The goal of the third-generation mobile systems is to provide worldwide operation, enhance service capabilities, and improve performance over the second-generation mobile systems. In this paper, we propose an authentication procedure for third-generation mobile systems. The authentication procedure is a protocol suite consisting of two subprotocols: a certificate-based authentication (CBA) protocol and a ticket-based authentication (TBA) protocol. Only two parties, MS and VLR, are involved in executing our protocol. Our authentication procedure uses both public- and secret-key cryptosystems. Our authentication procedure not only provides uniform authentication across domains, but also reduces computational costs in the process of repeated authentication. We provide firm proof of our procedure's correctness.