# Access structure

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Access_structure
> Markdown URL: https://mediated.wiki/source/Access_structure.md
> Source: https://en.wikipedia.org/wiki/Access_structure
> Source revision: 1348564633
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{Short description|Cryptography stub}}
{{more citations needed|date=November 2012}}
{{use dmy dates|date=May 2024}}

'''Access structures''' are used in the study of security systems where multiple parties need to work together to obtain a resource.<ref>{{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|hdl=1721.1/148961 |hdl-access=free }}</ref> Groups of parties that are granted access are called qualified. In [set theoretic](/source/set_theory) 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](/source/cryptography), the resource was a secret [shared](/source/secret_sharing) among the participants.<ref>{{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}}}}</ref>  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](/source/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.

==See also==
* [Access control](/source/Access_control)
* [Secret sharing](/source/Secret_sharing)
* [Threshold cryptosystem](/source/Threshold_cryptosystem)

== References ==
<references />

Category:Access control

{{crypto-stub}}

---
Adapted from the Wikipedia article [Access structure](https://en.wikipedia.org/wiki/Access_structure) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Access_structure?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.