How to Construct Strongly Secure Network Coding Scheme

We say that a network coding scheme is strongly 1-secure if a source node s can multicast n field elements {m(1), ... , m(n)} to a set of sink nodes {t(1), ... , t(q)} in such a way that any single edge leaks no information on any S subset of {m(1), ... , m(n)} with vertical bar S vertical bar = n - 1, where n = min(ti) max-flow(s, t(i)) is the maximum transmission capacity. We also say that a strongly h-secure network coding scheme is strongly ( h + 1)-secure if any h + 1 edges leak no information on any S subset of {m(1), ... , m(n)} with vertical bar S vertical bar = n - ( h + 1). In this paper, we show the first explicit algorithm which can construct strongly k-secure network coding schemes. In particular, it runs in polynomial time for fixed k.