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Date: Mon, 18 Mar 2024 06:19:02 -0700 (PDT)
From: Or Sattath <sattath@gmail.com>
To: Bitcoin Development Mailing List <bitcoindev@googlegroups.com>
Message-Id: <573ba0d7-522c-424e-898f-caa780c6ecf0n@googlegroups.com>
Subject: [bitcoindev] 51% Attack via Difficulty Increase with a Small Quantum Miner
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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(still not peer-reviewed) , we showed how a single quantum miner, with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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Hi,<div>In a recent <a href=3D"https://arxiv.org/abs/2403.08023">work</a>=
=C2=A0with=C2=A0Bolton Bailey (still not peer-reviewed)=C2=A0, we showed ho=
w a single quantum miner, with relatively little hashing power, can execute=
a 51% attack. <b>The attack isn't relevant for the=C2=A0<span style=3D"col=
or: rgb(0, 0, 0); font-family: "Lucida Grande", Helvetica, Arial,=
sans-serif; font-size: 13.608px;">forthcoming years, requiring an extremel=
y fast, noise-tolerant quantum computer.</span></b></div><div>The attack is=
surprisingly simple. The attacker creates a private fork, increasing the d=
ifficulty 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 le=
vel, but these blocks count as $c$ times more for the PoW. Therefore, by mi=
ning even a single epoch for a large enough $c$, the quantum miner can gene=
rate more proof-of-work than the competing (classical) chain. The complexit=
y of the attack is ~1/r^2 epochs, where r is the fraction of the block rewa=
rds that the quantum miner would have received if they mined honestly. This=
attack (or variants thereof) provides essentially the same benefits as cla=
ssical 51% attacks, including double spending, and all the revenue from the=
block rewards.=C2=A0</div><div><br /></div><div>This attack might be relev=
ant when considering future protocol modifications.</div><div><br /></div><=
div>Or</div><div><br /></div><div><br /></div><div><br /></div>
<p></p>
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