Ideal contrast visual cryptography schemes with reversing

A visual cryptography scheme (VCS) for a set of n participants is a method to encode a secret image, consisting of black and white pixels, into n transparencies, one for each participant. Certain qualified subsets of participants can “visually” recover the secret image by stacking their transparencies, whereas, other, forbidden, subsets of participants, cannot gain any information about the secret image.Recently, Viet and Kurosawa proposed a VCS with reversing, which is a VCS where the participants are also allowed to reverse their transparencies, i.e., to change black pixels to white pixels and vice-versa. They showed how to construct VCSs with reversing where the reconstruction of black (white, respectively) pixels is perfect, whereas, the reconstruction of white (black, respectively) pixels is almost perfect. In both their schemes there is a loss of resolution, since the number of pixels in the reconstructed image is greater than that in the original secret image.In this paper we show how to construct VCSs with reversing where reconstruction of both black and white pixels is perfect. In our schemes each participant is required to store a certain number of transparencies, each having the same number of pixels as the original secret image. Moreover, our schemes guarantee no loss of resolution, since the reconstructed image is exactly the same as the original secret image. Finally, compared to the schemes of Viet and Kurosawa, our schemes require each participant to store a smaller amount of information.