Characterization of certain types of r-plateaued functions

Jong Yoon Hyun, Jungyun Lee, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

Abstract

We study a subclass of p-ary functions in n variables, denoted by A n , which is a collection of p-ary functions in n variables satisfying a certain condition on the exponents of its monomial terms. Firstly, we completely classify all p-ary (n − 1)-plateaued functions in n variables by proving that every (n − 1)-plateaued function should be contained in A n . Secondly, we prove that if f is a p-ary r-plateaued function contained in A n with deg f > 1 + n−r 4 (p −1), then the highest degree term of f is only a single term. Furthermore, we prove that there is no p-ary r-plateaued function in A n with maximum degree (p − 1) n−r 2 + 1. As application, we partially classify all (n − 2)-plateaued functions in A n when p = 3, 5, and 7, and p-ary bent functions in A 2 are completely classified for the cases p = 3 and 5.

Original languageEnglish
Pages (from-to)1469-1483
Number of pages15
JournalJournal of the Korean Mathematical Society
Volume55
Issue number6
DOIs
StatePublished - 2018

Keywords

  • Bent function
  • Cryptographic function
  • Plateaued function

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