具有高阶代数免疫的弹性函数

具有高阶代数免疫的弹性函数 Resilient Boolean Functions with High Algebraic Immunity 张凤荣 ZHANG Fengrong1 1 first-author 胡予濮 HU Yupu1 1 田绪安 TIAN Xu’an2 2 谢敏 XIE Min1 1 高胜 GAO Sheng1 1 西安电子科技大学计算机网络与信息安全教育部重点实验室 西安电子科技大学计算机网络与信息安全教育部重点实验室 Key Laboratory of Computer Network and Information Security of Ministry of Education,Xidian University Key Laboratory of Computer Network and Information Security of Ministry of Education,Xidian University 西安通信学院 西安通信学院 Xi’an Communications Institutes Xi’an Communications Institutes 构造了一类具有一阶弹性的函数.该函数是级联4个具有一对拟线性变量的子函数得到的.给出了新函数代数次数不增加的充分必要条件,代数免疫阶不增加的必要条件.选取的初始函数不满足代数次数和代数免疫不增加的必要条件,那么得到函数和初始函数相比,代数免疫至少增加1阶,代数次数增加1次,并且具有1阶弹性. A new 1-resilient Boolean function was constructed by concatenating four subfunctions with a pair of quasilinear variables.A necessary and sufficient condition that the degree of the new Boolean function does not increase is given.A necessary condition that the algebraic immunity does not increase is proved too.The initial functions do not satisfy the necessary condition that the algebraic immunity and the degree of the new function do not increase,the new functions as compared with the initial functions increase at least 1 in algebraic immunity,1 in algebraic degree,with 1 order of resiliency. 布尔函数 代数免疫 弹性阶 非线性度 Boolean function algebraic immunity resiliency nonlinearity 10.14188/j.1671-8836.2010.02.007 TN918.1 国家自然科学基金资助项目（60833008,60503010）;国家重点基础研究发展计划（973）项目（2007CB31120） 2010-02-01 2021-04-01 2 56