With the ever-increasing use of large-scale IoT networks in different sectors of the industry, it has become critical to realise seamless and secure communication between devicesi n the network. Realising secure group-communication in the IoT requires solving the problem of group-key establishment. Int his work, we solve the problem designing a new lattice-based Key Encapsulation Mechanism (KEM) for resource-constrained devices that enables the distribution of a symmetric key or any other data between all the devices in a given network. This is achieved by coupling multiple private keys to a unique public key. Moreover, we present a proof-of-concept implementation based on the GGH algorithm. The results show it is feasible to use lattice-based cryptography to allow for a seamless and secure group communications within a decentralised IoT network. It has been bench-marked against other common post-quantum constructs and proven to be more practical with respect to memory consumption and security, although considerably slower due to lack of optimisation in the implementation