The problem of how to control access in a user hierarchy by cryptography was explored recently. However, these researchers focus on the centralized environment. This paper presents a new distributed approach to assigning cryptographic keys which enables a member of the organization to derive, from his own key, the keys of members below him in the hierarchy, and consequently to have access to information enciphered under those keys. This proposed scheme also maintains the strength of adding new security classes into a partially ordered hierarchy without affecting the existing keys.