Prefix Consensus For Censorship Resistant BFT

TL;DR

This work introduces Prefix Consensus, a censorship-resistant BFT primitive where input vectors yield two outputs $(v^{\sf low}, v^{\sf high})$ that extend the honest parties' common prefix rather than a single agreed value. It proves an asynchronous 3-round solution under optimal resilience $n=3f+1$, and then strengthens it to Strong Prefix Consensus, which enforces agreement on the high output via a leaderless, partially synchronous construction. Building on this, the authors design a leaderless, multi-slot BFT SMR protocol that achieves $f$-censorship resistance by iteratively demoting misbehaving proposers and using per-slot Strong Prefix Consensus on proposal hashes. They also connect Prefix Consensus to Graded and Binary/Validated Consensus, obtaining optimal-latency graded consensus (3 message delays) and leaderless Binary/Validated Consensus with $O(n^3)$ message complexity and $O(n^4)$ communication. Overall, Prefix Consensus provides a rigorous, asynchronous foundation for censorship-resistant, leaderless BFT, with practical multi-slot instantiations and strong latency/complexity guarantees for core primitives and their extensions.

Abstract

Despite broad use of BFT consensus in blockchains, censorship resistance is weak: leaders can exclude transactions, a growing concern for trading and DeFi. We address this by introducing a new abstraction and protocol stack. First, we introduce \emph{Prefix Consensus}, where parties input vectors and output $(v^{\sf low},v^{\sf high})$ that (i) extend the maximum common prefix of honest inputs and (ii) satisfy $v_i^{\sf low}\preceq v_j^{\sf high}$ for all honest $i,j$. Unlike classical consensus, no single output is required. We show Prefix Consensus is solvable asynchronously and give tight round-complexity bounds. We then define \emph{Strong Prefix Consensus}, requiring agreement on the \emph{high} output. Our protocol is leaderless and partially synchronous: one Prefix Consensus instance decides (possibly different) lows, and additional instances yield a unique safe-to-extend high, even if an adversary can suspend one party per round. We lift this to a leaderless, multi-proposer, censorship-resistant BFT SMR protocol: per slot, all parties broadcast proposals, deterministically rank them, and run one Strong Prefix Consensus on proposal hashes, committing honest proposals in \emph{four rounds}. A deterministic demotion rule updates the ranking when a party's proposal is excluded, implying that after GST at most $f$ slots can miss an honest proposal while progress remains leaderless under suspension and up to $f{-}1$ Byzantine faults. Finally, we connect Prefix Consensus to graded and binary/validated consensus: we obtain an optimal-latency graded consensus (3 message delays) and leaderless Binary/Validated Consensus with worst-case message complexity $O(n^3)$ and communication $O(n^4)$.

Figures (2)

• Figure 1: Executions $\rho_0$, $\rho_1$, and $\rho^*$ used in the lower-bound proof. For clarity, messages to Byzantine parties and messages sent at or after $2\hat{\delta}$ are omitted from the picture.
• Figure 2: Executions $\rho_1$, $\rho_1'$, and $\rho_1"$ from the proof of \ref{['lem:lb:rho-one']}. For clarity, messages to Byzantine parties and messages sent at or after $2\hat{\delta}$ are omitted from the picture.

Theorems & Definitions (57)

• Theorem 1.1: Informal
• Definition 1: Leaderless Termination (informal) antoniadis2021leaderless
• Definition 2: Prefix Consensus
• Corollary 1
• Theorem 2.1
• Definition 3: Strong Prefix Consensus
• Definition 4: Multi-slot Consensus
• Definition 5: Censorship Resistance
• Definition 6: Commit Latency
• Definition 7: Slot Latency