题目：Alphabet Size Reduction for Secure Network Coding: A Graph Theoretic Approach

主讲人：光炫教授

时间：2020年11月9日14：00-16：00

地址：腾讯会议ID，337 398 211

摘要：In this talk, we first talk about network coding. Then, we consider a communication network where there exist wiretappers who can access a subset of channels, called a wiretap set, which is chosen from a given collection of wiretap sets. The collection of wiretap sets can be arbitrary. Secure network coding is applied to prevent the source information from being leaked to the wiretappers. In secure network coding, the required alphabet size is an open problem not only of theoretical interest but also of practical importance, because it is closely related to the implementation of such coding schemes in terms of computational complexity and storage requirement. We develop a systematic graph-theoretic approach for improving the lower bound on the required alphabet size for the existence of secure network codes. The new lower bound thus obtained, which depends only on the network topology and the collection of wiretap sets, can be significantly smaller than the existing results. Our improved lower bound is graph-theoretical, which depends only on the network topology and the collection of the wiretap sets. Toward computing the lower bound efficiently, we introduce the concept of a primary minimum cut, by which we can bypass the complicated operations for determining the equivalence classes of wiretap sets and the domination relation among them. With this, a polynomial-time algorithm is developed for computing the lower bound. Toward developing our lower bound and the efficient algorithm for computing this bound, we have introduced/discussed various graph-theoretic concepts. Although in this paper these concepts are applied solely in the context of secure network coding, they appear to be of fundamental interest in graph theory and we expect that they will find applications in graph theory and beyond. This is a joint work with Dr. Raymond W. Yeung.

主讲人简介： 光炫博士，南开大学数学科学学院教授，博士生导师，入选“南开大学百名青年学科带头人培养计划”。2012年毕业于南开大学陈省身数学研究所，获博士学位，导师为符方伟教授。2011年1月至2012年8月在美国南加州大学从事联合培养博士，导师为张箴教授。2015年11月至2018年11月在香港中文大学网络编码研究所从事研究工作（“香江学者计划”），导师为杨伟豪教授。研究方向为信息论、编码理论与密码学；目前的研究兴趣为网络编码、网络函数计算、网络信息论。光炫博士近年来完成一部学术专著Linear Network Error Correction Coding，由德国Springer出版社出版发行；发表学术论文40余篇，其中在IEEE Trans. Inf. Theory上发表论文6篇，在IEEE J. Sel. Areas Commun.和IEEE Trans. Commun.等其他IEEE期刊上发表论文6篇。研究成果获多个国内外会议的最佳论文奖。2018年获得中国电子学会“信息论青年新星奖”、入选天津市“131创新人才计划”第二梯队人选；2016年入选“香江学者计划”；2014入选天津市“三年千人”高层次人才计划、获天津市优秀博士学位论文奖。

邀请人：文洁晶