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Location-based services (LBS) are available on a variety of mobile platforms like cellphones, PDA''s, etc. and an increasing number of users subscribe to and use these services. One of the basic privacy issues with LBS is that a user may not necessarily want to disclose their own location whenever they inquire about the location of places of interest to them e.g., nearest gas station, restaurant etc. The privacy aspect of LBS has received attention recently with a number of privacy-preserving methodologies being proposed for the client-server model where a querying client requests a location-based server to return some location that is of interest to it without revealing its own location to the server. In this paper, we consider privacy issues in the peer-to-peer model of LBS, where a group of users jointly compute a common location of interest to them such as a restaurant where they could all meet. In such scenarios, all peers in the group would like to jointly find a common location but might not want to reveal their individual locations to each other due to trust issues. We model this problem in the secure multi-party computation framework of cryptography and present a solution where all the peers can jointly compute a common location without the need for any user to reveal its individual location to anyone else. To this end, we present two privacy-preserving models and experimentally evaluate the performance of each of them.