Embodiments disclosed herein are directed to verifying query results of an untrusted server. A data owner outsources a data stream to the untrusted server, which is configured to respond to a query from a client with the query result, which is returned to the client. The data owner can maintain a vector associated with query results returned by the server and can generate a verification synopsis using the vector and a seed. The verification synopsis includes a polynomial, where coefficients of the polynomial are determined based on the seed. The data owner outputs the verification synopsis and the seed to a client for verification of the query results.