# Post-Quantum Delegated Proof of Luck for Blockchain Consensus Algorithm
## 1 Introduction  
Blockchain is a technology that securely records and manages transactions on a decentralized network, bringing innovation to various industries such as finance, supply chain management, healthcare, real estate, and energy [1, 2]. A key element of blockchain security is the elliptic-curve cryptography (ECC)-based signature method, which is widely used for transaction signing and verification due to its efficiency and relatively small key size. ECC has become the standard for blockchain implementations because it provides strong security with less computational overhead compared to other cryptographic methods. However, recent advancements in quantum computing present a significant threat to the security of ECC-based systems. Quantum computers leverage principles of quantum mechanics to perform calculations at speeds unattainable by classical computers. [PERSON]'s algorithm [3] can solve discrete logarithm problems on elliptic curves in polynomial time, effectively breaking ECC's security and rendering current blockchain systems vulnerable to quantum attacks that could compromise transaction integrity. As quantum computers approach practical use, transitioning to post-quantum cryptography (PQC) becomes crucial to ensure the long-term security of cryptographic systems. PQC algorithms are designed to withstand quantum attacks. However, integrating PQC into blockchain systems poses challenges [4]. These issues are particularly problematic for real-time blockchain applications, where the performance degradation severely limits transaction processing speeds. Post-quantum signature schemes result in larger signaturesand slower signing and verification times, which not only reduce transaction throughput and computational efficiency but also increase data transmission costs and cause longer propagation delays across the network. As a result, the system requires more storage and bandwidth. This delay in propagating transactions across the network slows down the validation and verification processes, which in turn reduces the overall throughput of the blockchain. To address these concerns, this paper proposes post-quantum delegated proof of luck (PQ-DPoL): a novel and efficient blockchain consensus algorithm. PQ-DPoL is designed to be secure and efficient even in the era of quantum computing, with the aim of fair participation among nodes. Previous consensus algorithms, such as proof of work (PoW), are energy-intensive and prone to centralization due to rising mining costs, while proof of stake (PoS) and delegated proof of stake (DPoS) also carry risks of centralization and collusion among delegated nodes, potentially undermining blockchain decentralization. To address these issues, PQ-DPoL combines the randomness and fairness inherent in proof of luck (PoL) with a delegated approach, enhancing both efficiency and security. Unlike PoL, which relies on trusted execution environments (TEEs) to ensure randomness and security, PQ-DPoL eliminates this dependency. Instead, it leverages verifiable random function (VRFs) to guarantee fairness and randomness in the selection process without relying on potentially vulnerable TEEs. Furthermore, PQ-DPoL employs the Falcon signature scheme, which was chosen during the NIST post-quantum cryptography standardization process, to enhance resistance against quantum attacks. While post-quantum cryptographic algorithms like Falcon introduce performance overheads, PQ-DPoL effectively balances security and performance, providing a viable solution for secure blockchain operations in a post-quantum era. This paper is structured as follows: Section 2, Related Work, reviews current blockchain consensus algorithms and the advancements in post-quantum cryptography (PQC), highlighting the need for quantum-resistant solutions. Section 3, PQ-DPoL Algorithm Description, explains the design and implementation of the post-quantum delegated proof of luck (PQ-DPoL) algorithm.