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Proofs of Useful Work from Arbitrary Matrix Multiplication

14 April 2025
Ilan Komargodski
Itamar Schen
Omri Weinstein
ArXiv (abs)PDFHTML
Main:17 Pages
Bibliography:2 Pages
Appendix:3 Pages
Abstract

We revisit the longstanding open problem of implementing Nakamoto's proof-of-work (PoW) consensus based on a real-world computational task T(x)T(x)T(x) (as opposed to artificial random hashing), in a truly permissionless setting where the miner itself chooses the input xxx. The challenge in designing such a Proof-of-Useful-Work (PoUW) protocol, is using the native computation of T(x)T(x)T(x) to produce a PoW certificate with prescribed hardness and with negligible computational overhead over the worst-case complexity of T(⋅)T(\cdot)T(⋅) -- This ensures malicious miners cannot ``game the system" by fooling the verifier to accept with higher probability compared to honest miners (while using similar computational resources). Indeed, obtaining a PoUW with O(1)O(1)O(1)-factor overhead is trivial for any task TTT, but also useless.

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@article{komargodski2025_2504.09971,
  title={ Proofs of Useful Work from Arbitrary Matrix Multiplication },
  author={ Ilan Komargodski and Itamar Schen and Omri Weinstein },
  journal={arXiv preprint arXiv:2504.09971},
  year={ 2025 }
}
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