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Computationally lightweight and unconditionally secure key agreement protocols are very useful for secure communication in public networks. Recently, Guan et al. proposed a key agreement protocol whose security is based on the unpredictability of channel noise rather than computationally hard problems. These protocols are efficient, computationally lightweight, and unconditionally secure. However, authentication was not integrated into these protocols. In this article, we propose a new protocol with authentication capability that enables two nodes in the network to establish a secret session key for secure communication. It is more efficient, and it also preserves the lightweight and unconditional secure features of the key agreement protocols proposed by Guan et al. Therefore, it is more suitable for devices with limited computing power, such as sensors in Internet of Things (IoT).