# Signature Split Method for a PQC-DSA Compliant with V2V Communication Standards
## 5 Discussion  
There are several main points of discussion in this section. The first is the need to apply an optimized PQC-DSA compared to the reference implementation. Based on a single packet, as shown in Table 3, the reference implementation already meets the run 5G-V2X requirement of less than 5 m/s latency. However, remote vehicles need to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Security** & **Ref** & **Correctness** & **This Work** & **Correctness** \\ \hline ECDSA (P-256) & 1 & 3.9 & ✓ & - & - \\ \hline \multirow{3}{*}{Crystals-Dilithium} & 2 & 2.8 & ✗ & 2.4 & ✓ \\ \cline{2-5}  & 3 & 5.2 & ✗ & 3.6 & ✓ \\ \cline{2-5}  & 5 & 6.1 & ✗ & 4.5 & ✓ \\ \hline \multirow{3}{*}{Falcon} & 1 & 14.3 & ✓ & 12.7 & ✓ \\ \cline{2-5}  & 5 & 38.9 & ✓ & 33.3 & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measurements including [generating key pair +“_run_remote_”+“_run_local_”] for 300 payloads (**ms/300**) on the WAVE protocol. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Security** & **Ref** & **Correctness** & **This Work** & **Correctness** \\ \hline ECDSA (P-256) & 1 & 3.9 & ✓ & - & - \\ \hline \multirow{3}{*}{Crystals-Dilithium} & 2 & 2.2 & ✓ & 1.9 & ✓ \\ \cline{2-5}  & 3 & 4.1 & ✓ & 2.4 & ✓ \\ \cline{2-5}  & 5 & 4.7 & ✓ & 3.0 & ✓ \\ \hline \multirow{3}{*}{Falcon} & 1 & 14.3 & ✓ & 12.7 & ✓ \\ \cline{2-5}  & 5 & 38.9 & ✓ & 33.3 & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measurement including [generating key pair +“_run_remote_”+“_run_local_”] for 300 payloads (**ms/300**) on C-V2X (advanced) protocol. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Security** & **Ref** & **This Work** \\ \hline ECDSA (P-256) & 1 & \(\frac{1.9}{1.6}\) & - \\ \hline \multirow{3}{*}{Crystals-Dilithium} & 2 & \(\frac{1.9}{0.5}\) & \(\frac{1.6}{0.4}\) \\ \cline{2-5}  & 3 & \(\frac{3.6}{1.7}\) & \(\frac{2.5}{0.8}\) \\ \cline{2-5}  & 5 & \(\frac{4.0}{1.4}\) & \(\frac{2.9}{1.0}\) \\ \hline \multirow{3}{*}{Falcon} & 1 & \(\frac{1.2}{0.1}\) & \(\frac{1.1}{0.1}\) \\ \cline{2-5}  & 5 & \(\frac{2.2}{0.2}\) & \(\frac{2.0}{0.1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Measurements result of the maximum termination delay time in “_run_remote_” and “_run_local_” marked by \(\frac{\textit{run\_remote}}{\textit{run\_local}}\) (**ms/300**) on the WAVE protocol. continuously transmit their location to nearby remote vehicles. Therefore, research should be advanced not only on the performance of a single \"_run_remote_\" but also on generating signatures concurrently using parallel implementations later. Simultaneous verification of signatures should also be considered for local vehicles. Therefore, parallel optimization implementation methodology for PQC should be considered in the future. The second case concerns when the signature size exceeds the limitation of the maximum packet size, such as the case with Crystals-Dilithium in the WAVE protocol. If the actual transmission layer does not guarantee packet ordering reliability, such as TCP, then it may not arrive in the correct order at the receiver. Especially in the case of Crystals-Dilithium, the signature size is basically 2000 bytes or more, so it is always divided and sent to the WAVE environment. We applied \"_Split way for Crystals-Dilithium_\" which ensures correctness while meeting IEEE standards. Of course, since this is a temporary solution, agreement for signature generation and verification between sender and receiver is essential. In our study, for the WAVE protocol, regardless of the Crystals-Dilithium security level, 3 bits could represent the order of a signature block, but protocols more restrictive than WAVE protocol may require more order-bits to align the signature. The final point of discussion is the choice of PQC-DSA in a V2V communication environment. The selected PQC-DSAs for standardization are Crystals-Dilithium, Falcon, and SPHINCS+.