Ideal Secret Sharing Schemes for Useful Multipartite Access Structures

This paper is a survey of the main results and open problems in a line of work that was initiated shortly after secret sharing was introduced. Namely, the construction of ideal linear secret sharing schemes for access structures that are natural generalizations of the threshold ones and have interesting properties for the applications. Some of them have hierarchical properties, while other ones are suitable for situations requiring the agreement of several parties. These access structures are multipartite, that is, the participants are distributed into several parts and all participants in the same part play an equivalent role in the structure. This line of work has received an impulse from a recently discovered connection between ideal multipartite secret sharing schemes and integer