Two-party key exchange protocol is a mechanism in which two parties communicate with each other over an insecure channel and output the same session key. A key exchange protocol that is secure against an active adversary who can control and modify the exchanged messages is called authenticated key exchange (AKE) protocol. LaMacchia, Lauter and Mityagin presented a strong security definition for public key infrastructure (PKI) based two-pass protocol, which we call the extended Canetti-Krawczyk (eCK) security model, and some researchers have provided eCK-secure AKE protocols in recent years. However, almost all protocols are provably secure in the random oracle model or rely on a special implementation technique so-called the NAXOS trick. In this paper, we present a PKI-based two-pass AKE protocol that is secure in the eCK security model. The security of the proposed protocol is proven without random oracles (under three assumptions), and does not rely on implementation techniques such as the NAXOS trick.