In an ad hoc network, we cannot assume a trusted certificate authority and a centralized repository that are used in ordinary Public-Key Infrastructure (PKI). Hence a PKI system of the web-of-trust type in which each node can issue certificates to others in a self-organizing manner has been studied. Although this system is useful for ad hoc networks whose topology can change, it has the problem that for authentication a node needs to find a certificate-chain to the destination node. In this paper, we formally model a web-of- trust-type PKI system, define the certificate-chain discovery problem, and propose a new distributed algorithm and its modifications that solve the problem. Furthermore, we propose a measure of communication cost, and according to the measure, we compare our algorithm with an existing method.