Cloud computing represents a transformative paradigm that offers flexible, on-demand, and cost-effective computing resources. However, as data is outsourced to cloud servers, significant privacy concerns arise. While numerous attribute-based encryption schemes have been developed to secure cloud storage, the focus has predominantly been on data content privacy and access control, with less emphasis on privilege control and identity privacy. In this paper, we introduce a semi-anonymous privilege control scheme, Anony Control, that not only enhances data privacy but also protects user identity within existing access control frameworks. Anony Control decentralizes authority to minimize identity exposure, achieving semi-anonymity. Additionally, it extends file access control to encompass privilege control, allowing for fine-grained management of all operations on cloud data. We also present Anony Control-F, which completely prevents identity leakage and ensures full anonymity. Our security analysis confirms that both Anony Control and Anony Control-F are secure under the decisional bilinear Diffie-Hellman assumption, and our performance evaluation demonstrates the practicality of our approaches.