Privacy concerns in outsourced cloud databases have become more and more important recently and many efficient and scalable query processing methods over encrypted data have been proposed. However, there is very limited work on how to securely process top-k ranking queries over encrypted databases in the cloud. In this paper, we focus exactly on this problem: secure and efficient processing of top-k queries over outsourced databases. In particular, we propose the first efficient and provable secure top-k query processing construction that achieves adaptively CQA security. We develop an encrypted data structure called EHL and describe several secure sub-protocols under our security model to answer top-k queries. Furthermore, we optimize our query algorithms for both space and time efficiency. Finally, in the experiments, we empirically analyze our protocol using real world datasets and demonstrate that our construction is efficient and practical. * Amazon