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CoBRA: A Universal Strategyproof Confirmation Protocol for Quorum-based Proof-of-Stake Blockchains

Zeta Avarikioti, Eleftherios Kokoris Kogias, Ray Neiheiser, Christos Stefo

TL;DR

This work presents a recovery mechanism that restores safety and liveness after consistency violations, even with up to $5/9$ Byzantine stake and $1/9$ rational stake, guaranteeing full reimbursement of provable client losses.

Abstract

The security of many Proof-of-Stake (PoS) payment systems relies on quorum-based State Machine Replication (SMR) protocols. While classical analyses assume purely Byzantine faults, real-world systems must tolerate both arbitrary failures and strategic, profit-driven validators. We therefore study quorum-based SMR under a hybrid model with honest, Byzantine, and rational participants. We first establish the fundamental limitations of traditional consensus mechanisms, proving two impossibility results: (1) in partially synchronous networks, no quorum-based protocol can achieve SMR when rational and Byzantine validators collectively exceed $1/3$ of the participants; and (2) even under synchronous network assumptions, SMR remains unattainable if this coalition comprises more than $2/3$ of the validator set. Assuming a synchrony bound $Δ$, we show how to extend any quorum-based SMR protocol to tolerate up to $1/3$ Byzantine and $1/3$ rational validators by modifying only its finalization rule. Our approach enforces a necessary bound on the total transaction volume finalized within any time window $Δ$ and introduces the \emph{strongest chain rule}, which enables efficient finalization of transactions when a supermajority of honest participants provably supports execution. Empirical analysis of Ethereum and Cosmos demonstrates validator participation exceeding the required $5/6$ threshold in over $99%$ of blocks, supporting the practicality of our design. Finally, we present a recovery mechanism that restores safety and liveness after consistency violations, even with up to $5/9$ Byzantine stake and $1/9$ rational stake, guaranteeing full reimbursement of provable client losses.

CoBRA: A Universal Strategyproof Confirmation Protocol for Quorum-based Proof-of-Stake Blockchains

TL;DR

This work presents a recovery mechanism that restores safety and liveness after consistency violations, even with up to Byzantine stake and rational stake, guaranteeing full reimbursement of provable client losses.

Abstract

The security of many Proof-of-Stake (PoS) payment systems relies on quorum-based State Machine Replication (SMR) protocols. While classical analyses assume purely Byzantine faults, real-world systems must tolerate both arbitrary failures and strategic, profit-driven validators. We therefore study quorum-based SMR under a hybrid model with honest, Byzantine, and rational participants. We first establish the fundamental limitations of traditional consensus mechanisms, proving two impossibility results: (1) in partially synchronous networks, no quorum-based protocol can achieve SMR when rational and Byzantine validators collectively exceed of the participants; and (2) even under synchronous network assumptions, SMR remains unattainable if this coalition comprises more than of the validator set. Assuming a synchrony bound , we show how to extend any quorum-based SMR protocol to tolerate up to Byzantine and rational validators by modifying only its finalization rule. Our approach enforces a necessary bound on the total transaction volume finalized within any time window and introduces the \emph{strongest chain rule}, which enables efficient finalization of transactions when a supermajority of honest participants provably supports execution. Empirical analysis of Ethereum and Cosmos demonstrates validator participation exceeding the required threshold in over of blocks, supporting the practicality of our design. Finally, we present a recovery mechanism that restores safety and liveness after consistency violations, even with up to Byzantine stake and rational stake, guaranteeing full reimbursement of provable client losses.

Paper Structure

This paper contains 33 sections, 22 theorems, 5 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contributions
  4. Preliminaries
  5. Model and Assumptions
  6. Definitions and Properties
  7. SMR Game and Coalition-Compliance
  8. Impossibility results
  9. Fewer Byzantine.
  10. Closing the gaps
  11. Beyond $n/3$ Byzantine.
  12. CoBRA: Finalization Rule
  13. Finality Gadget
  14. $\Delta^*$--old Blocks
  15. $\Delta^*$--recent Blocks
  16. ...and 18 more sections

Key Result

Theorem 3.1

Assuming silent clients, a static setting, and a partially synchronous network, no $q$-commitable SMR protocol can be $(n, k, f)$--resilient for any $q$ when $f \geq \lceil \frac{h}{2} \rceil$, where $h = n - k - f$.

Figures (2)

  • Figure 1: Design space of $2f+1$-committable SMR protocols.
  • Figure 2: Forking attack.

Theorems & Definitions (51)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7: SMR Game
  • Definition 8
  • Definition 9
  • Theorem 3.1
  • ...and 41 more