分组密码S盒的代数方程  

Algebraic equations of S-box block cipher

作　　者：李伟博[1] 解永宏[1] 胡磊[1] 

机构地区：[1]中国科学院研究生院信息安全国家重点实验室,北京100049

出　　处：《中国科学院研究生院学报》2008年第4期524-529,共6页Journal of the Graduate School of the Chinese Academy of Sciences

基　　金：国家自然科学基金(60573053);863计划(2006AA01Z416)资助课题

摘　　要：研究了几种著名的分组密码体制的S盒所满足的代数方程的个数,如DES、AES、MARS、SERPENT等,分别计算出这几种分组密码的S盒从低次到高次的代数方程的个数,并把计算结果和理论极小值进行了比较.此外,还针对一类对密码分析具有特别意义的不完全代数方程研究了S盒所满足的这类不完全代数方程的个数,通过这类方程的个数,可以看到它们的S盒与随机S盒的差别.This paper focuses on the number of algebraic equations, which describe the S-boxes of several famous block ciphers such as DES, AES, MARS and SERPENT. We compute the number of these algebraic equations from low degree to high degree. A comparison between the number of these equations and the theoretical minimum value is presented. Moreover, this paper introduces a kind of incomplete algebraic equations which are especially important to cryptanalysis. By comparing the number of these incomplete equations with that of a random S-box, a difference is shown between the S-boxes of these block ciphers and a random S-box.

关 键 词：分组密码 S盒 代数方程 

分 类 号：TN918[电子电信—通信与信息系统]