In a data auditing scheme, the data owner authorizes a third-party auditor (TPA) to check whether the data stored in the cloud remains intact. Researchers have given many data auditing schemes. However, there are still three significant shortcomings in these schemes. First of all, the security proofs of these schemes are completed in the random oracle model (ROM). As we all know, a scheme with provably security in ROM may be insecure in practical applications. Second, TPA in most known schemes is set to be completely reliable. However, TPA in reality may attempt to extract the data owner’s data. These schemes cannot resist the malicious behavior of TPA. Third, most known schemes require hash-to-point operations and enjoy high computation cost, so they are not suitable for computing-constrained environments. In this article, we first presented the system model and security demands for an identity-based data auditing (IBDA) scheme. We then came up with a new IBDA scheme and showed the security proofs in the standard model (SM). Finally, we made an analysis on performance for seven data auditing schemes. In our scheme, the computation cost required by TPA is a constant, independent of the number of data blocks participating in the challenge. Therefore, our scheme requires low computation cost and is suitable for computing-constrained environments.