XOR-Based Visual Cryptographic Schemes With Monotonously Increasing and Flawless Reconstruction Properties

A k out of n visual cryptographic scheme [(k, n)-VCS] encodes a secret image P into n transparencies (shares) in such a way that any k shares reveal P in a visual sense when they are superimposed (equivalent to the “OR” operation), while any k-1 or less cannot. A (k, n)-XVCS achieves the same goal with a better contrast on the reconstructed result of any k “XOR”ed shares. It has been proved that a (k, n)-VCS is also a (k, n)-XVCS. However, the monotonously increasing property (that any k+1,k+2,...,n shares also reveal P) in most conventional (k, n)-VCSs is not guaranteed when they are applied as (k, n)-XVCSs. This paper aims at developing efficient and flexible constructions for (k, n)-XVCSs with minimal pixel expansions, such that the monotonously increasing property, or even the flawless reconstruction of P when n shares are “XOR”ed, could be additionally fulfilled. Property analyses and comparisons against Tuyls et al.'s schemes are examined to demonstrate the applicability and superiority (in terms of the pixel expansion) of our schemes.