Sharing Multiple Secrets in XOR-Based Visual Cryptography by Non-Monotonic Threshold Property

Abstract

Multiple-secret visual cryptography scheme (MVCS) and fully incrementing visual cryptography scheme (FIVCS) have the same functionality that different secrets are gradually revealed by stacking different numbers of shadows. In essence, MVCS and FIVCS are the same. However, both of the two schemes suffer from large pixel expansion and deteriorated reconstructed image quality. In addition, MVCS and FIVCS require intensive computations to create base matrices. In this research, we exploit the capacity of sharing multiple secrets in XOR-based VCS (XVCS). First of all, three efficient base matrix constructions are proposed for realizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k, n)$ </tex-math></inline-formula> non-monotonic XVCS (NXVCS), where the secret image is only revealed by XOR-ing exact <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> shadows. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k, n)$ </tex-math></inline-formula> -NXVCS is adopted to constitute the multiple-secret XVCS (MXVCS). Theoretical analysis on the proposed constructions is provided. Extensive experiments and comparisons are conducted to illustrate that the pixel expansion, the visual quality of recovered image and the efficiency of generating base matrices are significantly improved by the proposed MXVCS, while comparing to MVCS and FIVCS.