Despite exciting progress on cryptography, secure and efficient query processing over outsourced data remains an open challenge. We develop a communication-efficient and information-theoretically secure system, entitled Obscure for aggregation queries with conjunctive or disjunctive predicates, using secret-sharing. Obscure is strongly secure (i.e., secure regardless of the computational-capabilities of an adversary) and prevents the network, as well as, the (adversarial) servers to learn the user's queries, results, or the database. In addition, Obscure provides additional security features, such as hiding access-patterns (i.e., hiding the identity of the tuple satisfying a query) and hiding query-patterns (i.e., hiding which two queries are identical). Also, Obscure does not require any communication between any two servers that store the secret-shared data before/during/after the query execution. Moreover, our techniques deal with the secret-shared data that is outsourced by a single or multiple database owners, as well as, allows a user, which may not be the database owner, to execute the query over secret-shared data. We further develop (non-mandatory) privacy-preserving result verification algorithms that detect malicious behaviors, and experimentally validate the efficiency of Obscure on large datasets, the size of which prior approaches of secret-sharing or multi-party computation systems have not scaled to.