The smart home is an environment, where heterogeneous electronic devices and appliances are networked together to provide smart services in a ubiquitous manner to the individuals. As the homes become smarter, more complex, and technology dependent, the need for an adequate security mechanism with minimum individuals intervention is growing. The recent serious security attacks have shown how the Internet-enabled smart homes can be turned into very dangerous spots for various ill intentions, and thus lead the privacy concerns for the individuals. For instance, an eavesdropper is able to derive the identity of a particular device/appliance via public channels that can be used to infer in the life pattern of an individual within the home area network. This paper proposes an anonymous secure framework (ASF) in connected smart home environments, using solely lightweight operations. The proposed framework in this paper provides efficient authentication and key agreement, and enables devices (identity and data) anonymity and unlinkability. One-time session key progression regularly renews the session key for the smart devices and dilutes the risk of using a compromised session key in the ASF. It is demonstrated that computation complexity of the proposed framework is low as compared with the existing schemes, while security has been significantly improved.