Further ideal multipartite access structures from integer polymatroids

Ideal access structures admit ideal secret sharing schemes where the shares have the minimal size.As multipartite access structures can well mirror the real social organizations, of which the participants arepartitioned into disjoint groups according to their properties, it is desirable to find expressive ideal multipartiteaccess structures. Integer polymatroids, due to their close relationship with ideal multipartite access structures,have been shown as a powerful tool to study the ideality of some multipartite access structures. In this paper, tocater for flexible applications, we consider several ideal multipartite access structures that further extend someknown results. We first explore a type of compartmented access structures with strictly lower bounds, whichprovide fairness among all the participant groups when recovering the secret. Then, we investigate ideal benchaccess structures where the participant set is divided into two parts, that is, line-up section and bench section.The participants in line-up section can delegate their capabilities to the participants in bench section in such away that the participants in bench section can take over the role of their delegators in line-up section, which isapplicable to emergency situations when there are no enough participants in line-up section for recovering thesecret. Finally, we propose two types of ideal partially hierarchical access structures which are suitable to morerealistic hierarchical social organizations than existing results.