Visual Cryptography for General Access Structures

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.

Visual cryptography schemes have been introduced in 1994 by Naor and Shamir as a mean to share images among a given group of participants. A visual cryptography scheme (VCS) for a set P of n participants encodes a secret image into n shadow images called shares each of which is given to a distinct participant. Certain qualified subsets of participants can recover the secret image, whereas forbidden subsets of participants have no information on the secret image. The shares given to participants in X ⊑ P are xeroxed onto transparencies. If X is qualified then the participants in X can visually recover the secret image by stacking their transparencies without any cryptography knowledge and without performing any cryptographic computation.In this paper we provide a new technique to derive lower bounds on the randomness of VCSs for any access structure. We also analyse minimum randomness (k, k)-threshold VCSs thus giving a new insight into the structure of these schemes.

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.

Most of the secret sharing schemes are based on algebraic calculations in their realizations. But there are some different realizations of the secret sharing schemes. Visual cryptography is one such secret sharing scheme. In a visual cryptographic scheme, for a set P of n participants, a secret image is split into n shadow images called shares, where each participant in P receives one share. Certain qualified subsets of participants can ldquovisuallyrdquo recover the secret image with some loss of contrast, but other forbidden sets of participants have no information about the secret image. In this paper we review with appropriate examples some of the methods for the construction of monochrome visual cryptographic schemes for general as well as for threshold access structures.

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.

Constructing visual cryptography scheme by hypergraph decomposition

Visual cryptography schemes (VCS) have been introduced by Naor and Shamir [NS94] and involve a dealer encoding a secret image into shares that are distributed to a number of participants. In general, the collection of subsets of participants that can recover the secret is organized in an access structure. In this paper we consider graph based access structures, where participants are nodes of a graph G and only subsets containing an edge are allowed to reconstruct the secret image. We provide some bounds on the pixel expansion of path and cycle graphs, showing also a simple construction for such graphs for a generic number of n participants.

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.

Hybrid commitments and their applications to zero-knowledge proof systems

In this paper, we propose a security-enhanced method for the visual cryptography schemes using recursion. Visual cryptography is interesting because decryption can be done with no prior knowledge of cryptography and can be performed without any cryptographic computations. The proposed method, the secret image is encoded into shares and subshares in a recursive way. By using recursion for the visual cryptography schemes, the security and reliability of the secret image can be improved than in the case of existing visual cryptography schemes.

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.

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.

Traditional k out of n visual cryptography scheme has been proposed to encrypt single secret image into n shares where only k or more shares can decode the secret image. Many existing schemes on visual cryptography are restricted to consider only binary images as secret which are not appropriate for many important applications. Store-and-Forward telemedicine is one such application where medical images are transmitted from one site to another via electronic medium to analyze the patient's clinical health status. The main objective of Store-and-Forward telemedicine is to provide remote clinical services via two-way communication between the patient and the healthcare provider using electronic medical image, audio and video means. In this paper, a new XOR based Continuous-tone Multi Secret Sharing scheme suitable for store-and-forward telemedicine is proposed to securely transmit the medical images. It also eliminates basic security constraints of VC like pixel expansion in shares/recovered secret images, random pattern of shares, explicit codebook requirement, lossy recovery of secret and limitation on number of secret and shares. Proposed approach is n out of n multi secret sharing scheme which is able to transmit n secret images simultaneously. All secrets could be revealed only after some computations with all n shares and one master share. Master share has been created with the secret key at encoding phase and it can be regenerated at the time of decoding using same secret key. Here all shares are meaningful in continuous-tone which may provide confidentiality to medical images during transmission. Proposed approach not only preserves all basic characteristics of traditional VC but also increases the capacity of secret image sharing. From the experiments we found that irrespective of visible contents of the shares, the probability of getting back the pixel values of respective original secret images at the receiver end is very high.

A hybrid approach combining data hiding with visual cryptography for secure extraction of data hiding

Conventional visual cryptography (VC) suffers from a pixel-expansion problem, or an uncontrollable display quality problem for recovered images, and lacks a general approach to construct visual secret sharing schemes for general access structures. We propose a general and systematic approach to address these issues without sophisticated codebook design. This approach can be used for binary secret images in non-computer-aided decryption environments. To avoid pixel expansion, we design a set of column vectors to encrypt secret pixels rather than using the conventional VC-based approach. We begin by formulating a mathematic model for the VC construction problem to find the column vectors for the optimal VC construction, after which we develop a simulated-annealing-based algorithm to solve the problem. The experimental results show that the display quality of the recovered image is superior to that of previous papers.