Private set intersection (PSI) allows two parties to compute the intersection of their private sets while revealing nothing except the intersection. With the development of fog computing, the need has arisen to delegate PSI on outsourced datasets to the fog. However, the existing PSI schemes are based on either fully homomorphic encryption (FHE) or pairing computation. To the best of our knowledge, FHE and pairing operations consume a huge amount of computational resource. It is therefore an untenable scenario for resource-limited clients to carry out these operations. Furthermore, these PSI schemes cannot be applied to fog computing due to some inherent problems such as unacceptable latency and lack of mobility support. To resolve this problem, we fi rst propose a novel primitive called"faster fog-aided private set intersection with integrity preserving", where the fog conducts delegated intersection operations over encrypted data without the decryption capacity. One of our technical highlights is to reduce the computation cost greatly by eliminating the FHE and pairing computation. Then we present a concrete construction and prove its security required under some cryptographic assumptions. Finally, we make a detailed theoretical analysis and simulation, and compare the results with those of the state-of-the-art schemes in two respects: communication overhead and computation overhead. The theoretical analysis and simulation show that our scheme is more e?cient and practical.