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Ofelimos: Combinatorial Optimization via Proof-of-Useful-Work

A Provably Secure Blockchain Protocol

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Book cover Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13508))

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Abstract

Minimizing the energy cost and carbon footprint of the Bitcoin blockchain and related protocols is one of the most widely identified open questions in the cryptocurrency space. Substituting the proof-of-work (PoW) primitive in Nakamoto’s longest-chain protocol with a proof of useful work (PoUW) has been long theorized as an ideal solution in many respects but, to this day, the concept still lacks a convincingly secure realization.

In this work we put forth Ofelimos, a novel PoUW-based blockchain protocol whose consensus mechanism simultaneously realizes a decentralized optimization-problem solver. Our protocol is built around a novel local search algorithm, which we call Doubly Parallel Local Search (DPLS), that is especially crafted to suit implementation as the PoUW component of our blockchain protocol. We provide a thorough security analysis of our protocol and additionally present metrics that reflect the usefulness of the system. DPLS can be used to implement variants of popular local search algorithms such as WalkSAT that are used for real world combinatorial optimization tasks. In this way, our work paves the way for safely using blockchain systems as generic optimization engines for a variety of hard optimization problems for which a publicly verifiable solution is desired.

This work is based upon work supported by the National Science Foundation under Grant No. 1801487.

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Notes

  1. 1.

    Closure ensures that concurrently extending a transcript does not break validity.

  2. 2.

    In the blockchain setting, the adversary sees blocks generated by other parties, simulated by oracle \(\mathcal M\), and sends out blocks that other parties may drop or adopt depending on whether they are valid, simulated by oracle \(\mathcal V\).

  3. 3.

    Even if there are no problem instances posted by clients on the blockchain, e.g., during bootstrapping, miners can always generate a MH problem based on the hash of the block they are extending (a fixed-time hash-based PoW ([4, 12]) is sufficient for this purpose). This amounts to a ‘fall-back’ DPLS computation.

  4. 4.

    Our PoUW “collapses” to this construction if we set \(p_2:=1, p_3:=0\).

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Acknowledgments

We thank Laurent Michel for providing us with valuable information about state-of-the-art stochastic local-search algorithms and their application to real-world problems.

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Authors and Affiliations

  1. IOHK, Singapore, Singapore

    Matthias Fitzi, Aggelos Kiayias, Giorgos Panagiotakos & Alexander Russell

  2. University of Edinburgh, Edinburgh, UK

    Aggelos Kiayias

  3. University of Connecticut, Storrs, USA

    Alexander Russell

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  1. Matthias Fitzi
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Corresponding author

Correspondence to Giorgos Panagiotakos .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Fitzi, M., Kiayias, A., Panagiotakos, G., Russell, A. (2022). Ofelimos: Combinatorial Optimization via Proof-of-Useful-Work. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13508. Springer, Cham. https://doi.org/10.1007/978-3-031-15979-4_12

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