In the age of information and communications technology (ICT), not only collecting data but also using such data is provided in various services. It is necessary to ensure data privacy in such services while providing efficient computation and communication complexity. In this paper, we propose the first interval test designed according to the notion of online and offline phases by executing our new empty-set check. Our protocol is proved to ensure both server and client privacy. Furthermore, neither the computational complexity of a client in the online phase nor the communicational complexity from a server to a client depends on the size of the set. As a result, even in a practical situation in which one server receives requests from numerous clients, the waiting time for a client to obtain the result of an interval test can be minimized.