Color visual cryptography schemes for black and white secret images

In this paper we propose the use of colors to improve visual cryptography schemes for black-and-white secret images. The resulting model is called colored-black-and-white visual cryptography (CBW-VC) model. Using this new model we exploit colors to obtain schemes to share b&w images using a smaller pixel expansion. In particular we provide (2, n)-threshold schemes with pixel expansion m = inverted right perpendicularlog(3) ninverted left perpendicular, improving on the best pixel expansion attainable in the normal b&w model (BW-VC). For the case of schemes with perfect reconstruction of black pixels we provide a general construction that allows us to transform any BW-VC scheme into a csw-vc scheme whose pixel expansion is 1/3 of the pixel expansion of the starting BW-VC scheme. 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. We also prove that there exist schemes with optimal contrast in the subset of schemes that use only full intensity colors; this is a direct consequence of the definition of contrast which distinguishes only black and non-black pixels. We discuss an alternative measure of contrast that takes into account the "distance" between colors. We conjecture that also with this definition of contrast there exist schemes that use only full intensity colors and achieve optimal contrast. (C) 2013 Elsevier B.V. All rights reserved.