Innovative medical applications based on networked implants foster the development of in-body communication technologies. Among the in-body communication technologies that are being considered, fat intra-body communication (Fat-IBC) is a very recent approach. Its main advantage lies in its higher data rate compared to earlier approaches based on capacitive and galvanic coupling. However, Fat-IBC faces privacy-, security-, as well as safety-related attacks. In this paper, we discuss security and privacy concerns about Fat-IBC, as well as corresponding countermeasures. Furthermore, we present our secure protocol stack for Fat-IBC and suggest directions for future research.