Paper 2025/616

State Machine Replication Without Borders

Abstract

A set of unacquainted parties, some of which may misbehave, communicate with each other over an unauthenticated and unreliable gossip network. They wish to jointly replicate a state machine $\mathrm{\Pi }$ so that each one of them has fair access to its operation. Specifically, assuming parties' computational power is measured as queries to an oracle machine $H(\cdot )$, parties can issue symbols to the state machine in proportion to their queries to $H(\cdot )$ at a given fixed rate. Moreover, if such access to the state machine is provided continuously in expected constant time installments we qualify it as fast fairness. A state machine replication (SMR) protocol in this permissionless setting is expected to offer consistency across parties and reliably process all symbols that honest parties wish to add to it in a timely manner despite continuously fluctuating participation and in the presence of an adversary who commands less than half of the total queries to $$ per unit of time. A number of protocols strive to offer the above guarantee together with fast settlement — notably, the Bitcoin blockchain offers a protocol that settles against Byzantine adversaries in polylogarithmic rounds, while fairness only holds in a fail-stop adversarial model (due to the fact that Byzantine behavior can bias access to the state machine in the adversary's favor). In this work, we put forth the first Byzantine-resilient protocol solving SMR in this setting with both expected-constant-time settlement and fast fairness. In addition, our protocol is self-sufficient in the sense of performing its own time keeping while tolerating an adaptively fluctuating set of parties.