Abstract
A ( k, n, ε) robust secret sharing scheme permits a secret to be shared among a set P of n participants in such a way that only subsets of P of size at least k can recover the secret, but any subsets of less than k participants have absolutely no information on the secret. Moreover, any coalition of less than k participants, called cheaters, has probability of successful cheating less than ε. In this paper we provide new bounds on the information distributed to participant in any ( k, n, ε) robust secret sharing scheme which relate the size of the shares, the size of the secret, the probability of cheating, and the probability of guessing.
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