Threshold Visual Cryptography Scheme Research Articles

A Tabu Search Algorithm for General Threshold Visual Cryptography Schemes

In Visual Cryptography Schemes (VCSs), for message n transparencies are generated, such that the original message is visible if any k of them are stacked. VCS especially for large values of k and n, the pixel expansion’s reduction and enhancement of the recovered images’ display quality continue to be critical issues. In addition to this, it is challenging to develop a practical and systematic approach to threshold VCSs. An optimization-based pixel-expansion-free threshold VCSs approach has been proposed for binary secret images’ encryption. Along with contrast, blackness is also treated as a performance metric for assessing the recovered images’ display quality. An ideally secure technique for a secret image’s protection through its partition into shadow images (known as shadows) is the Visual Secret Sharing (VSS) scheme. Acquirement of a smaller shadow size or a higher contrast is the VSS schemes’ latest focus. The white pixels’ frequency has been utilized to demonstrate the recovered image’s contrast in this work. While the Probabilistic VSS (ProbVSS) scheme is non-expansible, it can also be readily deployed depending upon the traditional VSS scheme. Initially, this work has defined the problem as a mathematical optimization model such that, while contingent on blackness and density-balance constraints, there is the maximization of the recovered images’ contrast. Afterward, an algorithm dependent on the Tabu Search (TS) is devised in this work for this problem’s resolution. Multiple complicated combinatorial problems have been successfully resolved with the powerful TS algorithm. Moreover, this work has attempted to bolster the contrast through the density-balance constraint’s slight relaxation. Compared to the older techniques, the proposed optimization-based approach is superior regarding the recovered images’ display quality and the pixel expansion factor from the experimental outcomes.

WITHDRAWN: A hybrid population based incremental learning algorithm with Particle Swarm Optimization for general threshold Visual Cryptography schemes

Abstract An effortless transfer of multimedia information over the Internet is achieved due to advances in the network’s technology. Commercial identifications, similarity maps, and numerous confidential data can be transferred over the Internet. When dealing with private videos and images, security challenges must be accounted for as hackers steal information by exploiting the weak links across communication networks. There has been the development of numerous schemes for the management of the security challenges of private images and videos. The encryption of a secret image onto n shares, wherein all participants can hold one or more shares, is known as the Visual Cryptography (VC) scheme. In the probabilistic VC scheme, the secret black pixels are reconstructed incompletely thus, the display quality obtained is not consistent with human visual perception. To enhance the display quality, it is required to optimize the threshold VCS. In this work, meta heuristic algorithms, Particle Swarm Optimization (PSO), and Population-Based Incremental Learning (PBIL) are modified to optimize the VCS threshold. PSO’s abilities like simplicity, convergence speed, and optimum global searches, have made it the most frequently-employed evolutionary variant among hybrid techniques. Substitution of a population’s individuals with a set of their statistics forms the basis of the concept behind the PBIL algorithm. Proposal for a hybrid Population-Based Incremental Learning algorithm with Particle Swarm Optimization (PBIL-PSO) has been provided in this work.

Visual Cryptography Scheme with Essential Participants

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.

Constructing visual cryptography scheme by hypergraph decomposition

A threshold visual cryptography scheme, denoted as (k, n)-VCS for short, can encrypt a secret image into n share images. The physical stacking of any k share images can reveal the secret content while any less than k share images will leak no information of the secret content. Besides the threshold access structure, general access structure VCSs are studied in the following works. In this paper, we first build a hyper star access structure VCS from a hyper star without center access structure VCS. Then we build a normal form hyper star access structure VCS from a full threshold VCS, and prove that its pixel expansion is optimal. At last, we propose a method of constructing general access structure VCS from its several decomposed normal form hyper star access structure VCSs.

VMVC: Verifiable multi-tone visual cryptography

Traditional k out of n threshold visual cryptography scheme is proposed to hide a secret image into n shares, where only k or more shares can visually reveal the secret image. Most of the previous state of art approaches on visual cryptography are almost restricted in processing of binary images as secret, which are inadequate for many applications like securely transmission of medical images(Store and Forward Telemedicine), forensic images etc. In this paper, a new Verifiable Multi-toned Visual Cryptography (VMVC) scheme is proposed to securely transmit the confidential images on web. Proposed approach also provides cheating prevention, since each pixel of shares contains a self embedding verifiable bit for integrity test of that pixel. Many existing approaches are suffering from many unnecessary encryption constraints like random shares, codebook requirement, contrast loss etc, which all are successfully addressed in proposed approach. Some comparisons with previously proposed methods are also made. Experimental results and analysis are used to prove the efficiency of proposed approach.

User-friendly threshold visual cryptography with complementary cover images

User-friendly threshold visual cryptography schemes (denoted (k,n)-FVCS) generate meaningful shares to cope with the management problem of conventional threshold visual cryptography. However, several issues remain in this research field, including: the pixel expansion problem, the residual traces problem, inter-images interference on meaningful shares, the inability to adjust visual quality, the lack of systematic encryption methods, and others. To solve these problems, this paper proposes a novel (k,n)-FVCS for sharing binary secret images in non-computer-aided decryption environments. Based on the probabilistic (k,n)-VCS, we propose a systematic method for embedding complementary cover images in shares for constructing the (k,n)-FVCSs. The proposed approach can address the above-mentioned issues of (k,n)-FVCSs for all k and n. In addition, the experimental results indicate that the proposed (k,n)-FVCS significantly outperforms the previous methods in terms of the visual quality of the recovered images and of the meaningful shares.

