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dc.contributor.authorXia, Yongbo
dc.contributor.authorZhang, Xianglai
dc.contributor.authorLi, Chunlei
dc.contributor.authorHelleseth, Tor
dc.date.accessioned2021-07-09T11:50:26Z
dc.date.available2021-07-09T11:50:26Z
dc.date.created2021-02-15T18:57:01Z
dc.date.issued2020
dc.identifier.issn1071-5797
dc.identifier.urihttps://hdl.handle.net/11250/2764059
dc.description.abstractA function f(x)from the finite field GF(pn)to itself is said to be differentially δ-uniform when the maximum number of solutions x ∈GF(pn)of f(x +a) −f(x) =bfor any a ∈GF(pn)∗and b ∈GF(pn)is equal to δ. Let p =3and d =3n−3. When n >1is odd, the power mapping f(x) =xdover GF(3n)was proved to be differentially 2-uniform by Helleseth, Rong and Sandberg in 1999. Fo r even n, they showed that the differential uniformity Δfof f(x)satisfies 1 ≤Δf≤5. In this paper, we present more precise results on the differential property of this power mapping. Fo r d =3n−3with even n >2, we show that the power mapping xdover GF(3n)is differentially 4-uniform when n ≡2 (mod 4) and is differentially 5-uniform when n ≡0 (mod 4). Furthermore, we determine the differential spectrum of xdfor any integer n >1.en_US
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.no*
dc.titleThe differential spectrum of a ternary power mappingen_US
dc.typeJournal articleen_US
dc.typePeer revieweden_US
dc.description.versionacceptedVersionen_US
dc.rights.holderCopyright 2020 Elsevieren_US
dc.source.articlenumber101660en_US
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode1
dc.identifier.doi10.1016/j.ffa.2020.101660
dc.identifier.cristin1890111
dc.source.journalFinite Fields and Their Applicationsen_US
dc.identifier.citationFinite Fields and Their Applications. 2020, 64, 101660.en_US
dc.source.volume64en_US


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Attribution-NonCommercial-NoDerivatives 4.0 Internasjonal
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