Secondary constructions of (non)weakly regular plateaued functions over finite fields


Mesnager S., ÖZBUDAK F., Sinak A.

TURKISH JOURNAL OF MATHEMATICS, vol.45, pp.2295-2306, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2104-5
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2295-2306
  • Keywords: p-ary functions, &nbsp, plateaued functions, &nbsp, (non)weakly regular plateaued functions, secondary construction, BENT FUNCTIONS, BOOLEAN FUNCTIONS

Abstract

Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We can distinguish two kinds of constructions of plateaued functions: secondary constructions and primary constructions. The first method uses already known functions to obtain new functions while the latter do not need to use previously constructed functions to obtain new functions. In this work, the first secondary constructions of (non)weakly regular plateaued (vectorial) functions are presented over the finite fields of odd characteristics. We also introduce some recursive constructions of (non)weakly regular plateaued p-ary functions by using already known such functions. We obtain nontrivial plateaued functions from the previously known trivial plateaued (partially bent) functions in the proposed construction methods.