有限域上遍历矩阵的特性研究  

On the Properties of the Ergodic Matrix over Finite Field

作　　者：赵永哲[1] 赵搏[1] 裴士辉[1] 

机构地区：[1]吉林大学计算机科学与技术学院,长春130012

出　　处：《数学学报（中文版）》2012年第3期457-468,共12页Acta Mathematica Sinica：Chinese Series

基　　金："十一五"国家密码发展基金资助项目(2006L014J00002)

摘　　要：对有限域上遍历矩阵的性质进行了分析,给出了有限域上遍历矩阵的计数定理,并对遍历矩阵序对(A,B)关于矩阵M的双侧幂乘集〈A〉M〈B〉的秩及基数进行了全面分析.给出了R_k(A,B)集的构成及其基数的有关定理,所得到的结论对利用遍历矩阵实现有关的公钥密码具有理论上的指导意义.We analyzed the properties of the ergodic matrix over finite field,And deduced the theorem on the number of the ergodic matrices over finite fields.We also comprehensively analyzes the rank and cardinal number of the two-side exponentiation set about the given matrix M and the ergodic matrix pair（A,B）.And given the related theorems about the structure and cardinal number of the set.The results have the important theoretical significance for constructing the public key cryptography based on the ergodic matrices.

关 键 词：有限域 遍历矩阵 遍历矩阵的双侧幂乘集 

分 类 号：O153.4[理学—数学]