An Efficient Construction of Secure Network Coding

ZHANG Jing-li, TANG Ping, MA Song-ya

doi:10.13371/j.cnki.chin.q.j.m.2016.01.008

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 1: 60 - 68

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.01.008

An Efficient Construction of Secure Network Coding

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1. School of Science, Henan University of Technology2. School of Mathematics and Statistics, Henan University

ZHANG Jing-li(1979-), female, native of Xuchang, Henan, a lecturer of Henan University of Technology, M.S.D., engages in the theory of Coding; TANG Ping(corresponding author)(1979-), female, native of Nanyang, Henan, a lecturer of Henan University, M.S.D., engages in the theory of coding.

Received date: 2015-10-19

Online published: 2020-11-18

Supported by

Supported by the National Natural Science Foundation of China(61201253)；

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Abstract

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.

Key words： secure network coding; global encoding kernel; local encoding kernel; wiretap; block lower triangular matrix

Cite this article

ZHANG Jing-li, TANG Ping, MA Song-ya . An Efficient Construction of Secure Network Coding[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(1) : 60 -68 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.01.008

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