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

Mesnager S., ÖZBUDAK F., SINAK A.

Turkish Journal of Mathematics, cilt.45, sa.5, ss.2295-2306, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 5
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2104-5
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2295-2306
  • Anahtar Kelimeler: (non)weakly regular plateaued functions, p-ary functions, plateaued functions, secondary construction
  • Akdeniz Üniversitesi Adresli: Hayır

Özet

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.