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Mobile peer-to-peer networks (MOPNETs) have become popular applications due to their ease of communication and resource sharing patterns in unfixed network infrastructures. As privacy and security are coming under increasing attention, many mobile and ad hoc network protocols attempt to provide mutual anonymity for users. Most existing anonymous designs, however, are path based, where the anonymous communications are achieved via a predetermined path. Such a design suffers from unreliable delivery and high processing overheads and is not practical. We propose a scalable secret-sharing-based mutual anonymity protocol, termed PUZZLE, which enables anonymous query issuance and file delivery for MOPNETs in ad hoc environments by employing Shamir's secret sharing scheme. We present the design of PUZZLE, analyze its degree of security and anonymity, and evaluate its performance by comprehensive trace-driven simulations. Experimental results show that compared with previous designs, PUZZLE achieves mutual anonymous communications with a lower cryptography processing overhead and higher degree of anonymity.