This paper presents a cryptographic key assignment scheme based on both Rabin public key system and Chinese remainder theorem to solve the dynamic access control problems in a user hierarchy. Compared with the used assignment schemes, our scheme ensures the security class in the higher level can derive secret keys of the successors efficiently. The dynamic access control problems, such as adding/deleting classes, adding/deleting relationships, and changing secret keys, are considered. Moreover, without altering the other present keys in the system, each user in the hierarchy can change his own key freely for the sake of security.