{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T04:15:16Z","timestamp":1778040916409,"version":"3.51.4"},"reference-count":28,"publisher":"International Association for Cryptologic Research","issue":"1","license":[{"start":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T00:00:00Z","timestamp":1759708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IACR CiC"],"accepted":{"date-parts":[[2025,12,2]]},"abstract":"<jats:p>In this article, we develop algebraic tools for fully homomorphic encryption over the torus in the setting of general composite cyclotomic indices. Working in cyclotomic rings and fields beyond the power\u2011of\u2011two case, we reframe and optimize key primitives\u2014reduction modulo the cyclotomic polynomial, homomorphic evaluation of trace operators, blind extraction and the blind rotation used in bootstrapping\u2014using systematic duality and trace techniques. Our approach yields a simpler, more modular description of bootstrapping, including a new systematic treatment of so\u2011called \u201cnega\u2011cyclicity\u201d conditions and featuring an optimal reduction of the input noise, and provides sharp error bounds showing that bootstrap noise growth remains mild compared with the classical power\u2011of\u2011two instantiation. In addition, we introduce a new fast packing strategy. These results broaden the algebraic toolkit for torus\u2011based FHE and pave the way for new cryptographic constructions and applications.<\/jats:p>","DOI":"10.62056\/ab0ljb0kr","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T18:09:08Z","timestamp":1777918148000},"update-policy":"https:\/\/doi.org\/10.62056\/adfjwm02dj","source":"Crossref","is-referenced-by-count":0,"title":["Exploring General Cyclotomic Rings in Torus-Based Fully Homomorphic Encryption"],"prefix":"10.62056","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7317-6558","authenticated-orcid":false,"given":"Philippe","family":"Chartier","sequence":"first","affiliation":[{"name":"INRIA-IRMAR-University of Rennes","place":["Campus de Beaulieu, Rennes, 35042, France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Koskas","sequence":"additional","affiliation":[{"name":"Ravel Technologies","place":["75 rue de Richelieu, Paris, 75002, France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7815-444X","authenticated-orcid":false,"given":"Mohammed","family":"Lemou","sequence":"additional","affiliation":[{"name":"CNRS-IRMAR-University of Rennes","place":["Campus de Beaulieu, Rennes, 35042, France"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"48349","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"key":"ref1:LPR","isbn-type":"print","first-page":"35","article-title":"A Toolkit for Ring-LWE Cryptography","author":"V. 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Chen","year":"2018"}],"container-title":["IACR Communications in Cryptology"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T04:00:54Z","timestamp":1778040054000},"score":1,"resource":{"primary":{"URL":"https:\/\/cic.iacr.org\/p\/3\/1\/4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,4]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,5,4]]}},"URL":"https:\/\/doi.org\/10.62056\/ab0ljb0kr","archive":["Internet Archive","Internet Archive"],"relation":{},"ISSN":["3006-5496"],"issn-type":[{"value":"3006-5496","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,4]]},"assertion":[{"value":"2025-10-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-12-02","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"cc2-4-29"}}