Randomness in Visual Cryptography

Abstract

A visual cryptography scheme for a set $\mathcal{P}$ of n participants is a method to encode a secret image into n shadow images called shares each of which is given to a distinct participant. Certain qualified subsets of participants can recover the secret image, whereas forbidden subsets of participants have no information on the secret image. The shares given to participants in $X \subseteq \mathcal{P}$ are xeroxed onto transparencies. If X is qualified then the participants in X can visually recover the secret image by stacking their transparencies without any cryptography knowledge and without performing any cryptographic computation.

This is the first paper which analyzes the amount of randomness needed to visually share a secret image. It provides lower and upper bounds to the randomness of visual cryptography schemes. Our schemes represent a dramatic improvement on the randomness of all previously known schemes.