The economic limits of permissionless consensus

An ideal permissionless consensus protocol would, in addition to satisfying standard consistency and liveness guarantees, render consistency violations prohibitively expensive for the attacker without collateral damage to honest participants---for example, by programatically confiscating an attacker's resources without reducing the value of honest participants' resources, as is the intention for slashing in a proof-of-stake protocol. We make this idea precise with our notion of the EAAC (expensive to attack in the absence of collapse) property, and prove the following results: • In the synchronous and dynamically available setting (in which the communication network is reliable but non-malicious players may be periodically inactive), with an adversary that controls at least one-half of the overall resources, no protocol can be EAAC. In particular, this result rules out EAAC for all typical longest-chain protocols (be they proof-of-work or proof-of-stake). • In the partially synchronous and quasi-permissionless setting (in which resource-controlling non-malicious players are always active but the communication network may suffer periods of unreliability), with an adversary that controls at least one-third of the overall resources, no protocol can be EAAC. In particular, slashing in a proof-of-stake protocol cannot achieve its intended purpose if message delays cannot be bounded a priori. • In the synchronous and quasi-permissionless setting, there is a proof-of-stake protocol with slashing that, provided the adversary controls less than two-thirds of the overall stake, satisfies the EAAC property. Our work formalizes the potential security benefits of proof-of-stake sybil-resistance coupled with slashing and the common belief that the merge has increased Ethereum's economic security. Our work also provides mathematical justifications for several key design decisions behind the post-merge Ethereum protocol, ranging from long cooldown periods for unstaking to economic penalties for inactivity.