Cloud computing opens a new stream in IT as it can provide various elastic and scalable IT services in a pay-as-you-go way, where its users can reduce the cost in their own IT infrastructure. In this way, users of cloud storage services do not physically maintain direct control over their data, which makes data security one of the major advantage of using cloud. Previous research work already allows data integrity to be verified without presence of the actual data file. When this verification is done by a trusted third party, the verification process is called as data auditing, and this third party is called an auditor. However, such schemes in existence suffer from several drawbacks .First ,the necessary authorization or authentication process is missing between the auditor and cloud service provider, means anyone can ask for challenge the cloud service provider about proof of integrity of certain file, in which the quality of the so-called `auditing-as-a-service' in risk; Second, although some of the previous work based on BLS signature which can  support fully dynamic data updates over fixed-size data blocks, they only support updates with fix-sized blocks as basic unit, which called as coarse-grained updates. As a result, every small update will cause re-computation and updating of the authenticator for whole file block, which in turn causes higher storage and communication overheads. In this paper, we provide an analysis for all possible types of fine-grained data updates and propose a scheme that can provide full support to authorized auditing and fine-grained update requests. Based on our scheme, we also propose the technique that can reduce communication overheads for verifying small updates. Theoretical analysis and experimental results show that our scheme can offer not only enhanced security and flexibility, but also significantly lower overhead for big data applications with a large number of frequent small updates, such as applications in social media and business transaction.