摘要： Providing top-k query services is relevant for storage servers which collect valuable ?les/data and process queries for data owners and mobile users. However, this kind of service could incur severe security concerns, because hackers or even the managers/administrators of the servers may steal important data sets and deceive users into responding to forged or incomplete query results. Therefore, these data sets need to be preserved in privacy, and moreover, the users should have the capability to verify the authenticity and integrity of the query results. As users will demand distinct information with various preferences and time domains in the pragmatic world, the traditional top-k queries are insuf?cient to satisfy their demands. To solve the problem, we provide the functional top-k queries in multi-dimensional space, such that the users can launch queries on the conjunction and sum of the dimensions/attributes. Some recent works have studied how to preserve data privacy and/or integrity for top-k queries on data storage applications. However, these prior works are limited to traditional top-k queries in preserving data privacy and/or integrity without permitting to systematically process top-k queries over encrypted domain in multi-dimensional space and without providing an ef?ciently veri?able mechanism for the corresponding query results. In this paper, we propose an ef?cient and effective method, called SFTopk, which addresses more challenging security problems in data privacy and veri?able functional top-k queries in multi-dimensional space. From performance evaluation experiments, it is shown that our proposed method is much more ef?cient than the prior works in terms of communication overhead and computation cost.