BOOLEAN XOR BASED (K,N) THRESHOLD VISUAL CRYPTOGRAPHY FOR GRAYSCALE IMAGES

Secure digital images is very important for today’s scenario which combining methods and techniques coming from cryptography and image processing. Visual Cryptography Scheme (VCS) is a new kind of cryptography technique which allows visual information (e.g. printed text, picture etc.) to be encrypted in such a way that decryption can be performed by the human visual system without any complex computation on computers. Here we proposed a Visual Cryptography Scheme based on image division of grey level images for the generation of Secret Shares. In this paper we represent the (k, n) Threshold Visual Cryptography Scheme in which the size of generated Shares as well as Recovered Image have same as the Secret Image rather than other VCS where k is the threshold value. Also we proposed the new technique to generate the Shadow Assignment Matrix with the help of Genetic Algorithm (GA). This Shadow Assignment Matrix helped us to distribute the Temporary shadow to the users according to their occurrence of 1’s in a row.

Progressive Visual Cryptography With Unexpanded Shares

The basic ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> )-threshold visual cryptography (VC) scheme is to share a secret image with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> participants. The secret image can be recovered while stacking <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> or more shares obtained; but we will get nothing if there are less than <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> pieces of shares being overlapped. On the contrary, progressive VC can be utilized to recover the secret image gradually by superimposing more and more shares. If we only have a few pieces of shares, we could get an outline of the secret image; by increasing the number of the shares being stacked, the details of the hidden information can be revealed progressively. Previous research, such as Jin in 2005, and Fang and Lin in 2006, were all based upon pixel-expansion, which not only causes the waste of storage space and transmission time but also gets a poor visual quality on the stacked image. Furthermore, Fang and Lin's research had a severe security problem that will disclose the secret information on each share. In this letter, we proposed a brand new sharing scheme of progressive VC to produce pixel-unexpanded shares. In our research, the possibility for either black or white pixels of the secret image to appear as black pixels on the shares is the same, which approximates to 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> . Therefore, no one can obtain any hidden information from a single share, hence ensures the security. When superimposing <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> (sheets of share), the possibility for the white pixels being stacked into black pixels remains 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> , while the possibility rises to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> for the black pixels, which sharpens the contrast of the stacked image and the hidden information, therefore, become more and more obvious. After superimposing all of the shares, the contrast rises to ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -1)/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> which is apparently better than the traditional ways that can only obtain 50% of contrast, consequently, a clearer recovered image can be achieved.

A Simulated Annealing Algorithm for General Threshold Visual Cryptography Schemes

Reducing the pixel expansion and improving the display quality of recovered images are still major issues in visual cryptography schemes (VCSs), particularly for large <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> . Moreover, the development of a systematic and practical approach for threshold VCSs is a challenge. In this paper, a pixel-expansion-free threshold VCSs approach based on an optimization technique is proposed in order to encrypt binary secret images. In addition to contrast, we consider blackness as a performance metric in the evaluation of the display quality of recovered images. We first formulate the problem as a mathematical optimization model in order to maximize the contrast of recovered images that are subject to density-balance and blackness constraints. We then develop a simulated-annealing-based algorithm to solve this problem. Furthermore, we try to promote the contrast by slightly relaxing the density-balance constraint. The experimental results show that the proposed optimization-based approach significantly outperforms previous methods in terms of both the pixel expansion factor and the display quality of recovered images.

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).

Visual cryptography schemes with optimal pixel expansion

A visual cryptography scheme encodes a black and white secret image into n shadow images called shares which are distributed to the n participants. Such shares are such that only qualified subsets of participants can “visually” recover the secret image. Usually, the reconstructed image will be darker than the background of the image itself. In this paper we consider visual cryptography schemes satisfying the model introduced by Tzeng and Hu [A new approach for visual cryptography, Designs, Codes and Cryptography 27 (3) (2002) 207–227]. In such a model, the recovered secret image can be darker or lighter than the background. We prove a lower bound on the pixel expansion of the scheme and, for ( 2 , n ) -threshold visual cryptography schemes, we provide schemes achieving the bound. Our schemes improve on the ones proposed by Tzeng and Hu.

Optimal Colored Threshold Visual Cryptography Schemes

Visual cryptography schemes allow the encoding of a secret image into n shares which are distributed to the participants. The shares are such that only qualified subsets of participants can "visually" recover the secret image. Usually the secret image consist of black and white pixels. In colored threshold visual cryptography schemes the secret image is composed of pixels taken from a given set of c colors. The pixels expansion and the contrast of a scheme are two measures of the goodness of the scheme.In this paper, we study c-color (k,n)-threshold visual cryptography schemes and provide a characterization of contrast-optimal schemes. More specifically we prove that there exists a contrast-optimal scheme that is a member of a special set of schemes, which we call canonical schemes, and that satisfy strong symmetry properties.Then we use canonical schemes to provide a constructive proof of optimality, with respect to the pixel expansion, of c-color (n,n)-threshold visual cryptography schemes.Finally, we provide constructions of c-color (2,n)-threshold schemes whose pixels expansion improves on previously proposed schemes.

