# Post-Quantum Delegated Proof of Luck for Blockchain Consensus Algorithm
## 4 Experiments
### Compression TPSs
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**(a)**} & \multicolumn{3}{c}{**(b)**} \\ \multicolumn{1}{c}{**Transaction**} & \multicolumn{1}{c}{**TPSs**} & \multicolumn{1}{c}{**Transaction**} & \multicolumn{1}{c}{**TPSs**} \\ \multicolumn{1}{c}{**Count**} & & **Count** & **TPSs** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: Transaction count and TPS data. (a) TPSs for different block sizes in Falcon. (b) TPSs for different block sizes in ECC. Figure 3: TPS comparison for different transaction counts and sizes using Falcon and Dilithium post-quantum cryptographic algorithms. However, its performance remains competitive, reaching a TPS count of approximately 64 at a transaction count of 19. This demonstrates that Falcon-1024 can still be a viable option for systems that require even stronger security assurances, albeit with a moderate reduction in TPS. On the other hand, the Dilithium algorithms exhibit lower TPS values across all transaction counts. Dilithium-2, which has a transaction size of 3800 bytes, achieves a maximum TPS value of only 44, and Dilithium-5, despite offering stronger security with a transaction size of 5300 bytes, peaks at around 84 TPS. The larger transaction sizes of the Dilithium algorithms, while providing enhanced security, result in a significant reduction in TPSs, making them less efficient for high-throughput blockchain systems. However, it is important to note that these measurements were obtained in a simulated environment using NS-3. Due to the constraints of the simulation environment, only small block sizes could be tested, which limits the extent to which the results can represent real-world performance. Especially in large-scale blockchain networks, block sizes may vary significantly, and the results from this experiment are derived from smaller-scale testing. Larger block sizes in actual implementations may yield different performance metrics. By quantifying these differences, it becomes evident that Falcon ensures robust security against potential quantum threats at the cost of performance efficiency. Despite the larger size of Falcon's cryptographic keys and signatures, the reduction in transactions per second (TPSs) is moderate. Falcon's cryptographic operations are more complex and data-intensive, yet its performance remains competitively efficient. This makes Falcon a viable option for blockchain systems that prioritize long-term security over immediate throughput. These results underscore the trade-offs between security and performance in the context of post-quantum cryptography. While Dilithium provides strong quantum resistance, its larger transaction sizes introduce substantial overhead, reducing the network's throughput. In contrast, Falcon, particularly Falcon-512, strikes a more favorable balance between security and performance, maintaining a higher TPS value even with post-quantum cryptographic requirements. This makes Falcon a more suitable choice for blockchain applications, where transaction throughput is critical, such sacrificing the necessary level of post-quantum security.