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.
出处
《西安电子科技大学学报》
EI
CAS
CSCD
北大核心
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)
