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Cloud computing has been envisioned as the next generation architecture of the IT enterprise, but there exist many security problems. A significant problem encountered in the context of cloud storage is whether there exists some potential vulnerabilities towards cloud storage system after introducing third parties. Public verification enables a third party auditor (TPA), on behalf of users who lack the resources and expertise, to verify the integrity of the stored data. Many existing auditing schemes always assume TPA is reliable and independent. This work studies the problem what if certain TPAs are semi-trusted or even potentially malicious in some situations. Actually, the authors consider the task of allowing such a TPA to involve in the audit scheme. They propose a feedback-based audit scheme via which users are relaxed from interacting with cloud service provider (CSP) and can check the integrity of stored data by themselves instead of TPA yet. Specifically, TPA generates the feedback through processing the proof from CSP and returns it to user which is yet unforgeable to TPA and checked exclusively by user. Through detailed security and performance analysis, the author's scheme is shown to be more secure and lightweight.