Using Colors to Improve Visual Cryptography for Black and White Images

Abstract

Black-and-white visual cryptography (BW-VC) allows the sharing of b&w secret images transforming a secret image into a number of b&w shares. Colored visual cryptography allows the sharing of color images by means of color shares. In this paper we propose a new model, called colored-black-and-white (CBW-VC), in which the secret image is b&w and the shares are color images. The motivation for the use of this new model is that of constructing schemes to share b&w images using a smaller pixel expansion. Using the CBW-VC model, we provide (2, n)-threshold schemes with pixel expansion m = ⌈log3 n⌉, improving on the best pixel expansion attainable in the BW-VC model. For the case of schemes with perfect reconstruction of black pixels we provide a general construction that allows to transform any BW-VC scheme into a CBW-VC scheme whose pixel expansion is 1/3 of the pixel expansion of the starting BW-VC scheme. When there are very few participants, namely n = 2, 3, the proposed CBW-VC (2, n)-threshold schemes have no pixel expansion! We prove that the above two cases are the only ones where it is possible to provide schemes without pixel expansion. That is, we prove that, in the CBW-VC model, it is not possible to construct (2, n)-threshold schemes, for n ≥ 4, and (k, n)-threshold schemes, for k ≥ 3, without pixel expansion.