  We consider the level of information security provided by random linear
network coding in network scenarios in which all nodes comply with the
communication protocols yet are assumed to be potential eavesdroppers (i.e.
"nice but curious"). For this setup, which differs from wiretapping scenarios
considered previously, we develop a natural algebraic security criterion, and
prove several of its key properties. A preliminary analysis of the impact of
network topology on the overall network coding security, in particular for
complete directed acyclic graphs, is also included.
