We focus on the problem that in an ad hoc network, how to send a message securely between two users using the certificate dispersal system. In this paper, we construct two efficient certificate dispersal algorithms. We can prove that for a strongly connected graph G = (V, E) and a directed graph H= (V?, E?), new upper bounds on dispersability cost on the average number of certificates stored in one node are O(D_G+|E|/|V|) and O(pd_max+|E?|/|V?|) respectively, where D_G is the diameter of G, d_max is the maximum diameter of strongly connected components of H and p is the number of strongly connected components of H. Furthermore, we can prove our algorithms are optimal for several graph classes.