# A Blockchain-Assisted Security Protocol for Group Handover of MTC Devices in 5G Wireless Networks
## 7 Performance Evaluation
### Communication Cost  
The communication costs for \(n\) MTCDs to perform handover authentication by the BSPGH scheme are evaluated and compared with the other three protocols. The communication costs include propagation time and transmission time. The propagation time is determined by the distance between the transmitter and the receiver and the propagation speed over the wireless communication channel, which is approximately \(3\times 10^{8}\) m/s. It is assumed that the radius of a cell is 200 m, and the data packets sent by an MTCD would take 200 m to propagate to the gNB at a speed of \(3\times 10^{8}\) m/s. According to the 3 GPP standard on 5G communication, the downlink data rate for the urban general area scenario is 50 Mbps, and the uplink data rate is 25 Mbps [29]. In Table 3, \"Amount of Information\" refers to the total amount of data transmitted during the communication process. \(T_{\text{t}}\) and \(T_{\text{p}}\) represent transmission delay and propagation delay, respectively. \"Up\" and \"Down\" denote uplink and downlink data transmission. Therefore, we compare them separately. When calculating communication costs, we consider only the authentication phases during the handover, including the first MTCD handover authentication, group handover authentication.  
Figure 7 demonstrates that when there is a large number of group MTCDs, the proposed BSPGH scheme exhibits superior performance in terms of communication overhead compared to the PPHAP and the NASS scheme. This advantage is attributed to the reduced information exchanged between MTCDs and gNBs in our protocol, leading to enhanced  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Protocol** & \(T_{MTCD}\) & \(T_{gNB}\) & \(T_{MTCD}\)(\(\mu\)s) & \(T_{gNB}\)(\(\mu\)s) \\ \hline
5G-AKA & \(4 nT_{H}\) & \(2 nT_{H}\) & \(0.084n\) & \(0.042n\) \\ \hline PPHAP & \(3n(T_{A}+T_{H})\)-\(2T_{H}\) & \((2T_{H}+3T_{A})\) n-\(T_{H}\) & \(0.123n-0.042\) & \(0.102n-0.021\) \\ \hline NASS & \(nT_{RW}\) & \(nT_{H}+2T_{E}+T_{RW}\) & \(1.445n\) & \(0.021n+2.775\) \\ \hline BSPGH & \(n(4T_{H}+2T_{PM})\) & \((3n+3)T_{H}+(3n+5)T_{PM}+3 nT_{PA}\) & \(0.486n\) & \(0.669n+1.068\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Computational costs of different protocols.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Protocol** & **Link** & **Amount of Information (bits)** & \(T_{\text{t}}\) (\(\mu\)s) & \(T_{\text{p}}\) (\(\mu\)s) \\ \hline
5G-AKA & Up & 128n & 5.12n & 0.67n \\ \hline  & Down & 768n & 15.36n & 0.67n \\ \hline PPHAP & Up & 608n \(-\) 160 & 24.32n \(-\) 6.4 & 0.34n \(+\) 1.068 \\ \hline  & Down & 800n \(+\) 448 & 16n \(+\) 8.96 & 1.01n \(+\) 0.34 \\ \hline NASS & Up & 512n \(+\) 288 & 20.48n \(+\) 11.52 & 0.67n \\ \hline  & Down & 832n \(+\) 832 & 16.64n \(+\) 16.64 & 0.67n \\ \hline BSPGH & Up & 768n \(+\) 64 & 30.72n \(+\) 2.56 & 0.67(n \(+\) 1) \\ \hline  & Down & 128n \(+\) 1824 & 2.56n \(+\) 36.48 & 0.67(n \(+\) 1) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Communication costs of different protocols.  
efficiency. In contrast, the communication overhead of the 5G-AKA scheme is lower, but it suffers from a lot of security vulnerabilities. Overall, the results indicate the better performance achieved by the BSPGH scheme.