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Mobile social networks extend social networks in the cyberspace into the real world by allowing mobile users to discover and interact with existing and potential friends who happen to be in their physical vicinity. Despite their promise to enable many exciting applications, serious security and privacy concerns have hindered wide adoption of these networks. To address these concerns, in this paper we develop novel techniques and protocols to compute social proximity between two users to discover potential friends, which is an essential task for mobile social networks.We make three major contributions. First, we identify a range of potential attacks against friend discovery by analyzing real traces. Second, we develop a novel solution for secure proximity estimation, which allows users to identify potential friends by computing social proximity in a privacy-preserving manner. A distinctive feature of our solution is that it provides both privacy and verifiability, which are frequently at odds in secure multiparty computation. Third, we demonstrate the feasibility and effectiveness of our approaches using real implementation on smartphones and show it is efficient in terms of both computation time and power consumption.