# Post-Quantum Delegated Proof of Luck for Blockchain Consensus Algorithm
## 4 Experiments
### Compression TPSs  
To simulate a realistic blockchain network environment, the open-source network simulator NS-3 was utilized. The performance and scalability of the blockchain network were evaluated based on the transactions per second (TPSs) metric. All related data and codes used in this simulation are publicly available at ([[https://github.com/amdjd0704/pq-dpol](https://github.com/amdjd0704/pq-dpol)]([https://github.com/amdjd0704/pq-dpol](https://github.com/amdjd0704/pq-dpol)) (accessed on 12 September 2024)). We utilized the NS3 simulator to implement a fully meshed network topology. The network consisted of N nodes, where each node was directly connected to every other node using point-to-point links. The data rate for each link was set to 3 Mbps with a latency of 3 ms. Each node was assigned an IP address within the 1.0.0.0/24 subnet, and the Internet stack was installed on all nodes. The simulation was configured using NS3's InternetStackHelper and PointToPointHelper modules, and the fully meshed network topology allowed for performance analysis of message transmission between nodes. Table 4 shows that the TPS measurements for the Falcon and ECC algorithms reveal significant differences in their performance. Falcon demonstrates lower TPS values compared to ECC across various transaction counts, reflecting the impact of larger signature sizes and more complex cryptographic operations. For instance, with a transaction count of 3, Falcon achieves a TPS count of 62.86, which is significantly lower than ECC's TPS count of 118.25, indicating that Falcon's performance is roughly 53% of ECC's at this transaction count. This trend continues as the transaction count increases. At a transaction count of 10, Falcon's TPS count is 111.11, while ECC's TPS count is 349.31, showing that Falcon performs at about 31% of ECC's efficiency. The gap remains consistent across higher transaction counts, with Falcon reaching a maximum TPSs of 136.36 at a transaction count of 18, whereas ECC reaches 563.66 at a transaction count of 19, meaning Falcon's TPSs are approximately 24% of ECC's. While Falcon offers robust security against quantum threats, its larger cryptographic keys and signatures slightly reduce TPSs. However, the performance remains competitive despite these more complex and data-intensive operations, making Falcon viable for blockchain systems prioritizing long-term security. This makes Falcon a viable option for blockchain systems that prioritize long-term security over immediate throughput. To further understand these performance implications, it is important to consider the underlying reasons for the observed differences. The larger size of Falcon's cryptographic keys and signatures necessitates more computational resources for processing each transaction. This increased computational load translates to longer processing times and higher data storage requirements, which directly impact the TPSs. However, Falcon's advantage lies in its enhanced security measures, which are designed to withstand quantum attacks, thereby providing a higher level of security assurance for blockchain applications. Figure 2: Compression ratio improvement as a function of increasing transaction data size. We further explore the impact of various post-quantum cryptographic algorithms on transactions per second (TPSs). To provide a comprehensive comparison, we measured the TPSs across multiple transaction counts and sizes for both the Falcon and Dilithium algorithms. Figure 3 presents a visual representation of the results, showing the TPS performances for Falcon-512, Falcon-1024, Dilithium-2, and Dilithium-5. Falcon-512 shows strong post-quantum security while maintaining a peak TPS of 136 at a transaction count of 18, making it well-suited for environments demanding both security and performance. Falcon-1024, while also delivering robust post-quantum security, shows lower TPS values compared to Falcon-512 due to its larger transaction size (3100 bytes).