The IP-based Internet of Things refers to the interconnection of smart devices in a Low-power and Lossy Network (LLN) with the Internet by means of protocols such as 6LoWPAN or CoAP. The mechanisms to protect the LLN from attacks from the Internet and provisioning of an end-to-end (E2E) secure connection are key requirements for functionalities ranging from network access to software updates. Interconnecting such resource constrained devices with high-performance machines requires new security mechanisms that cannot be covered by already known solutions. This paper describes attacks at transport layer against the LLN launched from the Internet. It also introduces approaches to ensure E2E security between two devices located in homogeneous networks using either HTTP/TLS or CoAP/DTLS by proposing a mapping between TLS and DTLS.