Cube-root-subgroups of SL_2 over imaginary quadratic integers

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dc.contributor.authorKureš, Miroslavcs
dc.coverage.issue2cs
dc.coverage.volume29cs
dc.date.issued2021-09-01cs
dc.description.abstractAll cube roots of the identity in the special linear group of $2\times 2$-matrices with entries in the ring of integers in $\mathbb Q[\sqrt{d}]$ are described. These matrices generate subgroups of the third order; it is shown that such subgroups may contain non-elementary matrices in the sense of P. M. Cohn. All this is viewed with respect to possible applications in lattice cryptography.en
dc.description.abstractAll cube roots of the identity in the special linear group of $2\times 2$-matrices with entries in the ring of integers in $\mathbb Q[\sqrt{d}]$ are described. These matrices generate subgroups of the third order; it is shown that such subgroups may contain non-elementary matrices in the sense of P. M. Cohn. All this is viewed with respect to possible applications in lattice cryptography.en
dc.formattextcs
dc.format.extent227-240cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationComputer Science Journal of Moldova. 2021, vol. 29, issue 2, p. 227-240.en
dc.identifier.issn1561-4042cs
dc.identifier.orcid0000-0001-6222-389Xcs
dc.identifier.other172038cs
dc.identifier.urihttp://hdl.handle.net/11012/201633
dc.language.isoencs
dc.publisherVladimir Andrunakievich Institute of Mathematics and Computer Sciencecs
dc.relation.ispartofComputer Science Journal of Moldovacs
dc.relation.urihttp://www.math.md/publications/csjm/issues/v29-n2/13338/cs
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1561-4042/cs
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/cs
dc.subjectimaginary quadratic fielden
dc.subjectring of integersen
dc.subjectnon-elementary matricesen
dc.subjectspecial linear groupen
dc.subjectpublic key cryptographyen
dc.subjectlattice based cryptosystemsen
dc.subjectimaginary quadratic field
dc.subjectring of integers
dc.subjectnon-elementary matrices
dc.subjectspecial linear group
dc.subjectpublic key cryptography
dc.subjectlattice based cryptosystems
dc.titleCube-root-subgroups of SL_2 over imaginary quadratic integersen
dc.title.alternativeCube-root-subgroups of SL_2 over imaginary quadratic integersen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-172038en
sync.item.dbtypeVAVen
sync.item.insts2025.10.14 15:06:53en
sync.item.modts2025.10.14 10:26:07en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
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