A general decomposition construction for incomplete secret sharing schemes

Abstract

A secret sharing scheme for an incomplete access structure (Γ, Δ) is a method of distributing information about a secret among a group of participants in such a way that sets of participants in Γ can reconstruct the secret and sets of participants in Δ can not obtain any new information about the secret. In this paper we present a more precise definition of secret sharing schemes in terms of information theory, and a new decomposition theorem. This theorem generalizes previous decomposition theorems and also works for a more general class of access structures. We demonstrate some applications of the theorem.