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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.
^Shamir, Adi (1 November 1979). "How to share a secret". Communications of the ACM. 22 (11): 612–613. doi:10.1145/359168.359176. ISSN 0001-0782.
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Daza, Vanesa; Herranz, Javier; Morillo, Paz; Ràfols, Carla (28 November 2008). Extended Access Structures and Their Cryptographic Applications (Report).
Daza, Vanesa; Herranz, Javier; Morillo, Paz; Ràfols, Carla (2010). "Extensions of access structures and their cryptographic applications". Applicable Algebra in Engineering, Communication and Computing. 21 (4): 257–284. doi:10.1007/s00200-010-0125-1.
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