Constructing Symmetric Boolean Functions With Maximum Algebraic Immunity

Abstract

Symmetric Boolean functions with even variables <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k</i> and maximum algebraic immunity AI <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(f)</i> = <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> have been constructed in Braeken's thesis (2006). In this paper, we show more constructions of such Boolean functions including the generalization of a result and prove a conjecture raised in Braeken's thesis (2006).