Cloud computing is internet based computing which enables sharing of services. Many users place their data in the cloud. However, the fact that users no longer have physical possession of the possibly large size of outsourced data makes the data integrity protection in cloud computing a very challenging and potentially formidable task, especially for users with constrained computing resources and capabilities. So correctness of data and security is a prime concern. This article studies the

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... em of ensuring the integrity and security of data storage in Cloud Computing. Security in cloud is achieved by signing the data block before sending to the cloud. Using Cloud Storage, users can remotely store their data and enjoy the on-demand high quality applications and services from a shared pool of configurable computing resources, without the burden of local data storage and maintenance. However, the fact that users no longer have physical possession of the outsourced data makes the data integrity protection in Cloud Computing a formidable task, especially for users with constrained computing resources. Moreover, users should be able to just use the cloud storage as if it is local, without worrying about the need to verify its integrity. Thus, enabling public audit ability for cloud storage is of critical importance so that users can resort to a third party auditor (TPA) to check the integrity of outsourced data and be worry-free. To securely introduce an effective TPA, the auditing process should bring in no new vulnerabilities towards user data privacy, and introduce no additional online burden to user. In this paper, we propose a secure cloud storage system supporting privacy-preserving public auditing. We further extend our result to enable the TPA to perform audits for multiple users simultaneously and efficiently. Extensive security and performance analysis show the proposed schemes are provably secure and highly efficient.