Rijndael S-box仿射运算研究  

Affine transformation observation on Rijndael S-box

作　　者：刘景美[1] 韦宝典[2] 王新梅[1] 

机构地区：[1]西安电子科技大学计算机网络与信息安全教育部重点实验室,陕西西安710071 [2]中山大学信息科学与技术学院,广东广州510275

出　　处：《西安电子科技大学学报》2005年第1期94-97,129,共5页Journal of Xidian University

基　　金：国家973项目(G1999035804);"十五"国家密码发展基金资助项目;国家863项目(2002AA143021)

摘　　要：证明了有限域上q 多项式、n阶矩阵和线性函数间的等价关系;然后通过证明有限域上同一线性函数在严格不同基下对应不同矩阵,扩展出一种通用的方法快速确定有限域上线性函数和n阶矩阵间的线性关系;提出了有限域上q 多项式和n阶矩阵相互确定的一种新方案,从本质上解释了RijndaelS box代数表达式的简洁性.First, a proof of the equivalence is presented among the q-polynomials, matrices of order n and linear functions over finite fields. And then based on the observation that one linear function will have distinct matrix forms under different bases, a generic scheme is extended to determine the relationship between the linear functions and matrices of order n over a finite field quickly. As another important contribution, a new scheme is also designed to determine their linear relation, with the advantage of full generality over available schemes. Finaly the essential reason why the algebraic expression for the Rijndael S-box is so simple is given.

关 键 词：AES RIJNDAEL S-BOX 有限域 q-多项式 

分 类 号：TN309.2[电子电信—物理电子学]