Distributed Renaming with Subquadratic Bits via Scalable Committee Election

2026-05-18

AI Summary

This work addresses the message complexity bottleneck in Byzantine renaming within the synchronous message-passing model, presenting two randomized strong order-preserving renaming algorithms that require no shared randomness. Relying solely on message authentication, both algorithms tolerate up to $(1/3 - \delta)n$ Byzantine nodes and achieve polylogarithmic round complexity with near-linear communication overhead. The first algorithm, assuming shared randomness, incurs total communication cost $\tilde{O}(n)$, while the second—operating without shared randomness—achieves $\tilde{O}(n + \min\{nf, T\})$, where $f$ denotes the actual number of faulty nodes and $T$ the total number of messages sent by faulty parties. The core contributions include the first Byzantine renaming protocol meeting these efficiency guarantees and a scalable committee election primitive applicable to a broad range of distributed tasks.

Abstract

In distributed computing, the renaming problem requires $n$ nodes with unique identities from a large namespace $[N]$ to acquire new, distinct identities from a smaller target namespace $[M]$. A solution is strong if $M=n$, and is order-preserving if the relative order of identities is maintained. In the synchronous message-passing model, although many fault-tolerant renaming algorithms achieve logarithmic time complexity, they universally incur a high message complexity of $Ω(n^2)$. Recent work breaks the quadratic barrier, but demands linear runtime and relies on shared randomness. This paper addresses the challenge of designing renaming algorithms that are simultaneously time-efficient, message-efficient, and Byzantine fault-tolerant, assuming only message authentication. We present two randomized algorithms for strong and order-preserving renaming that tolerate up to $(1/3-δ)n$ Byzantine failures for any constant $δ>0$. Our first algorithm, which assumes shared randomness, terminates in $O(\text{poly-log}(n))$ rounds with $\tilde{O}(n)$ total communication cost. This matches known lower bounds within poly-logarithmic factor. Our second algorithm eliminates the shared randomness assumption and achieves $O(\text{poly-log}(n))$ runtime with $\tilde{O}(n+\min\{nf,T\})$ total communication cost, where $f$ is the actual number of faulty nodes and $T$ is the amount of messages faulty nodes sent. This gives the first Byzantine renaming algorithm that achieves both poly-logarithmic runtime and subquadratic communication cost for a wide range of parameter regimes, without shared randomness. A key technical enabler is a novel and scalable committee election primitive that could be easily integrated into other algorithms to solve various distributed computing problems with low cost and strong fault-tolerance.

Problem

• distributed renaming
• Byzantine fault tolerance
• message complexity
• time efficiency
• order-preserving

Innovation

• Byzantine fault tolerance
• distributed renaming
• subquadratic communication
• committee election
• shared randomness