This research studies the problem of enabling users to verify that the results of analytical queries such as top k they receive from a potentially untrustworthy cloud are indeed correct. Existing work shows that it is possible for a data owner to create an authentication data structure (ADS) by which a cloud can build a verification object (VO) to prove the correctness of a query result. The current technique, however, has largely ignored the computation cost in VO construction and query result verification. In this paper, we extend and integrate Intersection tree (I-tree) and Merkle hash-tree (MH-tree) to develop a new ADS called Intersection Function Merkle Hash-tree (IFMH-tree). We propose two versions of the IFMH-tree, one-signature and multi-signature, and study their performance in supporting three representative types of analytic queries, including top-k, range, and KNN queries. Our results show that the new technique outperforms the existing solution to a large extent.

Data outsourcing is a cost-effective solution for data owners to tackle issues such as large volumes of data, huge number of users, and intensive computation needed for data analysis. They can simply upload their databases to a cloud and let it perform all management works, including query processing. One problem with this service model is how query issuers can verify the query results they receive are indeed correct. This concern is legitimate because, as a third party, clouds may not be fully trustworthy, and as a large data center, clouds are ideal targets for hackers. There has been significant work on query result verification, but most consider only simple queries where query results can be attained by checking the raw data against the query conditions directly. In this paper, we consider the problem of enabling users to verify the correctness of the results of analytic queries. Unlike simple queries, analytic queries involve ranking functions to score a database, which makes it difficult to build data structures for verification purposes. We propose two approaches, namelyone-signatureandmulti-signature, and show that they work well on three representative types of analytic queries, includingtop-k,range, andKNNqueries, through both analysis and experiments.