This document proposes two schemes, AnonyControl and AnonyControl-F, to address privacy issues in existing access control schemes for cloud storage. AnonyControl decentralizes the central authority to limit identity leakage and achieve semi-anonymity. It also generalizes file access control to privilege control. AnonyControl-F fully prevents identity leakage and achieves full anonymity. The schemes use attribute-based encryption and a multi-authority system to securely control user access privileges without revealing identity information. Security analysis shows the schemes are secure under certain cryptographic assumptions.