New privilege-based visual cryptography with arbitrary privilege levels

Recently, Hou et al. introduced a novel (2, n) privilege-based visual cryptography scheme (PVCS) with various privilege levels of shadow images. In this scheme, a shadow with a higher privilege contributes more recovered information, while a lower privileged shadow has the less recovery capability. Moreover, the visual quality of stacked result depends on the total sum of privilege levels for all involved shadows in reconstruction. Unfortunately, the PVC scheme has the inconsistency of the contrast of recovered image and the sum of privilege levels. Accordingly, an enhanced Hou et al.'s (2, n)-PVC scheme (EPVCS) is proposed to solve this inconsistency problem. However, the EPVCS is not a general solution to implement all PVCSs with arbitrary privilege levels, and it also has the unequal whiteness of shadows. In this paper, we first extend Hou et al.'s (2, n)-EPVCS with a correct privilege levels achieving the consistency of the contrast and the sum of privilege levels. Then we construct a (2, n)-PVCS to allow arbitrary privilege levels and provide the equal whiteness for each shadow.