Paper 2010/545

Optimal XOR based (2,n)-Visual Cryptography Schemes

Feng Liu and Chuankun Wu

Abstract

A (2,n)-Visual Cryptography Scheme (VCS) is a kind of secret sharing scheme, where n participants share a secret image, and any two of them can recover the secret image visually without any cryptographic knowledge and computation devices, but any one of them cannot get any information about the secret image other than the size of the secret image. This paper studies the (2,n)-VCS_{XOR}, and shows the smallest (optimal) pixel expansion of such schemes, and the largest possible contrast for the (2,n)-VCS_{XOR} given its optimal pixel expansion. It also shows the largest (optimal) contrast of the (2,n)-VCS_{XOR}, and the smallest possible pixel expansion of such schemes given their optimal contrast. The results of this paper show that the (2,n)-VCS_{XOR} can achieve smaller pixel expansion and larger contrast than that of (2,n)-VCS_{OR}. It also shows that the construction of the basis matrix of optimal contrast (2,n)-VCS_{XOR} is equivalent to the construction of binary codes when they reach the maximum capability, and the construction of a specific class of optimal contrast (2,n)-VCS_{XOR} for n=2^{k}-1 is given.

Note: The paper was first submitted in 2006, and has been reviewed for several times. During the reviewing procedure, many anonymous reviewers' comments are very valuable. We thank a lot to these anonymous reviewers.