IDEAL SECRET SHARING SCHEMES WITH MULTIPLE SECRETS

We consider secret sharing schemes which, through an initial issuing o f shares to a group of participants, permit a number of different secr ets to be protected. Each secret is associated with a (potentially dif ferent) access structure and a particular secret can be reconstructed by any group of participants from its associated access structure with out the need for further broadcast information. We consider ideal secr et sharing schemes in this more general environment. In particular, we classify the collections of access structures that can be combined in such an ideal secret sharing scheme and we provide a general method o f construction for such schemes. We also explore the extent to which t he results that connect ideal secret sharing schemes to matroids can b e appropriately generalized.