A recent publication introduced a Visual Crypto (VC) system, based on the polarisation of light. This VC system has goodresolution, contrast and colour properties.Mathematically, the VC system is described by the XOR operation (modulo two addition). In this paper we investigate Threshold Visual Secret Sharing schemes associated to XOR-based VC systems. Firstly, we show that n out of n schemes with optimal resolution and contrast exist, and that (2,n) schemes are equivalent to binary codes. It turns out that these schemes have much better resolution than their OR-based counterparts. Secondly, we provide two explicit constructions for general k out of n schemes. Finally, we derive bounds on the contrast and resolution of XOR-based schemes. It follows from these bounds that for k<n, the contrast is strictly smaller than one. Moreover, the bounds imply that XOR-based k out of n schemes for even k are fundamentally different from those for odd k.

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XOR-based Visual Cryptography Schemes

Visual cryptography is a powerful technique that combines the notions of perfect ciphers and secret sharing in cryptography with that of raster graphics. A binary image can be divided into shares that can be stacked together to approximately recover the original image. Unfortunately, it has not been used much primarily because the decryption process entails a severe degradation in image quality in terms of loss of resolution and contrast. Its usage is also hampered by the lack of proper techniques for handling gray-scale and color images. We develop a novel technique that enables visual cryptography of color as well as gray-scale images. With the use of halftoning and a novel microblock encoding scheme, the technique has a unique flexibility that enables a single encryption of a color image but enables three types of decryptions on the same ciphertext. The three different types of decryptions enable the recovery of the image of varying qualities. The physical transparency stacking type of decryption enables the recovery of the traditional visual cryptography quality image. An enhanced stacking technique enables the decryption into a halftone quality image. Finally, a computation-based decryption scheme makes the perfect recovery of the original image possible. Based on this basic scheme, we establish a progressive mechanism to share color images at multiple resolutions. We extract shares from each resolution layer to construct a hierarchical structure; the images of different resolutions can then be restored by stacking the different shared images together. Thus, our technique enables flexible decryption. We implement our technique and present results.

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Progressive color visual cryptography

Two common drawbacks of the visual cryptography scheme (VCS) are the large pixel expansion of each share image and the small contrast of the recovered secret image. In this paper, we propose a step construction to construct VCSOR and VCSXOR for general access structure by applying (2,2)-VCS recursively, where a participant may receive multiple share images. The proposed step construction generates VCSOR and VCSXOR which have optimal pixel expansion and contrast for each qualified set in the general access structure in most cases. Our scheme applies a technique to simplify the access structure, which can reduce the average pixel expansion (APE) in most cases compared with many of the results in the literature. Finally, we give some experimental results and comparisons to show the effectiveness of the proposed scheme.

Step Construction of Visual Cryptography Schemes

XOR-based visual cryptography scheme (XVCS) was proposed to solve the poor visual quality problem without darkening the background in the reconstructed secret image. However, investigations on XVCS are not sufficient. In this paper, we focus on the traditional model of VCS for general access structures and exploit some extended capabilities for XVCS. Our main contributions are: (1) we put forward constructions of perfect contrast XVCS using the linear algebraic technique without any assumptions such as participants may carry multiple shares or prior information about the shares are to be submitted during the secret reconstruction phase; (2) for some restricted access structures, we achieve perfect contrast and perfect pixel expansion, namely both 1, which is impossible for any OR-based visual cryptography scheme (OVCS); (3) for general access structures, we achieve perfect contrast with smaller pixel expansion compared with many of the results in the literature; (4) Theoretical analysis on the proposed constructions are provided, as well as extensive experimental results and comparisons for demonstrating the effectiveness and advantages of our constructions.

Perfect contrast XOR-based visual cryptography schemes via linear algebra

The handoff initiation in cellular systems depends on many environmental and system parameters. Various handoff initiation algorithms are available and most of them are based on relative signal strength (RSS) measurements. Some hysteresis margin in handoff decision criterion is allowed to avoid the ping-pong effect and hence frequent handoff requests from single user. The value of hysteresis margin plays a key role in handoff performance and affects the coverage of the cellular system. It is very difficult to choose a particular value for it. In this paper, the coverage of a handoff algorithm with dynamic hysteresis margin, based on the distance information between the mobile station and the serving base station, is analyzed for microcellular environment. Handoff probability is taken as performance parameter to evaluate handoff algorithms analytically.

Coverage Analysis of Handoff Algorithm with Adaptive Hysteresis Margin

This paper presents a new method for a visual cryptography scheme that uses phase masks and an interferometer. To encrypt a binary image, we divided it into an arbitrary number of slides and encrypted them using an XOR process with a random key or keys. The phase mask for each encrypted image was fabricated nuder the proposed phase-assignment rule. For decryption, phase masks were placed on any path of the Mach-Zehnder interferometer. Through optical experiments, we confirmed that a secret binary image that was sliced could be recovered by the proposed method.

Soo-Joong Kim Kim

Papers

Visual Cryptography Based on an Interferometric Encryption Technique