In order to solve the dynamic access control problems in a partially ordered user hierarchy, we present a novel cryptographic key assignment scheme in this paper. By using the scheme based on the discrete logarithms and polynomial interpolations, each security class will be assigned a secret key, which is used to derive his successors' secret keys efficiently. The dynamic access control problems, such as adding/deleting classes, adding/deleting relationships, and changing secret keys, are discussed. Furthermore, it is unnecessary to consider those security classes at lower levels that any user can freely change his own secret key for some security reasons.