向量布尔函数代数免疫性质研究

向量布尔函数代数免疫性质研究 Research on Algebraic Immunity of Vectorial Boolean Functions 王永娟 WANG Yongjuan 1 first-author 孙宇 SUN Yu 1 解放军外国语学院基础部 解放军外国语学院基础部 Department of Basis,PLA Uivercity of Foreign Language Department of Basis,PLA Uivercity of Foreign Language 通过讨论向量布尔函数零化子的代数次数,对向量布尔函数的代数免疫性质进行研究,得出其置换不变性,即在输入变量作仿射变换和输出变量作置换之后仍然保持不变,并得出向量布尔函数代数免疫与线性组合函数重量、Walsh谱以及非线性度之间的关系. By discussing the algebraic degree of the annihilators of vectorial Boolean functions,it is found that the algebraic immunity of vectorial Boolean functions remains invariant after affine transformation of the input variables.And after permutation of the output variables,the algebraic immunity also remains invariant.The relations between the Hamming weight of Component functions,the algebraic immunity,Walsh spectrum and the nonlinearity of vectorial Boolean functions were also investigated. 向量布尔函数 代数免疫 汉明重量 Walsh谱 非线性度 vectorial Boolean functions algebraic immunity Hamming weight Walsh spectrum nonlinearity 10.14188/j.1671-8836.2013.02.006 TN918.1 国家自然科学基金资助项目（60503011） 2013-02-01 2021-04-01 2 59