摘要： 提出一种二阶级联构造方法，通过选择恰当的参数s，使每次级联增加2个变元的同时代数免疫阶增加1、代数次数增加1。该方法在保持布尔函数弹性的同时能有效提高非线性度。在此基础上设计一类非线性度高于已知构造方法的代数免疫最优布尔函数以及一类非线性度好且满足一阶弹性的代数免疫至少次优的布尔函数，并利用二阶级联迭代构造密码学性质好的布尔函数。

关键词: 代数攻击, 代数免疫, 二阶级联, 非线性度, 弹性, 布尔函数

Abstract: This paper proposes a construction method for second-order concatenation. By choosing the proper parameter s, the degree and algebraic immunity are increased by one when two variables are added. It increases the nonlinearity effectively while holding the resiliency of the Boolean function. Based on the method, a class of functions with optimal algebraic immunity is constructed with better nonlinearity, and a class of function with at least suboptimal algebraic immunity is derived which has one-order of resiliency and good nonlinearity. The recursive method is used for constructing the cryptographic good Boolean functions.

Key words: algebraic attack, algebraic immunity, second-order concatenation, nonlinearity, resiliency, Boolean function

中图分类号: 

• TN918.1