Abstract
The proof of work mechanism by which many blockchain-based protocols achieve consensus may be undermined by the use of quantum computing in mining—even when all cryptographic primitives are replaced with post-quantum secure alternatives. First, we offer an impossibility result: we prove that quantum (Grover) speedups in solving a large, natural class of proof-of-work puzzles cause an inevitable incentive incompatibility in mining, by distorting the reward structure of mining in proof-of-work-based protocols such as Bitcoin. We refer to such distortion as the Superlinearity Problem. Our impossibility result suggests that for robust post-quantum proof-of-work-based consensus, we may need to look beyond standard cryptographic models. We thus propose a proof-of-work design in a random-beacon model, which is tailored to bypass the earlier impossibility. We conclude with a discussion of open problems, and of the challenges of integrating our new proof-of-work scheme into decentralised consensus protocols under realistic conditions.
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Notes
- 1.
Classical means computing without quantum computers.
- 2.
Classical network takeover attacks are also possible with the collusion of much less than half of mining power [24]. The Quantum Superlinearity Problem worsens those attacks too: basically, an attack that requires a certain fraction of classical mining power may require a much smaller fraction of quantum mining power.
- 3.
E.g., verifiable random functions and verifiable delay functions.
- 4.
This is not strictly true: the left hand side is bounded by 1 whereas t grows without bound. A refined definition of proportionality (Definition 4) handles this issue.
- 5.
This rules out deterministic proofs of work (whose reward functions are 0–1).
- 6.
The upper bound is necessary since probabilities are upper-bounded by 1.
- 7.
Jakobsson and Juels proposed a definition that includes interactive protocols [29].
- 8.
Stebila et al. proposed a definition where verification is keyed [49].
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Acknowledgments
We are grateful to Thaddeus Dryja for the conversation that sparked this research, and to Chris Peikert for a helpful discussion at early stages of the work.
SP’s work on this project was supported by a 2021–22 Computing Innovation Fellowship, funded by the National Science Foundation under Grant #2127309 to the Computing Research Association, by Cornell Tech’s Digital Life Initiative, and by the MIT Media Lab’s Digital Currency Initiative.
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Park, S., Spooner, N. (2024). The Superlinearity Problem in Post-quantum Blockchains. In: Baldimtsi, F., Cachin, C. (eds) Financial Cryptography and Data Security. FC 2023. Lecture Notes in Computer Science, vol 13950. Springer, Cham. https://doi.org/10.1007/978-3-031-47754-6_12
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