{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:52:30Z","timestamp":1753894350406,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T00:00:00Z","timestamp":1679356800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Let $S$ be a pool of $s$ parties and Alice be the dealer. In this paper, we\npropose a scheme that allows the dealer to encrypt messages in such a way that\nonly one authorized coalition of parties (which the dealer chooses depending on\nthe message) can decrypt. At the setup stage, each of the parties involved in\nthe process receives an individual key from the dealer. To decrypt information,\nan authorized coalition of parties must work together to use their keys. Based\non this scheme, we propose a threshold encryption scheme. For a given message\n$f$ the dealer can choose any threshold $m = m(f).$ More precisely, any set of\nparties of size at least $m$ can evaluate $f$; any set of size less than $m$\ncannot do this. Similarly, the distribution of keys among the included parties\ncan be done in such a way that authorized coalitions of parties will be given\nthe opportunity to put a collective digital signature on any documents. This\nprimitive can be generalized to the dynamic setting, where any user can\ndynamically join the pool $S$. In this case the new user receives a key from\nthe dealer. Also any user can leave the pool $S$. In both cases, already\ndistributed keys of other users do not change. The main feature of the proposed\nschemes is that for a given $s$ the keys are distributed once and can be used\nmultiple times.\n  The proposed scheme is based on the idea of hidden multipliers in encryption.\nAs a platform, one can use both multiplicative groups of finite fields and\ngroups of invertible elements of commutative rings, in particular,\nmultiplicative groups of residue rings. We propose two versions of this scheme.<\/jats:p>","DOI":"10.46298\/jgcc.2023.14.2.10150","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T04:00:30Z","timestamp":1679371230000},"source":"Crossref","is-referenced-by-count":1,"title":["Multi-recipient and threshold encryption based on hidden multipliers"],"prefix":"10.46298","volume":"Volume 14, Issue 2","author":[{"given":"Vitaly","family":"Roman'kov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2023,3,21]]},"container-title":["journal of Groups, complexity, cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/gcc.episciences.org\/10150\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/gcc.episciences.org\/10150\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T10:13:51Z","timestamp":1687256031000},"score":1,"resource":{"primary":{"URL":"https:\/\/gcc.episciences.org\/10150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,21]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/jgcc.2023.14.2.10150","relation":{"is-same-as":[{"id-type":"arxiv","id":"2210.06889","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2210.06889","asserted-by":"subject"}]},"ISSN":["1869-6104"],"issn-type":[{"type":"electronic","value":"1869-6104"}],"subject":[],"published":{"date-parts":[[2023,3,21]]},"article-number":"10150"}}