Access control is an essential security component of cloud computing, and hierarchical access management is of particular interest because different access privileges are granted in practice. As a solution to versatile and fine-grained hierarchical access control in cloud computing, this paper also presents a hierarchical key assignment scheme based on linear geometry. The encryption key of each class in the hierarchy is connected with a private vector and a public vector in our scheme, and the inner product of an ancestor class's private vector as well as the public variable of its decedent’s class could be used to deduce the encryption method of that descendant class. The proposed scheme is among the direct access strategies on hierarchical access control, which also means so each class at a higher level can straight derive this same encryption key of its decedent’s class without and need to iterate. In furthermore to this basic hierarchy key derivation, we propose a dynamic key management mechanism to handle possible changes in the hierarchy efficiently. Under the assumption of pseudo - random number functions, our scheme requires only light computations over a finite field by providing strong key in-distinguishability. Furthermore, the simulation demonstrates that our scheme maximises the trade-off among computation consumption as well as storage space.