Abstract: The existing two-party authentication and key agreement protocols for roaming service are provably secure in the CK model, and do not resist the attack of ephemeral secrets reveal. Based on elliptic curve cryptography and identity-based cryptosystem, we propose an anonymous two-party authentication and key agreement scheme for roaming service. The new scheme, based on the Schnorr signature, achieves mutual implicit authentication by a well designed “challenge-response” signature which is similar to the one in the HMQV protocol. We extend the ID-BJM model, a widely used security model for analyzing identity-based authenticated key agreement protocols, to simulate two-party authentication and key agreement schemes for roaming service. Furthermore, we demonstrate that the new scheme is eCK secure under the extended ID-BJM model, and that the security of the new scheme can be reduced to solve (by a polynomial-time adversary) computational Diffie- Hellman problems on an elliptic curve over finite fields. Comparative analysis shows that the new scheme has stronger security, achieves resistant to ephemeral secrets reveal, needs fewer cryptography libraries, and has lower computing, communication and storage overheads. The new scheme can be used to provide secure roaming authentication for resource constrained mobile terminals in global mobility networks, Internet of things or ubiquitous networks.