The Internet of Medical Things (IoMT) is one of the most promising applications of the newly emerging wearable devices and body-area networks. Generally, the IoMT devices are composed of lightweight facilities, which collect the health data (i.e., heart rate, body temperature, and respiratory rate) and upload them to the cloud. As the medical information is sensitive for the data owners (DOs), it is critical to ensure the integrity and confidentiality of these outsourced data. Normally, blinding (or encryption) and auditing are classical methods for achieving these goals. However, until to now, quite a few batch auditing schemes have been proposed, and they all share the following two shortcomings: 1) lacking of an efficient mechanism to identify the corrupted data files once the batch auditing task fails and 2) the communication overhead of audit phase increases linearly with the number of data files being audited or the number of data blocks being challenged. In order to overcome the above issues, in this paper, we propose an efficient batch auditing scheme based on the Lucas sequence for IoMT. To be specific, utilizing the self-query technique and polynomial commitment technique, we reduce the communication complexity of the batch auditing phase from linear to a constant scale. In addition, according to the recursion of the Lucas sequence, we design a novel search method for efficiently identifying the corrupted data files when the batch auditing task fails. The security of our scheme ensures that curious third-party auditor and cloud service provider cannot gain any real-data contents of the DO files. The detailed experiments show that our scheme is more efficient than the existing batch auditing schemes in terms of the communication overhead of the audit phase and the efficiency in identifying the corrupted files when the batch auditing task fails.INDEX TERMS Batch auditing, cloud storage, constant-size communication overhead, Lucas search, medical data integrity.