  This paper investigates the problem of secure communication in a wireline
noiseless scenario where a source wishes to communicate to a number of
destinations in the presence of a passive external adversary. Different from
the multicast scenario, where all destinations are interested in receiving the
same message, in this setting different destinations are interested in
different messages. The main focus of this paper is on characterizing the
secure capacity region, when the adversary has unbounded computational
capabilities, but limited network presence. First, an outer bound on the secure
capacity region is derived for arbitrary network topologies and general number
of destinations. Then, secure transmission schemes are designed and analyzed in
terms of achieved rate performance. In particular, for the case of two
destinations, it is shown that the designed scheme matches the outer bound,
hence characterizing the secure capacity region. It is also numerically
verified that the designed scheme matches the outer bound for a special class
of networks with general number of destinations, referred to as combination
network. Finally, for an arbitrary network topology with general number of
destinations, a two-phase polynomial time in the network size scheme is
designed and its rate performance {is} compared with the capacity-achieving
scheme for networks with two destinations.
