# Smart Grid Security: A PUF-Based Authentication and Key Agreement Protocol
## 6 Cost Analysis
Following these parameters, the communication overhead of PPSG includes \(M1\) at 512 bits, \(M2\) at 512 bits, \(M3\) at 192 bits, and \(M4\) at 160 bits, totaling 1376 bits. Figure 4: Simulation of a smart home system. In contrast, the study by [19] documented a communication cost of \(1184\) bits for identical parameters. However, our analysis uncovered a possible typographical error in their report, leading to an underestimation of the communication cost. This discrepancy might have originated from the mismatched bit lengths used for values calculated via symmetric encryption, a critical factor in accurate cost estimation. Examining the findings in Figure 5 (time and byte), our comprehensive evaluation clearly showcases PPSG's superiority, as it imposes significantly lower communication overhead compared to its counterparts. This discrepancy underscores the importance of precise calculations when assessing the efficiency of communication protocols. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Protocol** & **Computations** & **Time (ms)** & **Communications (Bit)** & **Energy (mJ)** \\ \hline
[15] & \(2\times T_{\text{2 ECC}}+6\times T_{\text{ECC}}+11\times\ T_{h}\) & 211 & 1600 & 18.568 \\ \hline
[16] & \(2\times T_{\text{2 ECC}}+6\times T_{\text{ECC}}+8\times T_{h}\) & 202 & 1344 & 17.776 \\ \hline
[17] & \(2\times T_{\text{2 ECC}}+6\times T_{\text{ECC}}+5\times T_{h}\) & 193 & 1632 & 16.984 \\ \hline
[18] & \(8\times T_{\text{ECC}}+10\times T_{h}+\) & 198 & 1440 & 17.424 \\ \hline
[19] & \(8\times T_{\text{ECC}}+4\times T_{\text{Es}}+19\times T_{h}\) & 240 & 2912 & 21.12 \\ \hline
[20] & \(8\times T_{h}+T_{\text{PUF}}+T_{\text{F}_{E,REC}}+3\times\) & 198 & 1408 & 17.414 \\ \hline
[21] & \(10\times T_{h}+4\times T_{\text{SE}}+7\times T_{\text{ECC}}\) & 205 & 1536 & 18.034 \\ \hline
[23] & \(11\times T_{h}+T_{\text{PUF}}+T_{\text{F}_{E,GEN}}+\) & 156 & 896 & 13.728 \\ \hline
[25] & \(9\times T_{h}+T_{\text{PUF}}+6\times T_{\text{ECC}}\) & 156 & 1408 & 13.728 \\ \hline
[32] & \(16\times T_{h}+1\times T_{\text{SE}}+3\times T_{\text{ECC}}+\) & 180 & 1664 & 15.835 \\ \hline
**PPSG** & \(8\times T_{h}+6\times T_{\text{ECC}}+1\times T_{\text{PUF}}\) & 153 & 1376 & 13.468 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Cost comparison of the related protocols and PPSG. Figure 5: Computation and communication comparison of PPSG versus related protocols [15; 16; 17; 18; 23; 25; 32]. Regarding computational complexity, \(SM_{i}\) involves four hash function calls (\(T_{h}\)), three ECC scalar multiplications (\(T_{ECC}\)), and one PUF invocation (\(T_{PUF}\)) during its operation. On the other hand, \(NAN_{j}\) performs four hash function calls and three ECC scalar multiplications (\(T_{ECC}\)). Consequently, the total computational cost for the login and key agreement phase in PPSG amounts to \(6\times T_{ECC}+1\times T_{PUF}+8\times T_{h}\). As per our analysis, the key agreement session within PPSG demonstrates remarkable efficiency, completing in a mere 153 ms, establishing its position as the fastest protocol among those under comparison. Energy consumption can be limited by the formula \(Ec=V_{max}.I_{max}.T_{c}\), where \(Ec\) represents energy consumption, \(I_{max}\) stands for maximum consumed current, \(V_{max}\) represents the upper limit of working voltage, and \(Tc\) signifies the cumulative computational time essential for session key sharing. Based on the specifications outlined in the ATmega328P datasheet [43], the maximum operational power, denoted as \((V.I)\), for the ATmega328P stands at 14 mA \(\times\) 5.5 V = 77 mW under active mode with a clock speed of 16 MHz. The energy measurement of PPSG on the Arduino board is depicted in Figure 6. In addition, the energy efficiency of PPSG was compared with other schemes, as illustrated in Figure 7. These findings reveal that the energy consumption for a PPSG session is notably lower compared to other schemes. LAS-SG [21], operating as a lightweight protocol, involves the transmission of only two messages totaling 205 bits.