Paper 2024/1337

Designing bent functions using the Maiorana-McFarland secondary construction

Abstract

We utilise the Maiorana-McFarland secondary construction to generate bent functions. Our process begins with a bent function of dimension $s-r$ and results in a new function of dimension $s+r$. To achieve this, we first consider affine spaces from which we can derive bent functions. Furthermore, we derive an expression to obtain bent functions by applying the case $r=1$ multiple times. We demonstrate that the two resulting expressions are distinct. In nearly all constructions, the bent functions we obtain are balanced when the domain is restricted to vectors with an even Hamming weight. Finally, we present an example algorithm, focusing on the case where $r=2$, as well as another algorithm that employs $r=1$ twice.