dc.contributor.author Xia, Yongbo dc.contributor.author Zhang, Xianglai dc.contributor.author Li, Chunlei dc.contributor.author Helleseth, Tor dc.date.accessioned 2021-07-09T11:50:26Z dc.date.available 2021-07-09T11:50:26Z dc.date.created 2021-02-15T18:57:01Z dc.date.issued 2020 dc.identifier.issn 1071-5797 dc.identifier.uri https://hdl.handle.net/11250/2764059 dc.description.abstract A 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.iso eng en_US dc.publisher Elsevier en_US dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internasjonal * dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/deed.no * dc.title The differential spectrum of a ternary power mapping en_US dc.type Journal article en_US dc.type Peer reviewed en_US dc.description.version acceptedVersion en_US dc.rights.holder Copyright 2020 Elsevier en_US dc.source.articlenumber 101660 en_US cristin.ispublished true cristin.fulltext postprint cristin.qualitycode 1 dc.identifier.doi 10.1016/j.ffa.2020.101660 dc.identifier.cristin 1890111 dc.source.journal Finite Fields and Their Applications en_US dc.identifier.citation Finite Fields and Their Applications. 2020, 64, 101660. en_US dc.source.volume 64 en_US
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