Partially bent functions and their properties

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dc.contributor.authorÇeşmelioğlu, Ayça
dc.contributor.authorMeidl, Wilfried
dc.contributor.authorTopuzoğlu, Alev
dc.date.accessioned2021-05-15T12:40:50Z
dc.date.available2021-05-15T12:40:50Z
dc.date.issued2014
dc.departmentMühendislik ve Doğa Bilimleri Fakültesi, Temel Bilimler Bölümüen_US
dc.descriptionCesmelioglu, Ayca/0000-0001-5049-9135
dc.description.abstractA function f : F-p(n) -> F-p is called partially bent if for all a is an element of F-p(n) the derivative D(a)f(x) = f(x + a) - f(x) is constant or balanced, i.e., every value in F-p is taken on p(n-1) times. Bent functions have balanced derivatives D(a)f for all nonzero a is an element of F-p(n), hence are partially bent. Partially bent functions may be balanced and highly nonlinear, and thus have favorable properties for cryptographic applications in stream and block ciphers. Hence they are of independent interest. Partially bent functions are also used to construct new bent functions. The aim of this article is to provide a deeper understanding of partially bent functions. We collect their properties and describe partially bent functions with appropriate generalizations of relative difference sets and difference sets. The descriptions of bent functions as relative difference sets and of Hadamard difference sets in characteristic 2, follow from our result as special cases. We describe Hermitian matrices related to partially bent functions and interpret a secondary construction of bent functions from partially bent functions in terms of relative difference sets.en_US
dc.identifier.endpage38en_US
dc.identifier.isbn978-1-107-07400-2
dc.identifier.scopus2-s2.0-84953638310
dc.identifier.scopusqualityN/A
dc.identifier.startpage22en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12939/688
dc.identifier.wosWOS:000356958200003
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorÇeşmelioğlu, Ayça
dc.language.isoen
dc.publisherCambridge Univ Pressen_US
dc.relation.ispartofApplied Algebra and Number Theory: Essays in Honor of Harald Niederreiter on the Occasion of His 70Th Birthday
dc.relation.publicationcategoryKitap Bölümü - Uluslararasıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBent Functionsen_US
dc.subjectEngineeringen_US
dc.subjectDualsen_US
dc.titlePartially bent functions and their properties
dc.typeBook Part

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