Abstract: Focusing on algebraic normal form and the construction requirements of Boolean function, the conditions that Boolean functionf does not exist annihator with deg(f) ≤m are analysed and the sufficient conditions satisfied by Boolean functionf with maximum algebraic immunity are obtained. Therefore a class of Boolean functions with optimal algebraic immunity are constructed, and the balanceness and count of the constructed functions are discussed.

Key words: Boolean function, algebraic normal form, algebraic immunity

摘要： 针对密码学中布尔函数的构造需求, 利用布尔函数的代数标准型, 分析了布尔函数不存在次数低于 m 的非零零化子的充分条件, 得到布尔函数达到最大代数免疫阶的条件, 从而构造了一类具有最高代数免疫阶的布尔函数, 并对所构造函数的平衡性和计数问题进行了分析。

关键词: 布尔函数, 代数标准型, 代数免疫阶