Property Analysis of XOR-Based Visual Cryptography

A $(k,n)$ visual cryptographic scheme (VCS) encodes a secret image into $n$ shadow images (printed on transparencies) distributed among $n$ participants. When any $k$ participants superimpose their transparencies on an overhead projector (OR operation), the secret image can be visually revealed by a human visual system without computation. However, the monotone property of OR operation degrades the visual quality of reconstructed image for OR-based VCS (OVCS). Accordingly, XOR-based VCS (XVCS), which uses XOR operation for decoding, was proposed to enhance the contrast. In this paper, we investigate the relation between OVCS and XVCS. Our main contribution is to theoretically prove that the basis matrices of $(k,n)$-OVCS can be used in $(k,n)$-XVCS. Meantime, the contrast is enhanced $2^{(k-1)}$ times.