  While the wiretap secret key capacity remains unknown for general source
models even in the two-user case, we obtained a single-letter characterization
for a large class of multi-user source models with a linear wiretapper who can
observe any linear combinations of the source. We introduced the idea of
irreducible sources to show existence of an optimal communication scheme that
achieves perfect omniscience with minimum leakage of information to the
wiretapper. This implies a duality between the problems of wiretap secret key
agreement and secure omniscience, and such duality potentially holds for more
general sources.
