Probabilistic visual cryptography schemes

Visual cryptography schemes allow the encoding of a secret image, consisting of black or white pixels, into n shares that are distributed to the set P of n participants. The shares are such that only qualified subsets of participants can “visually” recover the secret image. The secret pixels are shared with techniques based on subdividing each secret pixel into a certain number m, m = 2 of subpixels. Such a parameter m is called the pixel expansion, since the reconstructed shared image becomes m times bigger than the original. This cryptographic paradigm was introduced by Naor and Shamir [16]. They analyzed the case of (k, n)-threshold visual cryptography schemes, in which a black and white secret image is visible if and only if any k transparencies are stacked together.