Ciphertext-policy attribute-based encryption (CP-ABE) provides an encrypted access control mechanism for broadcasting messages. Basically, a sender encrypts a message with an access control policy tree which is logically composed of attributes; receivers are able to decrypt the message when their attributes satisfy the policy tree. A user's attributes stand for the properties that he currently owns. A user should keep his attributes up-to-date. However, this is not easy in CP-ABE because whenever one attribute changes, the entire private key, which is based on all the attributes, must be changed. In this paper, we introduce fading function, which renders attributes "dynamic" and allows users to update each attribute separately. We study how choosing fading rate for fading function affects the efficiency and security.We also compare our design with CP-ABE and find our scheme performs significantly better under certain circumstance.