Access structure
{{Short description|Cryptography stub}}
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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.{{Cite journal |last=Shamir |first=Adi |date=1979-11-01 |title=How to share a secret |journal=Communications of the ACM |volume=22 |issue=11 |pages=612–613 |doi=10.1145/359168.359176 |issn=0001-0782 |doi-access=free}} 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.
Background
In its original use in cryptography, the resource was a secret shared among the participants.{{multiref|
- {{Cite report|url=https://www.researchgate.net/publication/220334562|title=Extended Access Structures and Their Cryptographic Applications|last1=Daza|first1=Vanesa|last2=Herranz|first2=Javier|last3=Morillo|first3=Paz|last4=Ràfols|first4=Carla|date=2008-11-28}}
- {{Cite journal |last1=Daza |first1=Vanesa |last2=Herranz |first2=Javier |last3=Morillo |first3=Paz |last4=Ràfols |first4=Carla |year=2010 |title=Extensions of access structures and their cryptographic applications |journal=Applicable Algebra in Engineering, Communication and Computing |volume=21 |issue=4 |pages=257–284 |doi=10.1007/s00200-010-0125-1}}}} 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.