## Cryptology ePrint Archive: Report 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.

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