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In this paper, we address the problem of destination anonymity for applications in mobile ad hoc networks where geographic information is ready for use in both ad hoc routing and Internet services. Geographic forwarding becomes a lightweight routing protocol in favor of the scenarios. Traditionally the anonymity of an entity of interest can be achieved by hiding it among a group of other entities with similar characteristics, i.e., an anonymity set. In mobile ad hoc networks, generating and maintaining an anonymity set for any ad hoc node is challenging because of the node mobility, consequently the dynamic network topology. We propose protocols that use the destination position to generate a geographic area called an anonymity zone (AZ). A packet for a destination is delivered to all the nodes in the AZ, which make up the anonymity set. The size of the anonymity set may decrease because nodes are mobile, yet the corresponding anonymity set management is simple. We design techniques to further improve node anonymity and reduce communication overhead. We use analysis and extensive simulation to study the node anonymity and routing performance, and to determine the parameters that most impact the anonymity level that can be achieved by our protocol.