Some ideal secret sharing schemes

Abstract

A secret sharing scheme is a method of assigning shares for a secret to some participants such that only authorized coalitions of these participants can recover the secret. In this work, we study several access structure types: we give an ideal perfect secret sharing scheme for disjunctive multilevel access structures. We introduce joint compartmented access structures, which covers compartmented access structures and conjunctive hierarchical access structures as special cases. We provide an almost surely perfect scheme for those joint compartmented access structures that can be realized by an ideal perfect secret sharing scheme. Lastly, we suggest an alternative threshold secret sharing scheme, and we use this scheme to construct a disjunctive multilevel secret sharing scheme.