Explicit criteria for construction of plateaued functions

Jong Yoon Hyun, Jungyun Lee, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Plateaued functions are very important cryptographic functions due to theirdesirable cryptographic characteristics. We find explicit criteria forthe construction of p-ary r-plateaued functions with an odd prime p. We point out that 0-plateaued functions are bent functions, and so plateaued functions generalize the notion of bent functions. We first derive an explicit form forthe Walsh-Hadamard transform of a p-ary r-plateaued function. We then obtain an upperbound on the degree of p-ary r-plateaued functions, and we classify p-ary (n-1) -plateaued functions in n variables. We also obtain explicit criteria forthe existence of p-ary r-plateaued functions. Accordingly, these results lead to improved bounds on the existence of p-ary bent functions.

Original languageEnglish
Article number7506113
Pages (from-to)7555-7565
Number of pages11
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 2016

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Plateaued function
  • Walsh-Hadamard transform
  • bent function
  • cryptographic function
  • p-ary function


Dive into the research topics of 'Explicit criteria for construction of plateaued functions'. Together they form a unique fingerprint.

Cite this