Ideal secret sharing schemes with multipartite access structures

Abstract

The concept of quasi-threshold multipartite access structures for secret sharing schemes is introduced. These access structures allow one distinguished class of participants to retain control over the reconstruction of the secret, while allowing flexibility over the quorum of participants from other classes. While ideal bipartite access structures have been classified, the case for multipartite access structures is still open. Here it is shown that quasi-threshold multipartite access structures are ideal by constructing a projective space representation of the associated matroids.