Some applications of finite geometry for secure network coding

Journal of Mathematical Cryptology

Ligeti P.¹  Fancsali Sz. L.² 

[1] P. Ligeti, Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences;Sz. L. Fancsali, Department of Computer Science, Eötvös Loránd University, Budapest, Hungary. Email: [e-mail];

关键词: blocking sets;    multicast network coding;    secret sharing;    secure network coding;   

DOI  :  10.1515/JMC.2008.010

来源: DOAJ

【 摘 要 】

In this paper we examine the problem of linear and nonlinear secure network coding from a finite geometric point of view and give some negative and positive results if we require information theoretic security based on Cai and Yeung [N. Cai and R. W. Yeung, Secure Network Coding. Proceedings of the 2002 IEEE International Symposium on Information Theory (ISIT 2002), 2002.]. On the one hand we show that there is no universal secure network coding scheme. On the other hand we give a little improvement of the result of [N. Cai and R. W. Yeung, Secure Network Coding. Proceedings of the 2002 IEEE International Symposium on Information Theory (ISIT 2002), 2002.] for the bound of the size of the coding alphabet, and a bound similar to Feldman et al. [J. Feldman, T. Malkin, C. Stein, and R. A. Servedio, On the Capacity of Secure Network Coding. Proc. 42nd Annual Allerton Conference on Communication, Control, and Computing, 2004.]. Furthermore we present results for known linear network codings: we give some necessary and some sufficient conditions for the existence of optimal linear secure network coding, when the coding scheme is given.

【 授权许可】

Unknown