Efficient sharing of many secrets

Abstract

A multi-secret sharing scheme is a protocol to distribute n secrets s1,…,sn among a set of participants V in such a way that: 1) any non-qualified subset of participants A ⊆ P has absolutely no information on the secrets; 2) any qualified subset can recover all the secrets, but 3) any non-qualified subset knowing the value of a number of secrets might have some information on other secrets. In this paper we lay foundations for a general theory of multi-secret sharing schemes by using the entropy approach, as done in [4] and [6] to analyze singlesecret sharing schemes. We prove lower bounds on the size of information held by each participant in any multi-secret sharing scheme. We provide an optimal protocol for multi-secret sharing schemes on a particular access structure, where the access structure specifies the subsets of participants qualified to reconstruct the secret.