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Access structure
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<h2 id="background">Background</h2> <p>In its original use in <a href="/facts/Cryptography/e94PEVau">cryptography</a>, the resource was a secret <a href="/facts/Secret_sharing/umC4t0cD">shared</a> among the participants.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> 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 <a href="/facts/Digital_signature/tY7e2pnW">digital signature</a>, or decrypting an encrypted message. </p><p>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. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Access_control/08zE5Pz8">Access control</a></li> <li><a href="/facts/Secret_sharing/umC4t0cD">Secret sharing</a></li> <li><a href="/facts/Threshold_cryptosystem/4KKvNxW8">Threshold cryptosystem</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>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. <a href="https://doi.org/10.1145%2F359168.359176" target="_blank">https://doi.org/10.1145%2F359168.359176</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>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. <a href="https://www.researchgate.net/publication/220334562" target="_blank">https://www.researchgate.net/publication/220334562</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>