Visual cryptography for gray-level images by dithering techniques

A (k,n)-threshold visual cryptography scheme is proposed to encode a secret image into n shadow images, where any k or more of them can visually recover the secret image, but any k-1 or fewer of th...

Visual cryptography for gray-level images by dithering techniques

A (k,n)-threshold visual cryptography scheme is proposed to encode a secret image into n shadow images, where any k or more of them can visually recover the secret image, but any k−1 or fewer of them gain no information about it. The decoding process of a visual cryptography scheme, which differs from traditional secret sharing, does not need complicated cryptographic mechanisms and computations. Instead, it can be decoded directly by the human visual system. Previous efforts in this topic are almost restricted in processing binary images, which are insufficient for many applications. In this paper, a new visual cryptography scheme suitable for gray-level images is proposed. Instead of using gray subpixels directly to construct shares, a dithering technique is used first to convert a gray-level image into an approximate binary image. Then existing visual cryptography schemes for binary images are applied to accomplish the work of creating shares. The overall effect of the proposed method is the achievement of visual encryption and decryption functions for gray-level images. Some comparisons with a previously proposed method are also made. Some experimental results are shown to prove the feasibility of the proposed method. Finally, an application is mentioned to show its practicability.

Threshold Visual Cryptography Schemes with Specified Whiteness Levels of Reconstructed Pixels

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.

Improved Schemes for Visual Cryptography

A (k,n)-threshold visual cryptography scheme ((k,n)-threshold VCS, for short) is a method to encode a secret image SI into n shadow images called shares such that any k or more shares enable the “visual” recovery of the secret image, but by inspecting less than k shares one cannot gain any information on the secret image. The “visual” recovery consists of xeroxing the shares onto transparencies, and then stacking them. Any k shares will reveal the secret image without any cryptographic computation. In this paper we analyze visual cryptography schemes in which the reconstruction of black pixels is perfect, that is, all the subpixels associated to a black pixel are black. For any value of k and n, where 2\leq k\leq n, we give a construction for (k,n)-threshold VCS which improves on the best previously known constructions with respect to the pixel expansion (i.e., the number of subpixels each pixel of the original image is encoded into). We also provide a construction for coloured (2,n)-threshold VCS and for coloured (n,n)-threshold VCS. Both constructions improve on the best previously known constructions with respect to the pixel expansion.

Visual cryptography schemes with perfect reconstruction of black pixels

A ( k, n)-threshold visual cryptography scheme (( k, n)-threshold VCS, for short) is a method to encode a secret image SI into n shadow images called shares such that any k or more shares enable the “visual” recovery of the secret image, but by inspecting less than k shares one cannot gain any information on the secret image. The “visual” recovery consists of xeroxing the shares onto transparencies, and then stacking them. Any k shares will reveal the secret image without any cryptographic computation. Visual cryptography schemes are characterized by two parameters: The pixel expansion, which is the number of subpixels each pixel of the original image is encoded into, and the contrast which measures the “difference” between a black and a white pixel in the reconstructed image. In this paper we analyze visual cryptography schemes in which the reconstruction of black pixels is perfect, that is, all the subpixels associated to a black pixel are black. We show that the minimum pixel expansion of such schemes can be simply computed by solving a suitable linear programming problem. Moreover, we give a construction for (3, n)-threshold VCS and a construction for ( n−1, n)-threshold VCS. These two constructions improve on the best previously known constructions with respect to the pixel expansion.

Visual Cryptography for General Access Structures

A visual cryptography scheme for a set P of n participants is a method of encoding a secret image SI into n shadow images called shares, where each participant in P receives one share. Certain qualified subsets of participants can “visually” recover the secret image, but other, forbidden, sets of participants have no information (in an information-theoretic sense) on SI . A “visual” recovery for a set X ⊆ P consists of xeroxing the shares given to the participants in X onto transparencies, and then stacking them. The participants in a qualified set X will be able to see the secret image without any knowledge of cryptography and without performing any cryptographic computation. In this paper we propose two techniques for constructing visual cryptography schemes for general access structures. We analyze the structure of visual cryptography schemes and we prove bounds on the size of the shares distributed to the participants in the scheme. We provide a novel technique for realizing k out of n threshold visual cryptography schemes. Our construction for k out of n visual cryptography schemes is better with respect to pixel expansion than the one proposed by M. Naor and A. Shamir (Visual cryptography, in “Advances in Cryptology—Eurocrypt '94” CA. De Santis, Ed.), Lecture Notes in Computer Science, Vol. 950, pp. 1–12, Springer-Verlag, Berlin, 1995) and for the case of 2 out of n is the best possible. Finally, we consider graph-based access structures, i.e., access structures in which any qualified set of participants contains at least an edge of a given graph whose vertices represent the participants of the scheme.