具有最大代数免疫度函数的研究  

Study on Functions with Optimum Algebraic Immunity

作　　者：谯通旭[1] 王运兵[1] 谢上明[1] 董新锋[2] 张文政[2] 

机构地区：[1]中国电子科技集团公司第三十研究所,四川成都610041 [2]保密通信重点实验室,四川成都610041

出　　处：《通信技术》2013年第11期86-89,共4页Communications Technology

基　　金：国家自然科学基金(No.61309034)资助;四川省科技厅青年科学基金项目;中国电子科技集团创新人才项目资助~~

摘　　要：代数免疫度是私钥密码学中的重要概念。具有高代数免疫度的函数能抵抗新型攻击——代数攻击。CARLET Claude和FENG Keqin构造了具有最大代数免疫度的平衡函数及其线性等价函数,根据CARLET和FENG的构造,首先证明这类最大代数免疫度函数的数目,然后给出曹浩等人给出的定理6的简化证明,最后说明没有矩阵满足曹浩等人给出的定理7的条件(即不能用曹浩等人的方法构造具有最大代数免疫度的1阶弹性函数)。Algebraic immunity is an important notion in private-key cryptography . Functions with high al- gebraic immunity can successfully resist the new-type attack algebraic attack. CARLET Claude and FENG Keqin construct the balanced functions with optimum algebraic immunity and their linearly equiva- lent functions. In accordance with CARLET and FENG＇ s construction, the number of functions with opti- mum algebraic immunity is determined first, and then the simplified proof of theorem 6 by CAO Hao et al. is presented, finally it is pointed that there in no existence of the matrix which could satisfy the condition of theorem 7 given by CAO Hao et al.. This means that the first order resilient function with optimum alge- braic immunity couldn＇ t be usually constructed with CAO＇ s method.

关 键 词：最大代数免疫度 本原元 矩阵 弹性函数 

分 类 号：TN918.1[电子电信—通信与信息系统]