On the automorphisms and isomorphisms of MDS matrices and their efficient implementations

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dc.authoridAkleylek, Sedat/0000-0001-7005-6489
dc.authoridakkanat, kemal/0000-0002-6448-7378
dc.authoridRijmen, Vincent/0000-0001-7401-2088
dc.authorwosidAkleylek, Sedat/N-2620-2019
dc.contributor.authorSakalli, Muharrem Tolga
dc.contributor.authorAkleylek, Sedat
dc.contributor.authorAkkanat, Kemal
dc.contributor.authorRijmen, Vincent
dc.date.accessioned2024-06-12T11:08:09Z
dc.date.available2024-06-12T11:08:09Z
dc.date.issued2020
dc.departmentTrakya Üniversitesien_US
dc.description.abstractIn this paper, we explicitly define the automorphisms of MDS matrices over the same binary extension field. By extending this idea, we present the isomorphisms between MDS matrices over F-2m and MDS matrices over F-2mt, where t >= 1 and m > 1, which preserves the software implementation properties in view of XOR operations and table lookups of any given MDS matrix over F-2m. Then we propose a novel method to obtain distinct functions related to these automorphisms and isomorphisms to be used in generating isomorphic MDS matrices (new MDS matrices in view of implementation properties) using the existing ones. The comparison with the MDS matrices used in AES, ANUBIS, and subfield-Hadamard construction shows that we generate an involutory 4 x 4 MDS matrix over F-28 (from an involutory 4 x 4 MDS matrix over F-24) whose required number of XOR operations is the same as that of ANUBIS and the subfield-Hadamard construction, and better than that of AES. The proposed method, due to its ground field structure, is intended to be a complementary method for the current construction methods in the literature.en_US
dc.description.sponsorshipTUBITAK [EEEAG-116E279]en_US
dc.description.sponsorshipThe authors would like to express their gratitude to the anonymous reviewers for their invaluable suggestions in putting the present study into its final form. Sedat Akleylek was partially supported by TUBITAK under Grant No. EEEAG-116E279.en_US
dc.identifier.doi10.3906/elk-1906-151
dc.identifier.endpage287en_US
dc.identifier.issn1300-0632
dc.identifier.issn1303-6203
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85079855236en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage275en_US
dc.identifier.trdizinid334610en_US
dc.identifier.urihttps://doi.org/10.3906/elk-1906-151
dc.identifier.urihttps://search.trdizin.gov.tr/yayin/detay/334610
dc.identifier.urihttps://hdl.handle.net/20.500.14551/22320
dc.identifier.volume28en_US
dc.identifier.wosWOS:000510459900020en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakTR-Dizinen_US
dc.language.isoenen_US
dc.publisherTubitak Scientific & Technological Research Council Turkeyen_US
dc.relation.ispartofTurkish Journal Of Electrical Engineering And Computer Sciencesen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectMDS Matrixen_US
dc.subjectBranch Numberen_US
dc.subjectBlock Cipheren_US
dc.subjectGenerateen_US
dc.titleOn the automorphisms and isomorphisms of MDS matrices and their efficient implementationsen_US
dc.typeArticleen_US

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