On Secure Capacity of Multiple Unicast Traffic over Separable Networks

This paper studies the problem of information theoretic secure communication when a source has private messages to transmit to $m$ destinations, in the presence of a passive adversary who eavesdrops an unknown set of $k$ edges. The information theoretic secure capacity is derived over unit-edge capacity separable networks, for the cases when $k=1$ and $m$ is arbitrary, or $m=3$ and $k$ is arbitrary. This is achieved by first showing that there exists a secure polynomial-time code construction that matches an outer bound over two-layer networks, followed by a deterministic mapping between two-layer and arbitrary separable networks.