# Smart Grid Security: A PUF-Based Authentication and Key Agreement Protocol
## 3 System Model  
The infrastructure of a smart metering system is illustrated in Figure 1. As shown, an \(SM\), a \(NAN\), and a certificate authority (CA) server are the key components, and the communication between the CA and other parties is established via a secure channel. On the other hand, the \(SM\) and the \(NAN\) are connected over a public channel, which can be the weak point of this structure. Through this paper, we use the list of notations listed in Table 2.  
The proposed protocol adopts [PERSON]'s adversary model (CK-adversary model) [33], which is more robust than the commonly used Dolev-Yao (DY) adversary model [34] in many designs. In the DY-adversary model, the adversary possesses complete control over message transmission through a public channel. It can eavesdrop, delete, insert, or modify fake messages in different instances. Under the CK-adversary model, the adversary possesses all the powers of the DY model and more, enabling them to infiltrate session states and secret information, encompassing secret keys. Consequently, if these session states and secret details are exposed during a particular session, this revelation must not jeopardize the confidentiality of other involved parties, as emphasized in [35]. The CK-adversary model proves advantageous over the DY model, especially in contexts where forward secrecy is a vital protocol requirement. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Communication Cost** & **Time-Consuming** & **Method** & **Approved Attack** \\ \hline
[11] & \(\blacktriangle\) & \(\blacktriangle\) & ECC & ✓ \\
[13] & \(\blacktriangledown\) & \(\blacktriangle\) & ECC + MAC & ✓ \\
[15] & \(\blacktriangle\) & \(\blacktriangle\) & ECC & ✓ \\
[16] & \(\blacktriangledown\) & \(\blacktriangle\) & ECC & ✓ \\
[17] & \(\blacktriangle\) & \(\blacktriangledown\) & ECC & ✓ \\
[18] & \(\blacktriangledown\) & \(\blacktriangledown\) & ECC & ✓ \\
[19] & \(\blacktriangle\) & \(\blacktriangle\) & ECC & ✓ \\
[20] & \(\blacktriangledown\) & \(\blacktriangledown\) & ECC + AEAD & ✓ \\
[21] & \(\blacktriangle\) & \(\blacktriangledown\) & ECC & \(\times\) \\
[23] & \(\blacktriangledown\) & \(\blacktriangledown\) & PUF & ✓ \\
[25] & \(\blacktriangledown\) & \(\blacktriangledown\) & PUF & \(\times\) \\
[26] & \(\blacktriangle\) & \(\blacktriangledown\) & PUF & \(\times\) \\
[27] & \(\blacktriangledown\) & \(\blacktriangle\) & AES + IBE(ECC) & ✓ \\  & & & + PUF & \\
[32] & \(\blacktriangle\) & \(\blacktriangledown\) & Blockchain & \(\times\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of related work. To thwart potential attacks stemming from the exposure of secret information, we presume that every smart meter (\(SM\)) is equipped with a robust Physical unclonable function (\(PUF(.)\)). This measure is essential considering the attacker's capability to compromise a \(SM\) and extract its confidential data. Given challenges \(\mathcal{C}\
eq\mathcal{C}^{\prime}\), \(PUF(\mathcal{C})\) and \(PUF(\mathcal{C}^{\prime})\) are expected to be completely different. On the other hand, given the same challenge \(\mathcal{C}\) to \(PUF(. )\), it is expected to have the same response. However, different PUFs should return completely different responses for the same challenge with a high probability. It should be noted attempting to design such a PUF function is an active research area but out of the scope of this paper, although many proposed schemes are vulnerable to modeling attacks or machine learning attacks [36]. An example of such attempts is the proposed scheme by [37] [PERSON] et al., which is claimed to be reliable and secure against modeling attacks.