For secure communications in public network environments, various three-party authenticated key exchange (3PAKE) protocols are proposed to provide the transaction confidentiality and efficiency. In 2008, Chen et al. proposed a round-efficient 3PAKE protocol to provide the computation and communication efficiency for user authentication and session key exchange. However, we discover that the computation costs and communication loads of their protocol are still high so that it cannot be applied to mobile communications. Therefore, we propose an efficient three-party authenticated key exchange protocol based upon elliptic curve cryptography for mobile-commerce environments. Because the elliptic curve cryptography is used, the proposed 3PAKE protocol has low computation costs and light communication loads. Compared with Chen et al.?s protocol, the proposed protocol is more suitable and practical for mobile-commerce environments.
