Probability of shares in secret sharing schemes

A secret sharing scheme is a protocol to share a secret s among a set P of participants in such a way that only qualified subsets, pooling together th eir information, can reconstruct the secret s, but subsets of participants that are not enabled to recover the secret have no information on it. In this paper we analyze the sample space of shares for any set of particip ants. In particular, we prove tight bounds on the probability of shares and on the size of the space of shares in terms of the size of the secret set. (C) 1999 Published by Elsevier Science B.V. All rights reserved.