Internet of Things security is one of the most challenging parts of the domain. Combining strong cryptography and lifelong security with highly constrained devices under conditions of limited energy consumption and no maintenance time is extremely difficult task. This paper presents an approach that combines authentication and bootstrapping protocol (TEPANOM) with Extensible Authentication Protocol (EAP) framework optimized for the IEEE 802.15.4 networks. The solution achieves significant reduction of network resource usage. Additionally, by application of EAP header compacting approach, further network usage savings have been reached. The EAP-TEPANOM solution has achieved substantial reduction of 42% in the number of transferred packets and 35% reduction of the transferred data. By application of EAP header compaction, it has been possible to achieve up to 80% smaller EAP header. That comprises further reduction of transferred data for 3.84% for the EAP-TEPANOM method and 10% for the EAP-TLS-ECDSA based methods. The results have placed the EAP-TEPANOM method as one of the most lightweight EAP methods from ones that have been tested throughout this research, making it feasible for large scale deployments scenarios of IoT.