Generalized Construction of Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation
Shaojing Fu, Chao Li, Longjiang Qu · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2012
Because of the algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In 2011, X.Y. Zeng et al. proposed three constructions of balanced Boolean functions with maximum algebraic immunity, the constructions are based on univariate polynomial representation of Boolean functions. In this paper, we will improve X.Y. Zeng et al.' constructions to obtain more even-variable Boolean functions with maximum algebraic immunity. It is checked that, our new functions can have as high nonlinearity as X.Y. Zeng et al.' functions.