Abstract: Focusing on the algebraic immunity of Boolean function and its demands of construction, a recursive construction method to increase algebraic immunity of Boolean functions is proposed. In this method, the cascade properties of Boolean functions are used and a Boolean function with proper algebraic degree is selected. Meanwhile, the inference that the algebraic immunity of constructed Boolean functions is higher than the original one is proved. Also, through the above method, balanced Boolean functions with optimum algebraic immunity can be obtained. At the end, an example is given.

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

摘要： 针对密码学中布尔函数的代数免疫性和构造需求，通过选取适当次数的布尔函数，利用布尔函数的级联性质，提出了一种提高布尔函数代数免疫阶的递归构造法；同时证明了该构造法中所构造的布尔函数比原布尔函数的代数免疫阶高，利用该方法可以递归构造具有最优代数免疫阶平衡布尔函数，最后给出了一个具体实例。

关键词: 布尔函数, 代数标准型, 代数免疫阶