# Post-Quantum Delegated Proof of Luck for Blockchain Consensus Algorithm
## 4 Experiments
### Signature Algorithm Comparison  
In this subsection, we present a comprehensive performance comparison between the elliptic-curve digital signature algorithm (ECDSA), the Falcon post-quantum signature algorithm, and the Dilithium post-quantum signature algorithm by using the 'openssl speed' command for measurement. The Falcon and Dilithium algorithms were tested using the QS-OpenSSL-1.1.1 library, which provides implementations of these quantum-safe algorithms. The metrics evaluated include the number of signatures generated per second (Sign/s) and the number of verifications per second (Verify/s).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Public Key Size** & **Private Key Size** & **Signature Size** & **Public Key + Signature** \\ \hline ECC 256 & 64 & 32 & 64 & 128 \\ \hline Falcon-512 & 897 & 1280 & 666 & 1563 \\ \hline Dilithium2 & 1312 & 2528 & 2420 & 3732 \\ \hline SPHINCS+SHA2-128s & 32 & 64 & 7856 & 7888 \\ \hline SPHINCS+SHAKE-128f & 32 & 64 & 17,088 & 17,120 \\ \hline ECC 384 & 96 & 48 & 96 & 192 \\ \hline Falcon-1024 & 1793 & 2304 & 1280 & 3073 \\ \hline Dilithium3 & 1952 & 4000 & 3293 & 5245 \\ \hline SPHINCS+SHA2-192f & 48 & 96 & 35,664 & 35,712 \\ \hline SPHINCS+SHA2-192s & 48 & 96 & 16,224 & 16,272 \\ \hline Dilithium5 & 2592 & 4864 & 4595 & 7187 \\ \hline SPHINCS+SHA2-256f & 64 & 128 & 49,856 & 49,920 \\ \hline SPHINCS+SHA2-256s & 64 & 128 & 29,792 & 29,856 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of ECC, Falcon, Dilithium, and SPHINCS+ key and signature sizes (bytes).  
Table 3 highlights the performance differences between the ECDSA, Falcon algorithm, and Dilithium algorithm. Notably, both Falcon and Dilithium significantly outperform ECDSA in verification speed. Specifically, Dilithium2 achieves the highest verification speed of 41,114.4 verifications per second, followed by Falcon-512 with 24,078.9 verifications per second, compared to 16,063.7 verifications per second for ECC 256. This increased efficiency in verification makes both Falcon and Dilithium highly compelling choices for blockchain environments, where quick transaction validation is essential.  
However, while Falcon offers robust post-quantum security, Dilithium has certain advantages in both signing and verification speeds. For instance, Dilithium2 generates 15,197.0 signatures per second, outperforming both Falcon-512 (4107.6 signatures per second) and Falcon-1024 (2046.4 signatures per second). This makes Dilithium2 a more efficient choice in environments where higher signing speeds are required. Similarly, Dilithium5 performs better in both signing and verification than Falcon-1024, generating 7583.7 signatures per second and verifying 15,479.5 verifications per second.  
One key trade-off between Falcon, Dilithium, and ECDSA lies in the increased signature and public key sizes of the post-quantum cryptographic algorithms. Larger signature sizes in Falcon and Dilithium require more storage space, potentially reducing the number of transactions processed per block, which can negatively impact the transaction per second (TPS) rate of the blockchain.