Three-party authenticated key exchange protocols are designed for facilitating secure communication between two users with the assistance of an authentication server. To achieve this purpose, encrypted key exchanges are commonly adopted mechanisms to generate a shared session key for both users. However, this approach usually utilizes the server's public key to encrypt communication messages and hence raises the issue of key management. Without executing time-consuming modular exponentiation, recently, chaos-based systems have been widely employed in many security protocols. In this paper, the author will propose a chaotic map-based three-party authenticated key agreement without using the server's public key. Additionally, the computational efficiency with related mechanisms is also demonstrated. Copyright © 2014 John Wiley & Sons, Ltd.