偶变元MAI旋转对称布尔函数

摘要

Algebraic immunity has been considered as one of significant properties for Boolean functions. Two constructions of rotation symmetric Boolean functions (RSBFs) in even-variable with maximum algebraic immunity( MAI) were proposed. Furthermore, the nonlinearity of constructed RSBFs were investigated under special cases of Construction 2. When n≥18 , the constructed MAI RSBFs by using Construction 3 have higher nonlinearity than that of all known MAI RSBFs in even-variable.%代数免疫度是布尔函数的一个重要密码学指标.给出了具有最大代数免疫度的偶数元旋转对称布尔函数的两种构造方法.进一步地,研究了特殊情形时所构造的旋转对称布尔函数的非线性度,当n≥18时,构造3得到的MAI旋转对称布尔函数的非线性度优于已知构造的偶数元MAI旋转对称布尔函数的非线性度.