  We design polynomial time schemes for secure message transmission over
arbitrary networks, in the presence of an eavesdropper, and where each edge
corresponds to an erasure channel with public feedback. Our schemes are
described through linear programming (LP) formulations, that explicitly select
(possibly different) sets of paths for key-generation and message sending.
Although our LPs are not always capacity-achieving, they outperform the best
known alternatives in the literature, and extend to incorporate several
interesting scenaria.
