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dc.contributor.authorBudaghyan, Lilya
dc.contributor.authorHelleseth, Tor
dc.contributor.authorKaleyski, Nikolay Stoyanov
dc.date.accessioned2021-05-28T08:11:35Z
dc.date.available2021-05-28T08:11:35Z
dc.date.created2021-01-19T11:39:04Z
dc.date.issued2020
dc.PublishedIEEE Transactions on Information Theory. 2020, 66 (11), 7081-7087.
dc.identifier.issn0018-9448
dc.identifier.urihttps://hdl.handle.net/11250/2756784
dc.description.abstractThe binomial B(x) = x 3 +βx 36 (where β is primitive in F 2 2) over F 2 10 is the first known example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a power function, and has remained unclassified into any infinite family of APN functions since its discovery in 2006. We generalize this binomial to an infinite family of APN quadrinomials of the form x 3 +a(x 2i+1 )2 k +bx 3·2m +c(x2 i+m+2m ) 2k from which B(x) can be obtained by setting a = β, b = c = 0, i = 3, k = 2. We show that for any dimension n = 2m with m odd and 3 + m,setting(a, b, c)=(β, β 2 , 1) and i =m -2 or i = (m - 2) -1 mod n yields an APN function, and verify that for n = 10 the quadrinomials obtained in this way for i = m - 2 and i = (m - 2) -1 mod n are CCZ-inequivalent to each other, to B(x), and to any other known APN function over F 2 10.en_US
dc.language.isoengen_US
dc.publisherIEEEen_US
dc.titleA New Family of APN Quadrinomialsen_US
dc.typeJournal articleen_US
dc.typePeer revieweden_US
dc.description.versionacceptedVersionen_US
dc.rights.holderCopyright 2020 IEEEen_US
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode2
dc.identifier.doihttps://doi.org/10.1109/TIT.2020.3007513
dc.identifier.cristin1874169
dc.source.journalIEEE Transactions on Information Theoryen_US
dc.source.4066
dc.source.1411
dc.source.pagenumber7081-7087en_US
dc.identifier.citationIEEE Transactions on Information Theory. 2020, 66(11), 7081 - 7087en_US
dc.source.volume66en_US
dc.source.issue11en_US


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