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Fog architectures are currently present in many applications. Constrained devices equipped with sensors produce measurements that will be sent to a nearby gateway, called the fog. The fog verifies, aggregates and forwards them to the server. Group authentication among these devices allows them to securely accept messages of the group members, resulting in faster updates in their process. When defining a security scheme, it should be considered that edge and fog devices are susceptible to attacks. Privacy of the devices should be guaranteed, with respect to outsiders and the fog. It should be impossible to track the connection pattern of devices with different fogs, even if several fogs are captured by an attacker. Inclusion of protection against potentially malicious fogs has not yet been considered in literature, especially not for group-based communications. We present a server-controlled group authentication and key agreement scheme, executed by the fog in collaboration with the devices that it can reach. The server, assumed to be fully trusted, is responsible for the registration and authorisation of the devices and initiates the key update process, whereas the fog takes care of the secure distribution process among its members. At the end, all entities in the group are ensured to possess the correct group key. Moreover, a pairwise secret key between device and server is obtained during the process. The proposed scheme is very efficient as it relies on elliptic curve cryptography and Lagrange interpolation. No initially shared secret key material among the entities needs to be pre-stored. INDEX TERMS Edge-fog-cloud architecture, elliptic curve cryptography, group authentication, group key, Rubin logic.

Typical wearable devices use a dedicated mobile phone as relay node to transfer the collected sensor data to a server. However, such relay nodes can be faulty or inactive due to various reasons, leading to interruptions of the communication link. To mitigate this challenge, we propose a novel security-enhanced emergency situation detection system, where 3 rd party unknown mobile relays are used instead of dedicated gateways as opposed to many existing solutions for IoT healthcare applications. The proposed underlying key agreement and authentication scheme ensures anonymity and untraceability for both sensors (wearable devices) and relay nodes, and relies on symmetric key-based operations to function under resourceconstrained environments. We have also developed a prototype of the system using commercial off-the-shelf devices to verify the proposed method's validity and evaluate the performance advantage over existing approaches. Bluetooth Low Energy (BLE) communication technology is used to connect sensor nodes (wearable devices) and mobile relays. After sending medical data to the cloud server, the relay node is responsible for emergency detection and alert generation.

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