Security for Wiretap Networks via Rank-Metric Codes

The problem of securing a network coding communication system against a wiretapper adversary is considered. The network implements linear network coding to deliver $n$ packets from source to each receiver, and the wiretapper can eavesdrop on $\mu$ arbitrarily chosen links. A coding scheme is proposed that can achieve the maximum possible rate of $k=n-\mu$ packets that are information-theoretically secure from the adversary. A distinctive feature of our scheme is that it is universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying network code. In fact, even a randomized network code can be used. Our approach is based on Rouayheb-Soljanin's formulation of a wiretap network as a generalization of the Ozarow-Wyner wiretap channel of type II. Essentially, the linear MDS code in Ozarow-Wyner's coset coding scheme is replaced by a maximum-rank-distance code over an extension of the field in which linear network coding operations are performed.