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dc.contributor.authorGrover, Charles
dc.contributor.authorMendelsohn, Andrew
dc.contributor.authorLing, Cong
dc.contributor.authorVehkalahti, Roope
dc.date.accessioned2022-08-12T07:18:44Z
dc.date.available2022-08-12T07:18:44Z
dc.date.issued2022
dc.identifier.citationGrover, C., Mendelsohn, A., Ling, C., & Vehkalahti, R. (2022). Non-commutative Ring Learning with Errors from Cyclic Algebras. <i>Journal of Cryptology</i>, <i>35</i>(3), Article 22. <a href="https://doi.org/10.1007/s00145-022-09430-6" target="_blank">https://doi.org/10.1007/s00145-022-09430-6</a>
dc.identifier.otherCONVID_148956560
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/82493
dc.description.abstractThe Learning with Errors (LWE) problem is the fundamental backbone of modern lattice-based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often impractical, so Ring LWE was introduced as a form of ‘structured’ LWE, trading off a hard to quantify loss of security for an increase in efficiency by working over a well-chosen ring. Another popular variant, Module LWE, generalizes this exchange by implementing a module structure over a ring. In this work, we introduce a novel variant of LWE over cyclic algebras (CLWE) to replicate the addition of the ring structure taking LWE to Ring LWE by adding cyclic structure to Module LWE. We show that the security reductions expected for an LWE problem hold, namely a reduction from certain structured lattice problems to the hardness of the decision variant of the CLWE problem (under the condition of constant rank d). As a contribution of theoretic interest, we view CLWE as the first variant of Ring LWE which supports non-commutative multiplication operations. This ring structure compares favorably with Module LWE, and naturally allows a larger message space for error correction coding.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherSpringer Science and Business Media LLC
dc.relation.ispartofseriesJournal of Cryptology
dc.rightsCC BY 4.0
dc.subject.otheralgebraic number theory
dc.subject.otherlattices
dc.subject.otherlearning with errors
dc.subject.othernon-commutative algebra
dc.subject.otherpost-quantum cryptography
dc.titleNon-commutative Ring Learning with Errors from Cyclic Algebras
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202208124037
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.relation.issn0933-2790
dc.relation.numberinseries3
dc.relation.volume35
dc.type.versionpublishedVersion
dc.rights.copyright© The Author(s) 2022
dc.rights.accesslevelopenAccessfi
dc.subject.ysokryptografia
dc.subject.ysotietojärjestelmät
dc.subject.ysosalaus
dc.subject.ysoalgebra
dc.subject.ysovirheet
dc.subject.ysovirheanalyysi
dc.subject.ysolukuteoria
dc.subject.ysoparantaminen (paremmaksi muuttaminen)
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p5480
jyx.subject.urihttp://www.yso.fi/onto/yso/p3927
jyx.subject.urihttp://www.yso.fi/onto/yso/p5475
jyx.subject.urihttp://www.yso.fi/onto/yso/p12498
jyx.subject.urihttp://www.yso.fi/onto/yso/p148
jyx.subject.urihttp://www.yso.fi/onto/yso/p9865
jyx.subject.urihttp://www.yso.fi/onto/yso/p1988
jyx.subject.urihttp://www.yso.fi/onto/yso/p4229
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1007/s00145-022-09430-6
dc.type.okmA1


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