Permissionless Consensus in the Resource Model

Abstract

This paper introduces a new model that abstracts resource-restricted distributed computation and permits simpler reasoning about consensus protocols in the resource-restricted regime. Our model introduces a simple abstraction – simply called “resources” – to capture a resource-restricted primitive which is general enough to capture most Proof of X such as Proof of Work and Proof of Stake. The supply of such resources is scarce, and a single resource allows a party to send a single message with elevated protocol status. For example, every puzzle solution in Proof of Work or Proof of Stake is a resource; the message associated with each resource is the payload of the puzzle. We show the power of resources for the problem of consensus, in which participants attempt to agree on a function of their inputs. We prove that given few additional assumptions, resources are sufficient to achieve consensus in the permissionless regime, even in the presence of a full-information adversary that can choose which parties get resources and when they get them. In the resource model, the participants do not need to know a bound on network delay, they do not need clocks, and they can join and leave the execution arbitrarily, even after sending only a single message. We require only a known upperbound on the rate at which resources enter the system, relative to the maximum network delay (without needing to know the network delay), and that over the long term, a majority of resources are acquired by honest participants. Our protocol for consensus follows from a protocol for graph consensus, which we define as a generalization of blockchains. Our graph consensus works even when resources enter the system at high rates, but the required honest majority increases with the rate. We show how to modify the protocol slightly to achieve one-bit consensus. We also show that for every graph consensus protocol that outputs a majority of honest vertices there exists a one-bit consensus protocol.