有限域上遍历矩阵的特性研究

On the Properties of the Ergodic Matrix over Finite Field

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.