Cloud storage services allow users to outsource their data to cloud servers to save local data storage costs. However, unlike using local storage devices, users do not physically manage the data stored on cloud servers; therefore, the data integrity of the outsourced data has become an issue. Many public verification schemes have been proposed to enable a third-party auditor to verify the data integrity for users. These schemes make an impractical assumption—the auditors have enough computation capability to bear expensive verification costs. In this paper, we propose a novel public verification scheme for the cloud storage using indistinguishability obfuscation, which requires a lightweight computation on the auditor and the delegate most computation to the cloud. We further extend our scheme to support batch verification and data dynamic operations, where multiple verification tasks from different users can be performed efficiently by the auditor and the cloud-stored data can be updated dynamically. Compared with other existing works, our scheme significantly reduces the auditor’s computation overhead. Moreover, the batch verification overhead on the auditor side in our scheme is independent of the number of verification tasks. Our scheme could be practical in a scenario, where the data integrity verifications are executed frequently, and the number of verification tasks (i.e., the number of users) is numerous; even if the auditor is equipped with a low-power device, it can verify the data integrity efficiently. We prove the security of our scheme under the strongest security model proposed by Shi et al. (ACM CCS 2013). Finally, we conduct a performance analysis to demonstrate that our scheme is more efficient than other existing works in terms of the auditor’s communication and computation efficiency.