Algebraic normal form of a bent function: properties and restrictions

Natalia Tokareva

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 function bent function linear function quadratic function homogeneous 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}
}