The Internet of Things (IoT) provides transparent and seamless incorporation of heterogeneous and different end systems. It has been widely used in many applications such as smart homes. However, people may resist the IOT as long as there is no public confidence that it will not cause any serious threats to their privacy. Effective secure key management for things authentication is the prerequisite of security operations. In this paper, we present an interactive key management protocol and a non-interactive key management protocol to minimize the communication cost of the things. The security analysis, numerical analysis and simulation results show that the proposed schemes are efficient and resilient to various types of attacks.