51% Attack via Difficulty Increase with a Small Quantum Miner (2403.08023v2)

Abstract: We present a strategy for a single quantum miner with relatively low hashing power, with the same ramifications as a 51% attack. Bitcoin nodes consider the chain with the highest cumulative proof-of-work to be the valid chain. A quantum miner can manipulate the block timestamps to multiply the difficulty by $c$. The fork-choice rule counts every block with increased difficulty with weight $c$. By using Grover's algorithm, it is only $O(\sqrt c)$ harder for the quantum miner to mine such blocks. By picking a high enough $c$, the single quantum miner can create a competing chain with fewer blocks, but more cumulative proof-of-work. The time required is $O(\frac{1}{r^2})$ epochs, where $r$ is the fraction of the block rewards that the quantum miner would have received if they mined honestly. Most proof-of-work cryptocurrencies, including Bitcoin, are vulnerable to our attack. However, it will likely be impossible to execute in forthcoming years, as it requires an extremely fast and fault-tolerant quantum computer.

• The paper demonstrates that a small quantum miner can trigger a 51% attack by artificially increasing mining difficulty using Grover’s algorithm.
• It explains how fake timestamps and controlled epochs enable the creation of a chain with higher cumulative work despite fewer blocks.
• The study outlines the practical implications for PoW security and suggests future research and mitigation strategies to counter quantum threats.

Analysis of "51% Attack via Difficulty Increase with a Small Quantum Miner"

The paper "51% Attack via Difficulty Increase with a Small Quantum Miner" by Bolton Bailey and Or Sattath explores a novel threat to the security of proof-of-work (PoW) cryptocurrencies, such as Bitcoin, that could be facilitated by quantum computing. This threat allows a single quantum miner, even with a relatively low hashing power, to execute an attack with consequences equivalent to those of a traditional 51% attack. This essay will provide an expert overview of the paper's key concepts, methodologies, and implications.

Attack Mechanism

In PoW cryptocurrencies, the chain with the highest cumulative proof-of-work is deemed the valid chain. The authors propose that a quantum miner, leveraging Grover's algorithm, can artificially increase the difficulty of mining blocks. Grover's algorithm provides a quadratic speed-up for unstructured search problems and can be applied to mining, making it O(√c) harder for the quantum miner to mine blocks of increased difficulty.

By manipulating block timestamps, the quantum miner can make the network perceive an artificial increase in difficulty by a factor of $c$. In practice, this means that the chain maintained by the quantum miner could have fewer blocks but more cumulative proof-of-work compared to the chain maintained by classical miners. The proposed attack strategy involves the following steps:

1. Difficulty Increase: The quantum miner first mines an entire epoch with fake timestamps, creating blocks as if they are being created $c$ times more frequently than normal. This increases the difficulty by a factor of $c$.
2. Competing Chain Creation: The miner then continues to mine blocks at the increased difficulty for multiple epochs, creating a chain with higher cumulative work despite having fewer blocks.

Practical and Theoretical Implications

The attack described requires a quantum computer with sufficiently low noise and high computational speed, which currently does not exist. This ensures the immediate safety of current PoW cryptocurrencies. However, the theoretical implications are significant:

1. Security Assumptions: The commonly held belief that a single quantum miner does not pose a risk to Bitcoin's security is refuted. The attack leverages the network's difficulty adjustment mechanism, an aspect not accounted for in usual security models.
2. PoW Vulnerabilities: The work highlights a potential vulnerability in the fork-choice rule, which prioritizes chains with the highest cumulative proof-of-work. The attack demonstrates that this rule could be exploited if quantum computing advances allow feasible implementation.

Variants and Improvements

Several variants of the attack are discussed to address specific issues such as timestamp lag, revenue generation, and compatibility with existing difficulty adjustment mechanisms.

1. Lagging Timestamps Issue: Variant 2 resolves the issue where block timestamps lag behind real time by adjusting the quantum miner's block creation pace.
2. Revenue Issue: Variant 3 improves the attack by maximizing the quantum miner's revenue, achieving up to $1-\epsilon$ fraction of the maximal possible revenue. The runtime of the attack scales with $\frac{1}{\epsilon r^2}$.
3. Incompatible Difficulty Adjustments Issue: Variant 4 ensures that difficulty adjustments comply with Bitcoin’s constraint that difficulty cannot increase by more than a factor of four or decrease by a factor less than one-fourth between consecutive epochs.

Future Directions

Several possible future research directions and mitigation strategies are suggested:

• General PoW Consensus Mechanisms: The attack's applicability to other PoW systems and variants, such as multi-chain or DAG-based systems, should be analyzed.
• Optimal Attack Strategies: Different attacker models based on the attacker's resources and objectives should be investigated to develop optimal attack strategies.
• Mitigations: Potential mitigations include increasing the complexity of the hash function or exploring PoW schemes that cannot be accelerated by Grover's algorithm. Additionally, restructuring difficulty adjustment mechanisms to counteract such attacks should be considered.

Conclusion

The paper challenges the assumption that quantum miners pose no threat to Bitcoin's security. By exploiting the difficulty adjustment mechanism through Grover's algorithm, a low-hashing-power quantum miner could, in theory, orchestrate an attack with severe consequences akin to a 51% attack. While current technological limitations prevent executing this attack today, the work underscores the necessity for robust security models that anticipate future advances in quantum computing. Future research and proactive mitigations will be crucial in fortifying PoW cryptocurrencies against this emerging threat.