On Secure Network Coding with Uniform Wiretap Sets

This paper studies secure unicast communication over a network with uniform wiretap sets and shows that, when network nodes can independently generate randomness, determining the secrecy capacity is at least as difficult as the k-unicast network coding problem. In particular, we show that a general k-unicast problem can be reduced to the problem of finding the secrecy capacity of a corresponding single unicast network with uniform link capacities and any one wiretap link. We propose a low-complexity linear optimization-based achievable strategy involving global random keys that can be generated anywhere in the network, and an efficient greedy algorithm that further improves achieveable rate by exploiting local random keys.