Nowadays, we are immersed in a digital world with a huge number of sensors, and devices, connected following a great variety of typologies. Internet Protocol (IP) v6 and the standardization of the novel Internet of Things (IoT) protocols enable new services and applications. Moreover, the heterogeneity of IP and non-IP devices requires novel security techniques, allowing non-IP devices to connect over a short range with a mediator gateway, and then forming a capillary access network. Providing security and privacy is hard in the conventional Internet, and is even more challenging in the IoT because of global connectivity and heterogeneous and resource-constrained devices. In this chapter, we present the background on security algorithms for both uni- and bidirectional terminals, in the context of IoT scenarios. We review the current security and privacy solutions in the IoT, and discuss research challenges for novel IoT security and privacy solutions. Particularly, we deal with security algorithms based on a local key renewal, performed considering only the local clock time. Finally, conclusive remarks and future trends are outlined at the end of the chapter.