Abstract: This paper researches on algebraic immunity of concatenated function, uses concatenation construction method to construct Boolean function with good cryptographic properties. It discusses the algebraic immunity of Boolean function and . The upper bounds and the lower bounds of their algebraic immune degree are gotten. Meanwhile, a sufficient condition under which their upper bounds are obtained is presented respectively. Compared with other researches, the sufficient condition is easily satisfied and is effectively determined.

Key words: Boolean function, algebraic attack, concatenated function, algebraic immunity

摘要： 研究级联函数的代数免疫性，级联构造方法是构造具有良好密码学性质布尔函数的重要方法。讨论级联函数 和 的代数免疫性，得到它们代数免疫阶的上下界，并分别给出达到其上界的一个充分条件。与已有的研究相比，该充分条件在实际应用时更容易得到满足，且易于判别。

关键词: 布尔函数, 代数攻击, 级联函数, 代数免疫性

CLC Number: 

• TN918.1