As one fundamental data-mining problem, ANN (approximate nearest neighbor search) is widely used in many industries including computer vision, information retrieval, and recommendation system. LSH (Local sensitive hashing) is one of the most popular hash-based approaches to solve ANN problems. However, the efficiency of operating LSH needs to be improved, as the operations of LSH often involve resource-consuming matrix operations and high-dimensional large-scale datasets. Meanwhile, for resource-constrained devices, this problem becomes more serious. One way to handle this problem is to outsource the heavy computing of high-dimensional large-scale data to cloud servers. However, when a cloud server responsible for computing tasks is untrustworthy, some security issues may arise. In this study, we proposed a cloud server-aided LSH scheme and the application model. This scheme can perform the LSH efficiently with the help of a cloud server and guarantee the privacy of the client's information. And, in order to identify the improper behavior of the cloud server, we also provide a verification method to check the results returned from the cloud server. Meanwhile, for the implementation of this scheme on resource-constrained devices, we proposed a model for the real application of this scheme. To verify the efficiency and correctness of the proposed scheme, theoretical analysis and experiments are conducted. The results of experiments and theoretical analysis indicate that the proposed scheme is correct, verifiable, secure and efficient.