We study processing and authentication of long-running queries on outsourced data streams. In this scenario, a data owner (DO) constantly transmits its data to a service provider (SP), together with additional authentication information. Clients register continuous range queries to the SP. Whenever the data change, the SP must update the results of all affected queries and inform the clients accordingly. The clients can verify the correctness of the results using the authentication information provided by the DO. Compared to conventional databases, stream environments pose new challenges such as the need for fast structure updating, support for continuous query processing and authentication, and provision for temporal completeness. Specifically, in addition to the correctness of individual results, the client must be able to verify that there are no missing results in between updates. We face these challenges through several contributions. Since there is no previous work, we first pre...