**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.

**Category / Keywords: **foundations / Boolean function, bent function, linear function, quadratic function, homogeneous function

**Date: **received 27 Nov 2018

**Contact author: **tokareva at math nsc ru

**Available format(s): **PDF | BibTeX Citation

**Version: **20181203:030146 (All versions of this report)

**Short URL: **ia.cr/2018/1160

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