Some applications of finite geometry for secure network coding

Abstract

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 [5]. 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 [5] for the bound of the size of the coding alphabet, and a bound similar to Feldman et al. [7]. 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. © 2008 de Gruyter.