In this paper we consider secret communication between two special nodes ("source" and "destination") in a wireless network with authenticated relays: the message communicated to the destination is to be kept information-theoretically (unconditionally) secret from any eavesdropper within a class. A public feedback channel from the destination to all nodes may or may not be available. We focus on a one-relay network with a bottleneck link between the source and the relay to illustrate the ideas. For this particular network, we derive the rate-equivocation capacity region when the public feedback channel is absent, and an achievable secret key rate when public feedback is present.