Ideal secret sharing schemes with multiple secrets

We consider secret sharing schemes which, through an initial issuing of shares to a group of participants, permit a number of different secrets to be protected. Each secret is associated with a (potentially different) access structure and a particular secret can be reconstructed by any group of participants from its associated access structure without the need for further broadcast information. We consider ideal secret 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 of construction for such schemes. We also explore the extent to which the results that connect ideal secret sharing schemes to matroids can be appropriately generalized.The work of the second and third authors was supported by the Australian Research Council.