## 1 Introduction  
In modern society, the utilization of smart devices and services has become more prevalent. These encompass a vast range of industries, including home automation, manufacturing, medicine, finance, and transportation. The Internet of things (IoT) refers to the billions of interconnected devices that are equipped with sensors and actuators that can be accessed from virtually any location in the world through the Internet. A wireless sensor network (WSN), which is a subset of an IoT network, is a network that incorporates a large number of wireless sensor nodes, wireless communication, and data processing functions to monitor, gather, and transmit information from the environment. In contrast to the Internet, the construction of wireless sensor networks relies on low-complexity communication protocols. Low-power and wide-area communication networks, such as Zigbee and LoRa, are preferable for the development of WSNs, as they satisfy the constrained conditions of small sensor nodes. As the wireless network continues to expand, these nodes are scattered over a large area and are prone not only to physical attacks but also to cyberattacks. Therefore, it is crucial to provide security measures for WSNs just as much as the security measures for the Internet. A typical wireless sensor node is equipped with a sensing device, a wireless transceiver, a power management unit, and a central computing unit. The node devices in a WSN are inherently resource constrained, especially in batteryless and energy-harvesting applications: they have limited processing speed, storage capacity, and communication bandwidth. In a typical network, the sensor nodes communicate between themselves using radio signals. The constraints limit the integration of the high-security standard protocols used among modern computers, like SSL (secure sockets layer) or TLS (transport layer security). As mentioned, long range (LoRa), which is a widely adopted network in low-power applications, is a radio modulation technology that is capable of offering long-range, low-power, and secure data transmission for IoT devices. The LoRaWAN MAC protocol specifies the regulations for LoRa and defines the standards for LoRa networking. However, despite the lightweight feature, the LoraWAN protocol still faces significant threats from malicious parties [1; 2; 3]. [PERSON] and [PERSON] [4] indicated that the flaws of LoRaWAN lie in the key management and data confidentiality. Lacking a mechanism for session key establishment enables long-term leakage of the root key due to side-channel attacks in encryption and decryption with the AES cipher block. Such potential weaknesses of LoRaWAN outweigh the lightweight feature of applying the symmetric AES-128 cipher. Several attempts were proposed to improve LoRaWAN's security measures. [PERSON] et al. [5] proposed applying the concept of the session key to update the secret key every session of communication, thus enhancing the secure communication channels between the end node and the network server. [PERSON] and [PERSON] [4] proposed applying a lightweight Rabbit cipher in the key derivation function to the root key update scheme, and hence, strengthening the security of session keys. The lightweight feature of symmetric key cryptography is an essential property that a key establishment (KE) protocol for WSNs should possess. Other proposals also tried to benefit from symmetric key cryptography and add more security properties to establish secure communication channels. For example, [PERSON] et al. [6] proposed a lightweight KE protocol that provides an authentication property. The protocol applied a Tinkerbell chaotic map, a physical unclonable function (PUF), and a one-way hash function to provide an authentication session key agreement. Similarly, [PERSON] and [PERSON] [7] proposed a mutual authentication protocol that also relies on a hash and a PUF primitive for the key exchange between IoT endpoints.