A method for obtaining lower bounds on the higher order nonlinearity of Boolean function

Mikhail S.  Lobanov

Paper 2013/332

A method for obtaining lower bounds on the higher order nonlinearity of Boolean function

Mikhail S. Lobanov

Abstract

Obtainment of exact value or high lower bound on the $r$-th order nonlinearity of Boolean function is a very complicated problem (especial if $r > 1$). In a number of papers lower bounds on the $r$-th order nonlinearity of Boolean function via its algebraic immunity were obtain for different $r$. This bounds is rather high for function with maximum near maximum possible algebraic immunity. In this paper we prove theorem, which try to obtain rather high lower bound on the $r$-th order nonlinearity for many functions with small algebraic immunity.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Boolean function algebraic immunity algebraic degree nonlinearity higher order nonlinearity annihilator
Contact author(s): misha_msu @ mail ru
History: 2013-06-03: received
Short URL: https://ia.cr/2013/332
License: CC BY

BibTeX

@misc{cryptoeprint:2013/332,
      author = {Mikhail S.  Lobanov},
      title = {A method for obtaining lower bounds on the higher order nonlinearity of Boolean function},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/332},
      year = {2013},
      url = {https://eprint.iacr.org/2013/332}
}