Machine to machine (M2M) communications, also called machine-type communications (MTC), has widely been utilized in applications such as telemetry, industrial, automation, and SCADA systems. The group-based MTC, especially when MTC devices belong to non-3GPP network, will face new challenge of access authentication. In this paper, we propose a group authentication and key agreement protocol, called EG-AKA, for machine-type communications combining elliptic curve Diffie-Hellman (ECDH) based on

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... P framework. Compared with conventional EAP-AKA, our protocol guarantees stronger security and provides better performance. Detailed security analysis has shown that the proposed EG-AKA protocol is secure in terms of user and group identity protection and resistance to several attacks. Furthermore, formal verification implemented in AVISPA proves that the proposed protocol is secure against various malicious attacks. Moreover, performance evaluation demonstrates its efficiency in terms of the signaling overhead, the bandwidth consumption, and the transmission cost.