Cloud storage has attracted more and more concern since it permits cloud users to save and employ the corresponding outsourced files at arbitrary time, with arbitrary facility and from arbitrary place. To make sure data integrality, numerous public auditing constructions have been presented. However, existing constructions mainly have built on the PKI. In these constructions, to achieve data integrality, the auditor first must authenticate the legality of PKC, which leads to a great burden for the auditor. To eliminate the verification of time-consuming certificate, in this work, we present an efficient identity-based public auditing proposal. Our construction is an identity-based data auditing system in the true sense in that the algorithm to calculate authentication signature is an identity-based signature algorithm. By extensive security evaluation and experimental testing, the consequences demonstrate that our proposal is safe and effective; it can efficiently hold back forgery attack and replay attack. Finally, compared with the two identity-based public auditing proposals, our proposal outperforms the two proposals under the condition of overall considering computational cost, communication overhead, and security strength.