CONSTRUCTING 2m-VARIABLE BOOLEAN FUNCTIONSWITH OPTIMAL ALGEBRAIC IMMUNITY BASED ON POLAR DECOMPOSITION OF $\mathbb{F}^\ast_{2^{2m}}$
Jia Zheng, Baofeng Wu, Yufu Chen, Zhuojun Liu · International Journal of Foundations of Computer Science · 2014
Constructing 2m-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field [Formula: see text] seems to be a promising approach since Tu and Deng's work. In this paper, we consider the same problem in a new way. Based on polar decomposition of the multiplicative group of [Formula: see text], we propose a new construction of Boolean functions with optimal algebraic immunity. By a slight modification of it, we obtain a class of balanced Boolean functions achieving optimal algebraic immunity, which also have optimal algebraic degree and high nonlinearity. Computer investigations imply that this class of functions also behaves well against fast algebraic attacks.