Under the shared big data environment, most of the existing data auditing schemes rarely consider the authorization management of group users. Meanwhile, how to deal with the shared data integrity is a problem that needs to be pondered. Thus, in this paper, we propose a novel remote data checking possession scheme which achieves group authority management while completing the public auditing. To perform authority management work, we introduce a trusted entity – group manager. We formalize a new algebraic structure operator named authorization invisible authenticator (AIA). Meanwhile, we provide two versions of AIA scheme: basic AIA scheme and standard AIA scheme. The standard AIA scheme is constructed based on the basic AIA scheme and user information table (UIT), with advanced security and wider applicable scenarios. By virtue of standard AIA scheme, the group manager can perfectly and easily carry out authority management, including enrolling, revoking, updating. On the basis of the above, we further design a public auditing scheme for non-revoked users’ shared data. The scheme is based on identity-based encryption (IBE), which greatly reduce the necessary certificate management cost. Furthermore, the detailed security analysis and performance evaluation demonstrate that the scheme is safe and feasible.