## 4 Security Analysis  
This section presents a security analysis of the proposed protocol. The analysis was conducted by applying the informal (non-mathematical) methodology to provide a direct interpretation of the supported and non-supported security properties of the protocol. According to the criteria of the secure authentication and key agreement scheme, it satisfies several security properties and can defend against common attacks. _Mutual authentication_: In the level 1 secure channel, signcrypption assures that only the intended participants with valid identities can extract the correct session key \(K\). The modified ECQV scheme guarantees the server that only the sensor node having \(ID_{N}\) and a valid CPR can derive the correct key pair \((k_{N},k_{N})\) from the implicit certificate. On the other hand, knowing the server is the only one having stored its CRPs, the sensor node can be certain that only the server (with its valid private key \(k_{S}\)) can derive the correct session key \(K\). Therefore, the proposed protocol can achieve mutual authentication even for level 1 security communication channels. 2. _Integrity_: Both parties using ECQV and SKEM schemes verify their knowledge of a key pair and a symmetric key after successfully using the keys. Thus, the content of the exchange messages can be verified after meaningful communication is conducted. Any modification of the messages will result in invalid keys and meaningless decrypted messages. 3. _Impersonation attack_: We assumed that an adversary tries to impersonate a node with \(ID_{N}\) to communicate with the server. At level 1 security, the adversary cannot compute the session key due to lacking a valid key pair \((k_{N},K_{N})\) that is bound to the \(ID_{N}\) and the PUF's response \(\mathcal{R}^{t}\). While at level 2 security, the adversary cannot replicate a PUF primitive on the node; hence, it cannot derive the valid key pair \((k_{N},K_{N})\) without knowledge of the response \(\mathcal{R}^{t}\). * _Server impersonation attack_: With one-pass SKEM, the server does not respond to the sensor node; thus, we assumed that an adversary tries to impersonate the server to issue the implicit certificate. This attack is only possible if the adversary can break into the server and retrieve the CRP database. Otherwise, the certificate issued by the adversary is meaningless and shall result in an invalid key pair \((k_{N},K_{N})\). As a result, the malicious adversary cannot impersonate either a legitimate server or an IoT device. 4. _Known session key attack_: A protocol with this property can prevent an adversary from accessing future communication to the server, even if they obtain one or more previous session keys. In the proposed protocol, the generation of a sensor node's key pair and session keys requires ephemeral random materials. Therefore, if the session keys are revealed, the future communication channels will remain secure. 5. _Node capture attack_: We assumed that an adversary has captured a node with \(ID_{N}\). Through physical memory disclosure attacks, the adversary can retrieve stored data on the node device, such as the valid key pair. As a result, the communication with the level 1 channel would be compromised. To eliminate the risk, a level 2 secure channel computes a fresh key pair (requiring new random numbers and shuffling with new CRP) for every communication session. Another approach to mitigate the risk is to periodically update the key pair by triggering the ECQV scheme after a certain period. Consequently, the proposed protocol offers two methods: (a) complete immunity to the node capture attack and (b) a method that minimizes data leaking. 6. _Perfect/partial forward secrecy_: Perfect forward secrecy is a security property that ensures that compromising the key pair of one or both entities does not lead to the compromise of past session key establishment. Partial forward secrecy refers to a situation where some, but not all, past communications remain confidential, even if the key pairs are compromised.