The rapid proliferation of embedded devices has led to the growth of the Internet of Things (IoT) with applications in numerous domains such as home automation, healthcare, education and agriculture. However, many of the connected devices particularly in smart homes are the target of attacks that try to exploit security vulnerabilities such as hard-coded passwords and insecure data transfer. Recent studies show that there is a considerable surge in the number of phishing attacks targeting smart homes during the COVID-19 pandemic. Moreover, many of the existing user authentication protocols in the literature incur additional computational overhead and need to be made more resilient to smart home targeted attacks. In this paper, we propose a novel lightweight and privacy-preserving remote user authentication protocol for securing smart home applications. Our approach is based on Photo Response Non-Uniformity (PRNU) to make our protocol resilient to smart home attacks such as smartphone capture attacks and phishing attacks. In addition, the lightweight nature of our solution is suitable for deployment on heterogeneous and resource constrained IoT devices. Besides, we leverage geometric secret sharing for establishing mutual authentication among the participating entities. We validate the security of the proposed protocol using the AVISPA formal verification tool and prototype it on a Raspberry Pi to analyze the power consumption. Finally, a comparison with existing schemes reveals that our scheme incurs a 20% reduction in communication overhead on smart devices. Furthermore, our proposed scheme is usable as it absolves users from memorizing passwords and carrying smart cards.