### Algebraic normal form of a bent function: properties and restrictions

Natalia Tokareva

##### Abstract

Maximally nonlinear Boolean functions in $n$ variables, where n is even, are called bent functions. There are several ways to represent Boolean functions. One of the most useful is via algebraic normal form (ANF). What can we say about ANF of a bent function? We try to collect all known and new facts related to ANF of a bent function. A new problem in bent functions is stated and studied: is it true that a linear, quadratic, cubic, etc. part of ANF of a bent function can be arbitrary? The case of linear part is well studied before. In this paper we prove that a quadratic part of a bent function can be arbitrary too.

Available format(s)
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
Boolean functionbent functionlinear functionquadratic functionhomogeneous function
Contact author(s)
tokareva @ math nsc ru
History
Short URL
https://ia.cr/2018/1160

CC BY

BibTeX

@misc{cryptoeprint:2018/1160,
author = {Natalia Tokareva},
title = {Algebraic normal form of a bent function: properties and restrictions},
howpublished = {Cryptology ePrint Archive, Paper 2018/1160},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/1160}},
url = {https://eprint.iacr.org/2018/1160}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.