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However, in many applications, it is undesirable for nonshareholders to learn the secret. In these cases, pairwise secure channels are needed among shareholders to exchange the shares. In other words, a shared key needs to be established between every pair of shareholders. But employing an additional key establishment protocol may make the secret-sharing schemes significantly more complicated. To solve this problem, we introduce a new type of secret-sharing, called<jats:italic>protected secret-sharing<\/jats:italic>(PSS), in which the shares possessed by shareholders not only can be used to reconstruct the original secret but also can be used to establish the shared keys between every pair of shareholders. Therefore, in the secret reconstruction phase, the recovered secret is only available to shareholders but not to nonshareholders. In this paper, an information theoretically secure PSS scheme is proposed, its security properties are analyzed, and its computational complexity is evaluated. Moreover, our proposed PSS scheme also can be applied to threshold cryptosystems to prevent nonshareholders from learning the output of the protocols.<\/jats:p>","DOI":"10.1155\/2017\/5437403","type":"journal-article","created":{"date-parts":[[2017,9,27]],"date-time":"2017-09-27T21:01:05Z","timestamp":1506546065000},"page":"1-6","source":"Crossref","is-referenced-by-count":17,"title":["How to Share Secret Efficiently over Networks"],"prefix":"10.1155","volume":"2017","author":[{"given":"Lein","family":"Harn","sequence":"first","affiliation":[{"name":"Department of Computer Science Electrical Engineering, University of Missouri-Kansas City, Kansas City, MO 64110, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3847-7659","authenticated-orcid":true,"given":"Ching-Fang","family":"Hsu","sequence":"additional","affiliation":[{"name":"Computer School, Central China Normal University, Wuhan 430079, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhe","family":"Xia","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Wuhan University of Technology, Wuhan 430071, China"},{"name":"Hubei Key Laboratory of Transportation Internet of Things, Wuhan University of Technology, Wuhan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junwei","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Wuhan University of Technology, Wuhan 430071, China"},{"name":"Hubei Key Laboratory of Transportation Internet of Things, Wuhan University of Technology, Wuhan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"32","doi-asserted-by":"publisher","DOI":"10.1145\/359168.359176"},{"key":"2","first-page":"313","volume":"48","year":"1979","journal-title":"Proceedings of the National Computer Conference"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1983.1056651"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cdt:19941293"},{"key":"33","year":"2013","journal-title":"Advanced Materials Research"},{"issue":"4","key":"13","doi-asserted-by":"crossref","first-page":"461","DOI":"10.15388\/Informatica.2009.260","volume":"20","year":"2009","journal-title":"Informatica"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17373-8_25"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1145\/1053283.1053287"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.4156\/jcit.vol6.issue5.37"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2008.77"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2015.06.014"},{"key":"4","first-page":"383","year":"1985","journal-title":"Foundations of Computer Science"},{"key":"21","first-page":"499","volume-title":"Improving the round complexity of vss in point-to-point networks","year":"2008"},{"key":"3","first-page":"453","volume-title":"Analysis of key-exchange protocols and their use for building secure channels","year":"2001"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-44750-4_27"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0055722"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1049\/iet-ifs.2012.0105"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.24138\/jcomss.v11i1.113"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-013-9831-6"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2017\/5437403.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2017\/5437403.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2017\/5437403.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,18]],"date-time":"2020-10-18T10:25:25Z","timestamp":1603016725000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2017\/5437403\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"references-count":19,"alternative-id":["5437403","5437403"],"URL":"https:\/\/doi.org\/10.1155\/2017\/5437403","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"value":"1939-0114","type":"print"},{"value":"1939-0122","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}