De Prisco Search for other works by this author on: Oxford Academic Google Scholar A. De Santis A. De Santis Search for other works by this author on: Oxford Academic Google Scholar The Computer Journal, Volume 49, Issue 1, January 2006, Pages 97–107, https://doi.org/10.1093/comjnl/bxh152 Published: 01 December 2005 Article history Received: 04 February 2004 Revision received: 02 November 2005 Published: 01 December 2005

In 1994, Naor and Shamir introduced an unconditionally secure method for encoding black and white images. This method, known as a threshold visual cryptography scheme (VCS), has the benefit of requiring no cryptographic computation on the part of the decoders. In a (k, n)-VCS, a share, in the form of a transparency, is given to n users. Any k users can recover the secret simply by stacking transparencies, but k-1 users can gain no information about the secret whatsoever. In this paper, we first explore the issue of contrast, by demonstrating that the current definitions are inadequate, and by providing an alternative definition. This new definition motivates an examination of minimizing pixel expansion subject to fixing the VCS parameters h and l. New bounds on pixel expansion are introduced, and connections between these bounds are examined. The best bound presented is tighter than any previous bound. An analysis of connections between (2, n) schemes and designs such as BIBD's, PBD's, and (r, λ)-designs is performed. Also, an integer linear program is provided whose solution exactly determines the minimum pixel expansion of a (2, n)-VCS with specified h and l.

Visual cryptography schemes suffer from the drawback of large pixel expansion of share images and bad visual quality of the recovered image. To provide secrecy, we go for pixel expansion and increasing number of shares, this causes the bad visual quality of the recovered image. In this paper, we construct (n, n)-VCS and OR and XOR operations are used for share creation and stacking process, which proves better in contrast and pixel expansion. The proposed method uses additional matrix to increase the secrecy of the message in XOR operation.

In the area of secret image sharing (SIS), most papers focused on the schemes for threshold or some special access structures. Regarding general access structures (GAS), few results have been found in the literature. Two SIS schemes for GAS were proposed in 2001 and 2010, both are based on qualified sets. However, one distorts the reconstructed secret image, and some extra information is needed in both schemes. Here, we propose three polynomial based SIS schemes for GAS. Considering either qualified or forbidden sets, these schemes can reconstruct the secret image perfectly without any extra information needed. Some proof and analysis on the shadow sizes of the three schemes are given to lead us to choose the one with the smallest size. In addition, we also give some comparisons with two existing schemes, and security issue is also addressed in conclusion.

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.KeywordsVisual cryptographyEssential partiesPixel expansionRelative contrast

In the past decade, the researchers paid more attention to the cheating problem in visual cryptography (VC) so that many cheating prevention visual cryptography schemes (CPVCS) have been proposed. In this paper, the authors propose a novel method, which first makes use of Latin square to prevent cheating in VC. Latin squares are utilised to guide the choosing of authentication regions in different rows and columns of each divided block of the shares, which ensures that the choosing of authentication regions is both random and uniform. Without pixel expansion, the new method provides random regions authentication in each divided block of all shares. What is important is that the proposed method is applicable to both ( k , n )‐deterministic visual cryptography scheme (( k , n )‐DVCS) and ( k , n )‐probabilistic visual cryptography scheme (( k , n )‐PVCS). Experimental results and properties analysis are given to show the effectiveness of the proposed method.