In consideration of the unbalanced wireless network whose participants have unbalanced computing power, the article analyed the security of the IDentity-based Authenticated Group Key Agreement (ID-AGKA) protocol, and pointed out that the protocol could not resist the ephemeral key leakage attack. Then because the generation of the agreement signature was improved, the safety was improved, the computational cost and communication cost was reduced effectively, so the improved protocol was more suitable for the unbalanced wireless network. Meanwhile, the protocol used a designated verifier signature, which could effectively solve the privacy problem of the signer. Moreover, in this article, the dynamic mechanism of unbalanced network group key agreement protocol was improved by powerful node making full use of the low-power nodes' computation information before users join or leave. This improvement could greatly reduce the unnecessary computation of the low-power nodes, making the new protocol more conform the actual needs. Finally, the safety of the improved Group Key Agreement (GKA) protocol was proved based on Divisible Decisional Diffie-Hellman (DDDH) assumption in the random oracle model.

With the development of Wireless Sensor Network (WSN), user authentication in WSN is a critical security issue due to their unattended and hostile deployment in the field. To improve the security of user authentication, a new provably-secure two-factor authentication key exchange scheme based on Nam's first security model was proposed. The proposed scheme was based on elliptic curve cryptography, and it achieved authentication security and user anonymity. The safety of the improved protocol was proved based on ECCDH in the random oracle model. Performance analysis demonstrates that compared to Nam's schemes, the proposal is more efficient, and it is more suited to wireless sensor networks environments.