In a protection system, some mechanism is needed for determining the relationship between any two users so as to be used to help the decision making requests to change access attributes. In this paper, we propose a mechanism in the partially ordered user hierarchy, instead of the tree hierarchy discussed till now, by assigning each user an interpolating polynomial constructed from the user's own id number and his fathers'. In this way, any two users' relationship can be quickly determined from evaluating their associated polynomials. Moreover, whenever a new user is added into or deleted from the user hierarchy, none or only some relevant polynomial needs to be updated, different from allover the information needs to be reconstructed as shown in the previously proposed schemes.