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arXiv:1802.06763

Quantum-Assisted Blockchain

D. A. Sapaev, D. A. Bulychkov, Farid Mansurovich Ablayev, Alexander Vasiliev, Mansur Ziatdinov

Published Feb 19, 2018• 3 citations
arXivHTMLPDF

Abstract

Bitcoin and blockchain in general is a hot topic nowadays. In the paper we propose a quantum empowering of this technology and show how to speed-up the mining procedure using the modified Grover's algorithm.
DOI
10.48550/arxiv.1802.06763

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Our aim is to determine conditions for quantum computing technology to give rise to security risks associated with quantum Bitcoin mining. Specifically, we determine the speed and energy efficiency a quantum computer needs to offer an advantage over classical mining. We analyze the setting in which the Bitcoin network is entirely classical except for a single quantum miner who has a small hash rate compared to that of the network. We develop a closed-form approximation for the probability that the quantum miner successfully mines a block, with this probability dependent on the number of Grover iterations the quantum miner applies before making a measurement. Next, we show that for a quantum miner that is “peaceful”, this success probability is maximized if the quantum miner applies Grover iterations for 16 minutes before measuring, which is surprising as the network mines blocks every 10 minutes on average. Using this optimal mining procedure, we show that the quantum miner outperforms a classical computer in efficiency (cost per block) if the condition Q < Crb is satisfied, where Q is the cost of a Grover iteration, C is the cost of a classical hash, r is the quantum miner's speed in Grover iterations per second, and b is a factor that attains its maximum if the quantum miner uses our optimal mining procedure. This condition lays the foundation for determining when quantum mining, and the known security risks associated with it, will arise.
Abstract This paper explores the impact of quantum computing on the efficiency of blockchain mining, focusing on three cryptographic hash algorithms: SHA-256, BLAKE2b, and Keccak-256. Through simulations, we compare the performance of these algorithms in both classical and quantum environments, with a specific emphasis on the effects of increasing qubit counts. The study also examines the potential of Grover’s algorithm to accelerate mining times and improve overall mining efficiency. Our findings indicate significant reductions in mining times when using quantum computing, particularly with the application of Grover’s algorithm. While classical mining techniques are widely used today, the introduction of quantum computing presents both opportunities and challenges for the future of blockchain technology. This paper provides valuable insights into how quantum advancements could reshape blockchain mining, highlighting the need for continued exploration of quantum-resistant cryptographic methods.
Bitcoin miners equipped with purpose-built quantum computers that execute Grover’s algorithm on classical candidate blocks, measuring the resulting quantum state to yield a potentially valid proof-of-work, pose a threat to Bitcoin’s security against 51% attacks. I aim to assess this threat by employing a game-theoretic framework inspired by the Lee-Ray-Santha quantum races model, extending it to better reflect how quantum miners would behave in practice. These extensions address some of the simplifications of prior works, where quantum miners performed only one quantum measurement (which does not maximise their resources), and were assumed to employ a peaceful strategy, wherein the quantum miners discard the resources already invested into searching upon receiving a broadcast of a newly-mined block (which is not enforceable). I consider a setting in which the quantum miners perform multiple quantum measurements between successive blocks, employ Sattath’s Aggressive Quantum Mining Strategy (AQMS), and must allocate limited quantum resources across these measurements. When employing Sattah’s AQMS, a quantum miner halts their execution of Grover’s algorithm and measures the resulting quantum state upon receiving a broadcast of a newly mined block, attempting to create a temporary fork and thereby decreasing the effective hash rate required for a 51% attack. In this novel setting, I derive the payoff matrices for the quantum miners and compute optimal quantum mining strategies that correspond to Nash equilibria. I simulate the deployment of these optimal quantum mining strategies within the Bitcoin network and estimate their effect on Bitcoin’s security against a 51% attack. I determine how two quantum miners should optimally allocate their quantum resources based on the network difficulty. Overall, I find that even when behaving optimally, two quantum miners cannot create enough temporary forks to render the Bitcoin network vulnerable to this quantum threat, given realistic constraints on their quantum resources. This thesis contributes to the growing body of research on the potential threats posed by scalable quantum computers, using the case of two quantum miners as a step toward understanding how quantum miners in general could affect Proof-of-Work-based cryptocurrencies like Bitcoin.