Cloud computing users can use the cloud storage service remotely by enjoying various applications and services upon request from a group of cloud computing resources, all without the burden of storing data as well as maintaining it. However, cloud users can no longer possess data and this makes data integrity an important issue. Also, users should use cloud storage as if it is locally, without thinking about verifying the integrity of cloud data. To solve the problems and to provide auditing of cloud storage securely and effectively without additional burden on users, this paper proposes an efficient and secure auditing system of cloud storage that supports auditing and maintains users' privacy based on Boneh-Lynn-Shacham (BLS) signature. Besides, the proposed system worked with dynamic data integrity verification mechanisms as well. The safety and performance analysis of the system has proven the effectiveness and safety of the proposed system.