Data access control is an effective way to ensure the data security in the cloud.However, due to data outsourcing and untrusted cloud servers, the data access control becomes a challenging issue in cloud storage systems. Existing access control schemes are no longer applicable to cloud storage systems, because they either produce multiple encrypted copies of the same data or require a fully trusted cloud server.Ciphertext-Policy Attribute-based Encryption (CP-ABE) is a promising technique for access control of encrypted data. It requires a trusted authority manages all the attributes and distributes keys in the system.In cloud storage systems, there are multiple authorities co-exist scannot be directly applied to the access control for multi-authority cloud storage systems, due to the inefficiency of decryption and revocation.