In cloud storage services, users store their data remotely to the cloud and realize the data sharing with others. In Electronic Health Records (EHRs) system, the cloud file might contain some sensitive information. The sensitive information should not be known to others when the cloud file is shared. Encrypting the whole shared file realizes the sensitive information hiding, but will make this shared file unable to be used by others. How to realize data sharing with sensitive information hiding in remote data integrity auditing still has not been explored up to now. In order to address this problem, this paper proposes a remote data integrity auditing scheme that realizes data sharing with sensitive information hiding. Thus, enabling public auditability 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. This paper proposes a secure cloud storage system supporting privacypreserving public auditing and extend our result to enable the TPA to perform audits for multiple users simultaneously and efficiently. In addition, it articulates performance optimization mechanisms for this scheme, and in particular present an efficient method for selecting optimal parameter values to minimize the computation costs of clients and storage service providers. It shows that the solution introduces lower computation and communication overheads in comparison with non-cooperative approaches.