Probabilistic Visual Cryptography Schemes

Abstract

Visual cryptography schemes allow the encoding of a secret image, consisting of black or white pixels, 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. The secret pixels are shared with techniques that subdivide each secret pixel into a certain number m, m ≥ 2 of subpixels. Such a parameter m is called pixel expansion. Recently Yang introduced a probabilistic model. In such a model the pixel expansion m is 1, that is, there is no pixel expansion. The reconstruction of the image however is probabilistic, meaning that a secret pixel will be correctly reconstructed only with a certain probability. In this paper we propose a generalization of the model proposed by Yang. In our model we fix the pixel expansion m ≥ 1 that can be tolerated and we consider probabilistic schemes attaining such a pixel expansion. For m = 1 our model reduces to the one of Yang. For big enough values of m, for which a deterministic scheme exists, our model reduces to the classical deterministic model. We show that between these two extremes one can trade the probability factor of the scheme with the pixel expansion. Moreover, we prove that there is a one-to-one mapping between deterministic schemes and probabilistic schemes with no pixel expansion, where contrast is traded for the probability factor.

Journey of VCS from Black and White Images to Colored Images with their Performance Analysis

“…In 2007, Chen et al [3] extended the results to gray-scale images and proposed a gray-scale VCS scheme with the goal of no pixel expansion. Although, their scheme does not support colored images and only supports (k,k) threshold setting.…”

“…All the methods given by Hou are based on the subtractive model. Afterwards, Yang-Chen [3]proposed another algorithm that uses additive model in a probabilistic way. Finally we compare Wu-Wong-Li [4] method which is the first one satisfying all the properties with no pixel expansion.…”

K out of K Extended Visual Cryptography Scheme Based on “XOR”

“…Because the visual quality of a recovered image is degraded by a large pixel expansion, most studies try to reduce the pixel expansion [7]- [10]. For example, Yang et al [7] proposed a scheme to construct VCS with no pixel expansion using probabilistic method (PVCS).…”

Secure Two-Party Computation: A Visual Way

“…Visual cryptography has been extensively studied; we refer the interested reader to [9] for a collection of surveys on several aspects of visual cryptography. For the goal of this paper we will be using a particular type of visual cryptography: probabilistic visual cryptography [21,10].…”