  The topological interference management (TIM) problem refers to the study of
the K-user partially connected interference networks with no channel state
information at the transmitters (CSIT), except for the knowledge of network
topology. In this paper, we study the TIM problem with confidential messages
(TIM-CM), where message confidentiality must be satisfied in addition to
reliability constraints. In particular, each transmitted message must be
decodable at its intended receiver and remain confidential at the remaining
(K-1) receivers.
  Our main contribution is to present a comprehensive set of results for the
TIM-CM problem by studying the symmetric secure degrees of freedom (SDoF). To
this end, we first characterize necessary and sufficient conditions for
feasibility of positive symmetric SDoF for any arbitrary topology. We next
present two achievable schemes for the TIM-CM problem: For the first scheme, we
use the concept of secure partition and, for the second one, we use the concept
of secure independent sets. We also present outer bounds on symmetric SDoF for
any arbitrary network topology. Using these bounds, we characterize the optimal
symmetric SDoF of all K=2-user and K=3-user network topologies.
