Polynomial Time Algorithm for the Two-Side Exponentiation Problem about Ergodic Matrices over Finite Field  

作　　者：GU Chunsheng JING Zhengjun YU Zhiming 

机构地区：[1]School of Computer Engineering, Jiangsu Teachers University of Technology, Changzhou 213001, Jiangsu, China [2]School of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, Anhui, China

出　　处：《Wuhan University Journal of Natural Sciences》2012年第3期233-237,共5页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (70671096);Jiangsu Teachers University of Technology (KYY08004,KYQ09002)

摘　　要：By using the minimal polynomial of ergodic matrix and the property of polynomial over finite field,we present a polynomial time algorithm for the two-side exponentiation problem about ergodic matrices over finite field （TSEPEM）,and analyze the time and space complexity of the algorithm.According to this algorithm,the public key scheme based on TSEPEM is not secure.By using the minimal polynomial of ergodic matrix and the property of polynomial over finite field,we present a polynomial time algorithm for the two-side exponentiation problem about ergodic matrices over finite field （TSEPEM）,and analyze the time and space complexity of the algorithm.According to this algorithm,the public key scheme based on TSEPEM is not secure.

关 键 词：ergodic matrix characteristic polynomial finite field public key cryptography 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]