Cryptology ePrint Archive: Report 2017/203

Proofs of Useful Work

Marshall Ball and Alon Rosen and Manuel Sabin and Prashant Nalini Vasudevan

Abstract: We give Proofs of Work (PoWs) whose hardness is based on a wide array of computational problems, including Orthogonal Vectors, 3SUM, All-Pairs Shortest Path, and any problem that reduces to them (this includes deciding any graph property that is statable in first-order logic). This results in PoWs whose completion does not waste energy but instead is useful for the solution of computational problems of practical interest.

The PoWs that we propose are based on delegating the evaluation of low-degree polynomials originating from the study of average-case fine-grained complexity. We prove that, beyond being hard on the average (based on worst-case hardness assumptions), the task of evaluating our polynomials cannot be amortized across multiple~instances.

For applications such as Bitcoin, which use PoWs on a massive scale, energy is typically wasted in huge proportions. We give a framework that can utilize such otherwise wasteful work.

Note: An updated version of this paper is available at The update is to accommodate the fact (pointed out by anonymous reviewers) that the definition of Proof of Useful Work in this paper is already satisfied by a generic naive construction.

Category / Keywords: Proofs of work, Fine-Grained, Delegation, Blockchain

Original Publication (with major differences): IACR-CRYPTO-2018

Date: received 27 Feb 2017, last revised 26 Feb 2021

Contact author: msabin at berkeley edu, marshallball at gmail com, alon rosen at idc ac il, prashantv91 at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20210226:193606 (All versions of this report)

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