Development of the Internet of Things (IoT) opens many new challenges. As IoT devices are getting smaller and smaller, the problems of so-called “constrained devices” arise. The traditional Internet protocols are not very well suited for constrained devices comprising localized network nodes with tens of devices primarily communicating with each other (e.g., various sensors in Body Area Network communicating with each other). These devices have very limited memory, processing, and power resources, so traditional security protocols and architectures also do not fit well. To address these challenges the Fog computing paradigm is used in which all constrained devices, or Edge nodes, primarily communicate only with less-constrained Fog node device, which collects all data, processes it and communicates with the outside world. We present a new lightweight secure self-authenticable transfer protocol (SSATP) for communications between Edge nodes and Fog nodes. The primary target of the proposed protocol is to use it as a secure transport for CoAP (Constrained Application Protocol) in place of UDP (User Datagram Protocol) and DTLS (Datagram Transport Layer Security), which are traditional choices in this scenario. SSATP uses modified header fields of standard UDP packets to transfer additional protocol handling and data flow management information as well as user data authentication information. The optional redundant data may be used to provide increased resistance to data losses when protocol is used in unreliable networks. The results of experiments presented in this paper show that SSATP is a better choice than UDP with DTLS in the cases, where the CoAP block transfer mode is used and/or in lossy networks.