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In hostile environments, the enemy can launch traffic analysis against interceptable routing information embedded in routing messages and data packets. Allowing adversaries to trace network routes and infer the motion pattern of nodes at the end of those routes may pose a serious threat to covert operations. We propose ANODR, an anonymous on-demand routing protocol for mobile ad hoc networks deployed in hostile environments. We address two closely related problems: For route anonymity, ANODR prevents strong adversaries from tracing a packet flow back to its source or destination; for location privacy, ANODR ensures that adversaries cannot discover the real identities of local transmitters. The design of ANODR is based on "broadcast with trapdoor information", a novel network security concept which includes features of two existing network and security mechanisms, namely "broadcast" and "trapdoor information". We use simulations and implementation to validate the effectiveness of our design.