A new matrix form to generate all 3 x 3 involutory MDS matrices over F2m

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dc.authoridYilmazguc, Gozde/0000-0003-2127-5735
dc.authoridAkleylek, Sedat/0000-0001-7005-6489
dc.authoridRijmen, Vincent/0000-0001-7401-2088
dc.authoridGuzel, Gozde/0000-0003-0192-9797
dc.authorwosidYilmazguc, Gozde/IUN-8401-2023
dc.authorwosidAkleylek, Sedat/N-2620-2019
dc.authorwosidyilmazguc, Gulsum Gozde/JXL-1403-2024
dc.authorwosidAkleylek, Sedat/D-2090-2015
dc.contributor.authorGuzel, Gulsum Gozde
dc.contributor.authorSakalli, Muharrem Tolga
dc.contributor.authorAkleylek, Sedat
dc.contributor.authorRijmen, Vincent
dc.contributor.authorCengellenmis, Yasemin
dc.date.accessioned2024-06-12T10:58:55Z
dc.date.available2024-06-12T10:58:55Z
dc.date.issued2019
dc.departmentTrakya Üniversitesien_US
dc.description.abstractIn this paper, we propose a new matrix form to generate all 3 x 3 involutory and MDS matrices over F-2(m) and prove that the number of all 3 x 3 involutory and MDS matrices over F-2(m) is (2(m) - 1)(2) . (2(m) - 2) . (2(m) - 4), where m > 2. Moreover, we give 3 x 3 involutory and MDS matrices over F-2(3), F-2(4) and F-2(8) defined by the irreducible polynomials x(3) +x+ 1, x(4) +x + 1 and x(8) + x(7) + x(6) + x + 1, respectively, by considering the minimum XOR count, which is a metric used in the estimation of hardware implementation cost. Finally, we provide the maximum number of 1s in 3 x 3 involutory MDS matrices. (C) 2019 Elsevier B.V. All rights reserved.en_US
dc.description.sponsorshipTUBITAK [EEEAG-116E279]en_US
dc.description.sponsorshipSedat Akleylek is partially supported by TUBITAK under grant no. EEEAG-116E279. The authors would like to express their gratitude to the anonymous reviewers for their invaluable suggestions (especially for XOR count part) in putting the present study into its final form.en_US
dc.identifier.doi10.1016/j.ipl.2019.02.013
dc.identifier.endpage68en_US
dc.identifier.issn0020-0190
dc.identifier.issn1872-6119
dc.identifier.scopus2-s2.0-85063406209en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage61en_US
dc.identifier.urihttps://doi.org/10.1016/j.ipl.2019.02.013
dc.identifier.urihttps://hdl.handle.net/20.500.14551/20251
dc.identifier.volume147en_US
dc.identifier.wosWOS:000467892500013en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevier Science Bven_US
dc.relation.ispartofInformation Processing Lettersen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectCryptographyen_US
dc.subjectMDS Matricesen_US
dc.subjectDiffusion Layeren_US
dc.subjectInvolutory Matricesen_US
dc.titleA new matrix form to generate all 3 x 3 involutory MDS matrices over F2men_US
dc.typeArticleen_US

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