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Despite extensive research on cryptography, secure and efficient query processing over outsourced data remains an open challenge. We develop communication-efficient and information-theoretically secure algorithms for privacy-preserving aggregation queries using multi-party computation (MPC). Specifically, query processing techniques over secret-shared data outsourced by single or multiple database owners are developed. These algorithms allow a user to execute queries on the secret-shared database and also prevent the network and the (adversarial) clouds to learn the user's queries, results, or the database. We further develop (non-mandatory) privacy-preserving result verification algorithms that detect malicious behaviors, and experimentally validate the efficiency of our approach over large datasets, the size of which prior approaches to secret-sharing or MPC systems have not scaled to.