{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:36:40Z","timestamp":1764981400374,"version":"3.46.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2014,3,6]],"date-time":"2014-03-06T00:00:00Z","timestamp":1394064000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100003825","name":"Hungarian Academy of Sciences","doi-asserted-by":"crossref","award":["Lend\u00fclet Program"],"award-info":[{"award-number":["Lend\u00fclet Program"]}],"id":[{"id":"10.13039\/501100003825","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,6,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n                  <jats:p>The\nmotivation for extending secret sharing schemes to cases when either the\nset of players is infinite or the domain from which the secret and\/or the\nshares are drawn is infinite or both, is similar to the case when switching\nto abstract probability spaces from classical combinatorial probability. It\nmight shed new light on old problems, could connect seemingly unrelated\nproblems, and unify diverse phenomena.\nDefinitions equivalent in the finitary case could be very much different\nwhen switching to infinity, signifying their difference. The standard\nrequirement that qualified subsets should be able to determine the secret\nhas different interpretations in spite of the fact that, by assumption, all\nparticipants have infinite computing power. The requirement that unqualified\nsubsets should have no or limited information on the secret suggests that\nwe also need some probability distribution. In the infinite case events with\nzero probability are not necessarily impossible, and we should decide\nwhether bad events with zero probability are allowed or not.\nIn this paper, rather than giving precise definitions, we enlist an abundance\nof hopefully interesting infinite secret sharing schemes. These\nschemes touch quite diverse areas of mathematics such as projective\ngeometry, stochastic processes and Hilbert spaces. Nevertheless our main\ntools are from probability theory. The examples discussed here serve as\nfoundation and illustration to the more theory oriented companion paper\n[arXiv:1310.7423].<\/jats:p>","DOI":"10.1515\/jmc-2013-0005","type":"journal-article","created":{"date-parts":[[2014,3,5]],"date-time":"2014-03-05T16:03:03Z","timestamp":1394035383000},"page":"141-168","source":"Crossref","is-referenced-by-count":2,"title":["Infinite secret sharing \u2013 Examples"],"prefix":"10.1515","volume":"8","author":[{"given":"Alexander","family":"Dibert","sequence":"first","affiliation":[{"name":"Department of Mathematics, Central European University, Zrinyi utca 14, 1051 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L\u00e1szl\u00f3","family":"Csirmaz","sequence":"additional","affiliation":[{"name":"Computer and Statistics Center, Central European University, Nador utca 9, 1051 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,3,6]]},"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2013-0005\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2013-0005\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:33:22Z","timestamp":1764981202000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2013-0005\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,6]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,1,24]]},"published-print":{"date-parts":[[2014,6,1]]}},"alternative-id":["10.1515\/jmc-2013-0005"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2013-0005","relation":{},"ISSN":["1862-2984","1862-2976"],"issn-type":[{"type":"electronic","value":"1862-2984"},{"type":"print","value":"1862-2976"}],"subject":[],"published":{"date-parts":[[2014,3,6]]}}}