Constructing Boolean Functions with Maximum Algebraic Immunity

Because of the recent algebraic attacks, a high algebraic immunity is now an absolutely necessary property for Boolean functions used in stream ciphers. For a n-variable Boolean function f, the algebraic immunity AI(f) is no more than n/2. If AI(f) equals n/2, the immune of f resisting algebraic attack is optimal. In this paper, focusing on algebraic normal form and the construction requirements of Boolean function, the conditions that Boolean function f does not exists annihator with deg(f)≤m are analysed. The sufficient conditions that Boolean function f reaches the maximum algebraic immunity are obtained¡DTherefore a new class of Boolean functions with optimal algebraic immunity are constructed, and the balanceness and count of the constructed functions are discussed.