Access structure

Access structures are used in the study of security systems where multiple parties need to work together to obtain a resource.[1] Groups of parties that are granted access are called qualified. In set theoretic terms they are referred to as qualified sets; in turn, the set of all such qualified sets is called the access structure of the system. Less formally it is a description of who needs to cooperate with whom in order to access the resource. In its original use in cryptography, the resource was a secret shared among the participants.[2] Only subgroups of participants contained in the access structure are able to join their shares to recompute the secret. More generally, the resource can also be a task that a group of people can complete together, such as creating a digital signature, or decrypting an encrypted message.

It is reasonable to assume that access structures are monotone in the sense that, if a subset S is in the access structure, all sets that contain S as a subset should also form part of the access structure.