正规性和代数免疫  

Affine subspace and algebraic immunity

作　　者：王永娟[1,2] 范淑琴[1] 冀会芳[1] 韩文报[1] 

机构地区：[1]解放军信息工程大学信息工程学院,河南郑州450002 [2]解放军外国语学院,河南洛阳471003

出　　处：《解放军理工大学学报（自然科学版）》2009年第4期329-333,共5页Journal of PLA University of Science and Technology(Natural Science Edition)

基　　金：国家863计划资助项目(2006AA01Z425);国家973计划资助项目(2007CB807902);国家自然科学基金资助项目(60503011;90704003);河南省杰出青年基金资助项目(0612000100)

摘　　要：布尔函数的代数免疫性是衡量其抵抗代数攻击能力的重要指标,为快速计算布尔函数的代数免疫,进而有效实施代数攻击,利用布尔函数特征矩阵代数结构和代数次数之间的关系,首次给出了正规性与代数免疫度的制约关系。得到代数免疫度的一个上界,若n元布尔函数是k-正规的,则其代数免疫度满足AI(f)≤min{degf,n-k},且当变元个数≤5时上式等号成立。作为推论,给出了布尔函数代数免疫度为1和2时的充分条件,为判定布尔函数是否存在低次零化子提供了理论支持。The algebraic immunity of Boolean functions is an important index to determine its ability to resist algebraic attack. To caculate the algebraic immunity of Boolean functions lastly and make algebraic attack on a cipher, the relationship between the character matrix of a Boolean function and its algebraic degree was researched to get the relationship between normality and the algebraic immunity of Boolean functions. It was suggested that n variables Boolean function satisfied that AI（f）≤min {degf,n-k } if the function was k-normal. The sufficient condition under which Boolean functions algebraic immunity was 1 and 2 was obtained. The research provides some low degree. proof to ensure that a Boolean function has annilator of

关 键 词：代数攻击 流密码 仿射子空间 k-正规性 

分 类 号：TN918.1[电子电信—通信与信息系统]