In this paper, we proposed an advanced authentication structure for reducing the certificate acquisition time which is one of the factors that should be improved in a conventional wireless PKI. A conventional key exchange method simply performs the key exchange setup step based on discrete algebraic subjects. But the mutual-authentication procedure of wireless PKI for reducing authentication time uses an elliptical curve for a key exchange setup step. We simulated and compared the authentication structure proposed by Sufatrio, K. Lam[4] and proposed authentication structure in terms of the authentication time. Simulation results show that the proposed method reduces the authentication time compared to the conventional wireless PKI authentication method.