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 reconstruct the value of s whereas any other subset of P, non-qualified to know s, cannot determine anything about the value of the secret. In this paper we prove that the entropy of the shares of any non-qualified set is independent from the probability distribution according to which the secret is chosen. This result implies that several recent bounds on the shares' size and on the randomness required to construct secret sharing schemes can be strengthened.

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