Secret Sharing Schemes with Veto Capabilities

A secret sharing scheme permits a secret to be shared among participants in such a way that only qualiied subsets of participants can recover the secret, but any non-qualiied subset has absolutely no information on the secret. In this paper we consider the problem of designing eecient secret sharing schemes having the additional feature that qualiied minorities can forbid any other set of participants from reconstructing the secret key. This problem was rst considered by Beutelspacher 2] who gave an algorithm, based on projective geometries, to construct threshold schemes in which qualiied minorities have this \veto" capability. We show that well known tools from Error Correcting Coding Theory allow to modify the classical Shamir secret sharing algorithm 22] to handle this more general problem.