In this paper, we introduce the first fully implemented two-way authentication security scheme for the Internet of Things (IoT) based on existing Internet standards, specifically the Datagram Transport Layer Security (DTLS) protocol. By relying on an established standard, existing implementations, engineering techniques and security infrastructure can be reused, which enables easy security uptake. Our proposed security scheme is therefore based on RSA, the most widely used public key cryptography algorithm. It is designed to work over standard communication stacks that offer UDP/IPv6 networking for Low power Wireless Personal Area Networks (6LoWPANs). Our implementation of DTLS is presented in the context of a system architecture and the scheme’s feasibility (low overheads and high interoperability) is further demonstrated through extensive evaluation on a hardware platform suitable for the Internet of Things.