# Post-Quantum Delegated Proof of Luck for Blockchain Consensus Algorithm
## 3 PQ-DPoL  
PQ-DPoL is a consensus algorithm designed to address quantum computing challenges while enhancing blockchain performance and security. This section provides an overview of the key components of PQ-DPoL and how they work together to create a resilient blockchain solution. 1. **Quantum resistance:** Traditional cryptographic methods are vulnerable to quantum computers, which can efficiently solve problems that are currently intractable for classical computers. To ensure long-term security against quantum threats, PQ-DPoL integrates post-quantum cryptography (PQC) algorithms such as the Falcon signature scheme, which is known for its small signature size and computational efficiency, making it well-suited for blockchain applications. This integration helps protect the blockchain system from the potential threats posed by quantum computing. 2. **Randomness and fairness:** The selection of nodes for block generation should be random and fair to prevent any single entity from dominating the network. PQ-DPoL leverages verifiable random functions (VRFs) to ensure that the selection process is both random and verifiable, thereby enhancing the fairness and security of the consensus mechanism. Randomness is crucial because it prevents predictable patterns in node selection, which could otherwise be exploited by attackers aiming to manipulate the network. By ensuring that the selection process is verifiable and random, PQ-DPoL enhances decentralization and overall network security. 3. **Execution speed:** Achieving consensus in a distributed network should be computationally efficient to minimize processing time. PQ-DPoL optimizes execution speed by reducing computational overhead and streamlining the consensus process. Fast \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Algorithm** & **Parameter Set** & **NIST Security Level** & \begin{tabular}{c} **Public Key Size** \\ **(Bytes)** \\ \end{tabular} & \
\begin{tabular}{c} **Secret Key Size** \\ **(Bytes)** \\ \end{tabular} &
\begin{tabular}{c} **Signature Size** \\ **(Bytes)** \\ \end{tabular} \\ \hline Dilithium & Dilithium2 & 1 & 1312 & 2528 & 2420 \\ \hline Dilithium3 & 3 & 1952 & 4000 & 3293 \\ \hline Dilithium5 & 5 & 2592 & 4864 & 4459 \\ \hline Falcon & Falcon-512 & 1 & 897 & 1280 & 666 \\ \hline \multirow{2}{*}{Sphincs+} & Falcon-1024 & 5 & 1793 & 2305 & 1280 \\ \hline \multirow{2}{*}{Sphincs+} & Sphincs+-128s & 1 & 32 & 64 & 8064 \\ \hline \multirow{2}{*}{Sphincs+128s} & \multirow{2}{*}{1} & 32 & 64 & 17,088 \\ \cline{2-2} \cline{4-4}  & Sphincs+-192s & 3 & 48 & 96 & 17,856 \\ \hline \multirow{2}{*}{Sphincs+192f} & \multirow{2}{*}{3} & 48 & 96 & 35,664 \\ \cline{2-2} \cline{4-4}  & Sphincs+-256s & 5 & 64 & 128 & 29,792 \\ \hline \multirow{2}{*}{Sphincs+256f} & \multirow{2}{*}{5} & 64 & 128 & 49,856 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: NIST PQC algorithm parameter sets and sizes. transaction finality is essential for maintaining blockchain performance, particularly for block generation and validation. 4. **Energy efficiency:** Minimizing energy consumption is crucial for the sustainability of blockchain networks. PQ-DPoL uses a delegated approach to reduce the number of nodes involved in the consensus process at any given time, significantly cutting down on energy consumption compared to traditional methods like proof of work (PoW). PQ-DPoL addresses key blockchain challenges by combining quantum resistance, randomness, fairness, execution speed, and energy efficiency. These elements work together to create a scalable and robust blockchain solution that is designed to enhance both security and performance. Figure 1 illustrates how PQ-DPoL operates in rounds, with each consisting of two main stages: the selection of delegate nodes and block generation and verification. At the beginning of each round, nodes generate random values using an indexed verifiable random function (iVRF).