Secure relay and jammer selection for physical-layer security is studied in a wireless network with multiple intermediate nodes and eavesdroppers, where each intermediate node either helps to forward messages as a relay, or broadcasts noise as a jammer. We derive a closed-form expression for the secrecy outage probability (SOP), and we develop two relay and jammer selection methods for SOP minimization. In both methods a selection vector and a corresponding threshold are designed and broadcast by the destination to ensure each intermediate node knows its own role while knowledge of the relay and jammer set is kept secret from all eavesdroppers. Simulation results show the SOP of the proposed methods are very close to that obtained by an exhaustive search, and that maintaining the privacy of the selection result greatly improves the SOP performance.