Recently, mobile networks are more and more popular in providing the most pursuing pervasive networking services. Many technologies are deployed in mobile networks, such as Universal Mobile Telecommunication System (UMTS). In these communication systems, user secrecy and privacy are important issues and should be managed seriously. To avoid security threats, many studies on authentication in the mobile networks are proposed. In 2008, Juang and Wu introduced an authentication scheme with user privacy protection in UMTS networks. It resisted and avoided many security attacks and threats, but there are still some problems, such as the incomplete defense against the impersonation attack and data with International Mobile Subscriber Identity exchanged outside home networks. In this paper, we proposed a simple and rapid authentication scheme in mobile networks. The proposal applies the Elliptic Curve Diffie–Hellman key agreement protocol to exchange the session key safely and Elliptic Curve Digital Signature Algorithm to improve the mobile security. It also deploys the temporary key mechanism to speed up the authentication while user is roaming in the mobile networks. The analysis shows that our mechanism not only improves Juang and Wu's proposal but also is a more secure and simple authentication protocol. Copyright © 2011 John Wiley & Sons, Ltd.