Edge computing is recognized as an architecture which is well suited for the integration with the Internet of Things. A new layer of devices, also called nodes, between cloud services and end-users, can provide new services with fast response and great quality. On the other hand, new layer devices introduce more architectural and security challenges which were not yet considered. In this paper, the main focus is directed towards security issues, especially those concerning safe (re) authentication of the nodes in the already established IoT system. We defined a two-step process for a secure registration of the nodes in IoT system that includes a solution for protection against the physical replacement of the nodes with corrupted ones. Our approach uses public key cryptography based on ECCDH algorithm and communication between nodes, gateways and authentication services in the cloud.