On the p-ary (cubic) bent and plateaued (vectorial) functions

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dc.contributor.authorMesnager, Sihem
dc.contributor.authorOzbudak, Ferruh
dc.contributor.authorSinak, Ahmet
dc.date.accessioned2024-02-23T13:56:03Z
dc.date.available2024-02-23T13:56:03Z
dc.date.issued2018
dc.departmentNEÜen_US
dc.description.abstractPlateaued functions play a significant role in cryptography, sequences for communications, and the related combinatorics and designs. Comparing to their importance, those functions have not been studied in detail in a general framework. Our motivation is to bring further results on the characterizations of bent and plateaued functions, and to introduce new tools which allow us firstly a better understanding of their structure and secondly to get methods for handling and designing such functions. We first characterize bent functions in terms of all even moments of the Walsh transform, and then plateaued (vectorial) functions in terms of the value distribution of the second-order derivatives. Moreover, we devote to cubic functions the characterization of plateaued functions in terms of the value distribution of the second-order derivatives, and hence this reveals non-existence of homogeneous cubic bent (and also (homogeneous) cubic plateaued for some cases) functions in odd characteristic. We use a rank notion which generalizes the rank notion of quadratic functions. This rank notion reveals new results about (homogeneous) cubic plateaued functions. Furthermore, we observe non-existence of a function whose absolute Walsh transform takes exactly 3 distinct values (one being zero). We finally provide a new class of functions whose absolute Walsh transform takes exactly 4 distinct values (one being zero).en_US
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TUBITAK)-BIDEB 2211 programen_US
dc.description.sponsorshipThe authors would like to thank the anonymous reviewers and the editor for their valuable comments and suggestions, which improved the quality of the manuscript. The third author is partially supported by the Scientific and Technological Research Council of Turkey (TUBITAK)-BIDEB 2211 program.en_US
dc.identifier.doi10.1007/s10623-017-0427-4
dc.identifier.endpage1892en_US
dc.identifier.issn0925-1022
dc.identifier.issn1573-7586
dc.identifier.issue8en_US
dc.identifier.scopus2-s2.0-85015247095en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage1865en_US
dc.identifier.urihttps://doi.org/10.1007/s10623-017-0427-4
dc.identifier.urihttps://hdl.handle.net/20.500.12452/11068
dc.identifier.volume86en_US
dc.identifier.wosWOS:000434261800013en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofDesigns Codes And Cryptographyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectVectorial Functionsen_US
dc.subjectP-Ary Bent Functionsen_US
dc.subjectP-Ary Plateaued Functionsen_US
dc.subjectCubic Functionsen_US
dc.titleOn the p-ary (cubic) bent and plateaued (vectorial) functionsen_US
dc.typeArticleen_US

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