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A zone-based anonymous positioning routing protocol for ad hoc networks, enabling anonymity of both source and destination, is proposed and analyzed. According to the proposed algorithm, a source sends data to an anonymity zone, where the destination node and a number of other nodes are located. The data is then flooded within the anonymity zone so that a tracer is not able to determine the actual destination node. Source anonymity is also enabled because the positioning routing algorithms do not require the source ID or its position for the correct routing. We develop anonymity protocols for both routeless and route-based data delivery algorithms. To evaluate anonymity, we propose a "measure of anonymity," and we develop an analytical model to evaluate it. By using this model, we perform an extensive analysis of the anonymity protocols to determine the parameters that most impact the anonymity level.