Secret Key Agreement and Secure Omniscience of Tree-PIN Source with Linear Wiretapper

In this paper, we obtain a single-letter characterization of the wiretap secret key capacity for a large class of multiterminal source models (namely, tree-PIN models) with a linear wiretapper that can observe arbitrary linear combinations of the source. For this class of sources, we also show a duality between the problems of wiretap secret key agreement and secure omniscience, which suggests that such duality potentially holds for more general sources.