An Efficient Construction of Secure Network Coding  

作　　者：ZHANG Jing-li TANG Ping MA Song-ya 

机构地区：[1]School of Science, Henan University of Technology [2]School of Mathematics and Statistics, Henan University

出　　处：《Chinese Quarterly Journal of Mathematics》2016年第1期60-68,共9页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China(61201253)

摘　　要：Under the assumption that the wiretapper can get at most r(r < n) independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q^(-1). They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the(n- r) ×(n- r)and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction.Under the assumption that the wiretapper can get at most r（r 〈 n） independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q^（-1）. They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the（n- r） ×（n- r）and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction.

关 键 词：secure network coding global encoding kernel local encoding kernel WIRETAP block lower triangular matrix 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]