ON SECRET SHARING SCHEMES

A secret sharing scheme is a protocol to share a secret s among a set of participants P in such a way that only qualified subsets of P can r econstruct the value of s whereas any other subset of P, non-qualified to know s, cannot determine anything about the value of the secret. I n this paper we prove that the entropy of the shares of any non-qualif ied set is independent from the probability distribution according to which the secret is chosen. This result implies that several recent bo unds on the shares' size and on the randomness required to construct s ecret sharing schemes can be strengthened. (C) 1998 Elsevier Science B .V.