拟Bent函数的代数免疫性  

Algebraic immunity of Quasi-Bent functions

作　　者：刘志高[1] 

机构地区：[1]马鞍山职业技术学院,安徽马鞍山243031

出　　处：《武汉工程大学学报》2014年第11期75-78,共4页Journal of Wuhan Institute of Technology

基　　金：2014安徽省高校优秀青年人才支持计划资助

摘　　要：基于布尔函数非线性度与代数免疫度之间的关系,利用Walsh谱、组合数等工具得到了判定拟Bent函数存在低次零化子的一个充分条件,它不需要利用Walsh循环谱或代数正规形来判定,非常直观有效.据此充分条件可知,在变元个数确定的情况下,拟Bent函数的阶数越高,其存在低次零化子的可能性越大,抵抗代数攻击的能力越弱.反之,在阶数确定的情况下,拟Bent函数的变元个数越大,其存在低次零化子的可能性越小,抵抗代数攻击的能力越强.Based on the relationship betw een the nonlinearity and the algebraic immunity of Boolean functions ,a sufficient condition for judging the quasi bent function existing low degree annihilators is given by Walsh spectrum and combination tools ,w hich need not to use the Walsh cyclic spectrum or al‐gebraic normal form to judge ,so it is very intuitive and effective .It concludes that the order of quasi bent functions is higher ,the possibility of low degree annihilators is bigger and the ability to resist alge‐braic attack is weaker in the case of variable number under certain ;on the other hand ,the variable number of quasi bent functions is bigger ,the possibility of low degree annihilators is smaller and the a‐bility to resist algebraic attack is stronger in the case of the order numbers under certain conditions .

关 键 词：布尔函数 代数攻击 Walsh循环谱 

分 类 号：TN918.1[电子电信—通信与信息系统] O158[电子电信—信息与通信工程]