Authentication of Multi-Dimensional Top-$K$ Query on Untrusted Server

Consider a database where each record has multiple attributes. An untrusted server is in charge of processing queries over this database, and we want to provide a mechanism for users to verify the correctness of their query results. Here each query, referred to as a multi-dimensional top-$k$ query, retrieves $k$ records whose output with user-supplied ranking function is among top $k$. Multi-dimensional top-$k$ query is widely used in real applications. However, as the traditional query authentication methods cannot be directly deployed on multi-dimensional top-$k$ query, it is still a challenging problem to authenticate the multi-dimensional top-$k$ query results. In this paper, we propose an authentication solution to support multi-dimensional top-$k$ query based on signature chain. By using signature chain for each record and its successors on each dimension, our solution allows users to efficiently verify the soundness and completeness of multi-dimensional top-$k$ query results. Through theoretical analysis and simulation, we demonstrate the effectiveness of our proposed solution.