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Privacy is needed in ad hoc networks. An ad hoc on-demand position-based private routing algorithm, called AO2P, is proposed for communication anonymity. Only the position of the destination is exposed in the network for route discovery. To discover routes with the limited routing information, a receiver contention scheme is designed for determining the next hop. Pseudo identifiers are used for data packet delivery after a route is established. Real identities (IDs) for the source nodes, the destination nodes, and the forwarding nodes in the end-to-end connections are kept private. Anonymity for a destination relies on the difficulty of matching a geographic position to a real node ID. This can be enforced by the use of secure position service systems. Node mobility enhances destination anonymity by making the match of a node ID with a position momentary. To further improve destination privacy, R-AO2P is proposed. In this protocol, the position of a reference point, instead of the position of the destination, is used for route discovery. Analytical models are developed for evaluating the delay in route discovery and the probability of route discovery failure. A simulator based on ns-2 is developed for evaluating network throughput. Analysis and simulation results show that, while AO2P preserves communication privacy in ad hoc networks, its routing performance is comparable with other position-based routing algorithms.