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Nowadays, anyone carrying a mobile device can enjoy the various location-based services provided by the Internet of Things (IoT). 'Aggregate nearest neighbor query' is a new type of location-based query which asks the question, 'what is the best location for a given group of people to gather?' There are numerous, promising applications for this type of query, but it needs to be done in a secure and private way. Therefore, a trajectory privacy-preserving scheme, based on a trusted anonymous server (TAS) is proposed. Specifically, in the snapshot queries, the TAS generates a group request that satisfies the spatial K-anonymity for the group of users—to prevent the location-based service provider (LSP) from an inference attack—and in continuous queries, the TAS determines whether the group request needs to be resent by detecting whether the users will leave their secure areas, so as to reduce the probability that the LSP reconstructs the users' real trajectories. Furthermore, an aggregate nearest neighbor query algorithm based on strategy optimization, is adopted, to minimize the overhead of the LSP. The response speed of the results is improved by narrowing the search scope of the points of interest (POIs) and speeding up the prune of the non-nearest neighbors. The security analysis and simulation results demonstrated that our proposed scheme could protect the users' location and trajectory privacy, and the response speed and communication overhead of the service, were superior to other peer algorithms, both in the snapshot and continuous queries. [ABSTRACT FROM AUTHOR]