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 |