Boolean Operation Based Visual Cryptography

Abstract

A ( $k$ , $n$ )-Traditional Visual Cryptographic Scheme (VCS) based on basis matrices encoded a secret image into $n$ shadow images distributed among $n$ participants. When any $k$ participants superimposed their shadow images, the secret image can be visually revealed. This stacking operation in decoding process is equivalent to perform OR operation. Basis matrices of a ( $k$ , $n$ ) OR-operation based VCS (OVCS) have been proved in the ( $k$ , $n$ ) XOR-operation based VCS (XVCS) underlying XOR operation to enhance the contrast $2^{(k-1)}$ times. Although XOR operation has been used to excavate good property of basis matrices in OVCS, other properties of basis matrices are obviously ignored in visual cryptography. In this paper, we define two new Boolean-operation based VCSs, AND-operation based VCS (AVCS) and NOT-operation based VCS (NVCS), and prove that basis matrices in a ( $k$ , $n$ )-OVCS can be used as basis matrices in ( $k~n$ )-AVCS and ( $k$ , $n$ ) NVCS, respectively. Furthermore, we obtain a general converting formula of their contrasts among OVCS, AVCS, XVCS, and NVCS. With OVCS, there does not exist perfect whiteness. However, with other Boolean-operation based VCSs (XVCS, AVCS, and NVCS), there may exist this situation. Therefore, new contrast is also given to precisely evaluate visual quality of Boolean-operation based VCSs. Some observations and results demonstrate how to properly use these Boolean-operation based VCSs for decoding.