Proofs of Useful Work

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 https://eprint.iacr.org/2018/559. 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