Paper 2018/1160
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.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Boolean functionbent functionlinear functionquadratic functionhomogeneous function
- Contact author(s)
- tokareva @ math nsc ru
- History
- 2018-12-03: received
- Short URL
- https://ia.cr/2018/1160
- License
-
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},
url = {https://eprint.iacr.org/2018/1160}
}
