Database outsourcing is unavoidable in the near future. In the scenario of data stream outsourcing, the data owner continuously publishes the latest data and associated authentication information through a service provider. Clients may register queries to the service provider and verify the result's correctness, utilizing the additional authentication information. Research on On-line Stream Analytics (OLSA) is motivated by extending the data cube technology for higher multi-level abstraction on

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... the low-level-abstracted data streams. Existing work on OLSA fails to consider the issue of database outsourcing, while previous work on stream authentication does not support OLSA. To close this gap and solve the problem of OLSA query authentication while outsourcing data streams, we propose MDAHRB and MDAHB, two multi-dimensional authentication approaches. They are based on the general data model for OLSA, the stream cube. First, we improve the data structure of the H-tree, which is used to store the stream cube. Then, we design and implement two authentication schemes based on the improved H-trees, the HRB-and HB-trees, in accordance with the main stream query authentication framework for database outsourcing. Along with a cost models analysis, consistent with state-of-the-art cost metrics, an experimental evaluation is performed on a real data set. It exhibits that both MDAHRB and MDAHB are feasible for authenticating OLSA queries, while MDAHRB is more scalable.