Subject: [bitcoindev] 51% Attack via Difficulty Increase with a Small Quantum Miner

From: Or Sattath <[email-masked]>
Date: Mon, 18 Mar 2024 06:19:02 -0700 (PDT)

Hi,
In a recent work <https://arxiv.org/abs/2403.08023> with Bolton Bailey 
(still not peer-reviewed) , we showed how a single quantum miner, with 
relatively little hashing power, can execute a 51% attack. *The attack 
isn't relevant for the forthcoming years, requiring an extremely fast, 
noise-tolerant quantum computer.*
The attack is surprisingly simple. The attacker creates a private fork, 
increasing the difficulty by a factor c. Due to the properties of Grover's 
algorithm, it is only \sqrt c harder for the quantum miner to mine at the 
new difficulty level, but these blocks count as $c$ times more for the PoW. 
Therefore, by mining even a single epoch for a large enough $c$, the 
quantum miner can generate more proof-of-work than the competing 
(classical) chain. The complexity of the attack is ~1/r^2 epochs, where r 
is the fraction of the block rewards that the quantum miner would have 
received if they mined honestly. This attack (or variants thereof) provides 
essentially the same benefits as classical 51% attacks, including double 
spending, and all the revenue from the block rewards. 

This attack might be relevant when considering future protocol 
modifications.

Or

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