Traceable visual cryptography

Abstract

In this paper we present a new k out of n visual cryptography scheme which does not only meet the requirements of a basic visual cryptography scheme defined by Naor and Shamir [5] but is also traceable. A k out of n visual cryptography scheme is a special instance of a k out of n threshold secret sharing scheme [6]. Thus, no information about the original secret can be revealed if less than k share-holders combine their shares. In those systems it is inherently assumed that even if there are k or more share-holders with an interest in the abuse of the secret, then it is almost impossible that they can meet up as an entirety (e.g. because they are to cautious to inform too many others about their intentions) and combine their shares to misuse the secret. But in real scenarios it might not be too unlikely that the betrayers find together in small groups. Even though each one of these groups is too small to compute the original secret, the betrayers of such a group can impose a major security risk on the system by publishing the information about their shares. Suppose for example that k − 1 betrayers find each other and do the publishing. Then all the other n − k + 1 share-holders can potentially reveal the secret without ever meeting up with at least k − 1 other share-holders as is intended by the system. In order to cope with this lack of security, we present in this paper the idea of traceable visual cryptography schemes which allows to track down the publishing saboteurs.

This research was done while the author was a member of the Graduiertenkolleg Informatik at the University of Saarbruecken, a fellowship program of the DFG (Deutsche Forschungsgemeinschaft).