question: Contact tracing is a critical tool in containing epidemics such as COVID-19. Researchers have carried out a lot of work on contact tracing. However, almost all of the existing works assume that their clients and authorities have large storage space and powerful computation capability and clients can implement contact tracing on their own mobile devices such as mobile phones, tablet computers, and wearable computers. With the widespread outbreaks of the epidemics, these approaches are of less robustness to a larger scale of datasets when it comes to resource-constrained clients. To address this limitation, we propose a publicly verifiable contact tracing algorithm in cloud computing (PvCT), which utilizes cloud services to provide storage and computation capability in contact tracing. To guarantee the integrity and accuracy of contact tracing results, PvCT applies a novel set accumulator-based authentication data structure whose computation is outsourced, and the client can check whether returned results are valid. Furthermore, we provide rigorous security proof of our algorithm based on the q-Strong Bilinear Diffie–Hellman assumption. Detailed experimental evaluation is also conducted on three real-world datasets. The results show that our algorithm is feasible within milliseconds of client CPU time and can significantly reduce the storage overhead from the size of datasets to a constant 128 bytes.