一类正形置换的差分分析  

Differential Cryptanalysis of an Orthormophic Permutation

作　　者：白淑君[1] 张欣[1] 

机构地区：[1]海军计算技术研究所,北京100841

出　　处：《通信技术》2016年第7期896-901,共6页Communications Technology

摘　　要：正形置换是一类完全映射,也是一种特殊的布尔置换。阅读大量文献,探讨正形置换的构造问题和相关性质的研究现状,分析利用布尔函数簇构造的正形置换的差分转移概率能达到的最大值及最小值,给出这种构造方法所构造的n元t次正形置换的非平凡的差分转移概率P的一个共同特点,即1/2^(n-3)≤P≤(2^(t-1)-1)/2^(t-1),讨论显示这类正形置换有良好的代数次数,并且代数免疫度为1。需注意的是,为了抵抗代数攻击,这类正形置换不能直接应用到密码系统中。Orthomorphic permutation is a complete mappings, and a special Boolean permutation as well. By reading a lot of literatures, exploring the research status of structural problems and related properties of orthomorphic permutations, and analyzing the maximal and minimal values of the differential transitional probability of the orthormophic permutation constructed with Boolean functions class, the common characteristics of nontrivial differential transitional probability P of this t-degree orthormophic permutation in n variables are given, that is, 1/2^（n-3）≤ P ≤ （2^（t-）-1）/2^（t-1）.The study indicates that this orthormophic permutation is of high algebraic degree,and has an algebraic immunity of 1. However, it should be noticed that this permutation chould not be applied in cryptosystem directly for resisting algebraic attacks.

关 键 词：t次正形置换 非平凡的差分转移概率 布尔函数簇 代数次数 代数免疫阶 

分 类 号：TN918.1[电子电信—通信与信息系统]