Conquering Generals: an NP-Hard Proof of Useful Work

Abstract

Proof of Work systems are used in cryptocurrencies to obtain consensus in distributed peer-to-peer systems that share no trust. Miners of cryptocurrency compete by engaging in the Proof of Work to solve a cryptographic challenge. The first to successfully provide a solution to the challenge wins by minting new currency. The process of mining also simultaneously prevents double-spending through the creation of an append-only distributed database known as the blockchain. The most widely adopted Proof of Work is the Hashcash scheme and the most widely deployed miners are ASIC-based. Despite the popularity of Hashcash, two issues are commonly identified its use. Firstly, the high energy consumption of the scheme is perceived as wasteful because the solutions found provide no useful output, and secondly, the computational complexity class of the scheme is not formally known. Based on these deficiencies, we propose a novel Proof of Work system which achieves the following goals: - to provide a fiscally incentivized platform for algorithm research that aims to optimize an NP-Hard computational problem. This provides indirect insight into the P Versus NP Clay Institute Millennium problem, thus providing useful output. - to construct a challenge within a known hard computational complexity class. - to ensure the Proof of Work created is inclusive of ASIC hardware. Our proposal is a hybrid Proof of Work system that initially uses the Hashcash scheme and which subsequently constructs an instance of the NP-Hard Travelling Salesman Problem. We build on the ambitions of others to develop Proofs of Useful Work. We differentiate our paper from related work as the first to consider the current capital investment into ASIC hardware, thus including them in our proposal.