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While many protocols for sensor network security provide confidentiality for the content of messages, contextual information usually remains exposed. Such contextual information can be exploited by an adversary to derive sensitive information such as the locations of monitored objects and data sinks in the field. Attacks on these components can significantly undermine any network application. Existing techniques defend the leakage of location information from a limited adversary who can only observe network traffic in a small region. However, a stronger adversary, the global eavesdropper, is realistic and can defeat these existing techniques. This paper first formalizes the location privacy issues in sensor networks under this strong adversary model and computes a lower bound on the communication overhead needed for achieving a given level of location privacy. The paper then proposes two techniques to provide location privacy to monitored objects (source-location privacy)-periodic collection and source simulation-and two techniques to provide location privacy to data sinks (sink-location privacy)-sink simulation and backbone flooding. These techniques provide trade-offs between privacy, communication cost, and latency. Through analysis and simulation, we demonstrate that the proposed techniques are efficient and effective for source and sink-location privacy in sensor networks.