Outsourced databases provide a solution for data owners who want to delegate the task of answering database queries to third-party service providers. However, distrustful users may desire a means of verifying the integrity of responses to their database queries. Simultaneously, for privacy or security reasons, the data owner may want to keep the database hidden from service providers. This security property is particularly relevant for aggregate databases, where data is sensitive, and results should only be revealed for queries that are aggregate in nature. In such a scenario, using simple signature schemes for verification does not suffice. We present a solution in which service providers can collaboratively compute aggregate queries without gaining knowledge of intermediate results, and users can verify the results of their queries, relying only on their trust of the data owner. Our protocols are secure under reasonable cryptographic assumptions, and are robust to collusion among k dishonest service providers. [ABSTRACT FROM AUTHOR]