An intermediate entity can generate a necessary credential to allow two other entities to bypass the intermediate entity when establishing communications between two other entities in a computing system represented by either a directed or an undirected graph. The intermediate entity receives credentials for communications links between itself and each of the other two entities. The intermediate entity also receives a chaining parameter associated with the intermediate entity. With the two credentials and the chaining parameter, the intermediate entity can compute a necessary credential to allow communication between the other two entities. In addition, the intermediate entity can compute the necessary credential independent of a security manager during the computation operation.