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Majorum: Ebb-and-Flow Consensus with Dynamic Quorums

Francesco D'Amato, Roberto Saltini, Thanh-Hai Tran, Yann Vonlanthen, Luca Zanolini

TL;DR

Majorum addresses dynamic participation in permissionless Byzantine consensus by pairing a majority-quorum dynamically available component (based on TOB-SVD) with a partially synchronous finality gadget. It introduces probabilistic safety via a $\kappa$-deep confirmation and, under favorable conditions, fast confirmations when all validators are online and a $>\tfrac{2}{3}n$ quorum aligns, enabling block finality in as few as three slots with a single voting phase per slot. The protocol integrates an ebb-and-flow design to keep the live chain under synchrony while finalizing a safe prefix during partitions or extended asynchrony, and it provides accountability through slashing for equivocation. Practically, Majorum reduces optimistic time to finality relative to deployed ebb-and-flow systems and preserves the communication complexity of the underlying dynamically available protocol, making it attractive for scalable, permissionless networks.

Abstract

Dynamic availability is the ability of a consensus protocol to remain live despite honest participants going offline and later rejoining. A well-known limitation is that dynamically available protocols, on their own, cannot provide strong safety guarantees during network partitions or extended asynchrony. Ebb-and-flow protocols [SP21] address this by combining a dynamically available protocol with a partially synchronous finality protocol that irrevocably finalizes a prefix. We present Majorum, an ebb-and-flow construction whose dynamically available component builds on a quorum-based protocol (TOB-SVD). Under optimistic conditions, Majorum finalizes blocks in as few as three slots while requiring only a single voting phase per slot. In particular, when conditions remain favourable, each slot finalizes the next block extending the previously finalized one.

Majorum: Ebb-and-Flow Consensus with Dynamic Quorums

TL;DR

Majorum addresses dynamic participation in permissionless Byzantine consensus by pairing a majority-quorum dynamically available component (based on TOB-SVD) with a partially synchronous finality gadget. It introduces probabilistic safety via a -deep confirmation and, under favorable conditions, fast confirmations when all validators are online and a quorum aligns, enabling block finality in as few as three slots with a single voting phase per slot. The protocol integrates an ebb-and-flow design to keep the live chain under synchrony while finalizing a safe prefix during partitions or extended asynchrony, and it provides accountability through slashing for equivocation. Practically, Majorum reduces optimistic time to finality relative to deployed ebb-and-flow systems and preserves the communication complexity of the underlying dynamically available protocol, making it attractive for scalable, permissionless networks.

Abstract

Dynamic availability is the ability of a consensus protocol to remain live despite honest participants going offline and later rejoining. A well-known limitation is that dynamically available protocols, on their own, cannot provide strong safety guarantees during network partitions or extended asynchrony. Ebb-and-flow protocols [SP21] address this by combining a dynamically available protocol with a partially synchronous finality protocol that irrevocably finalizes a prefix. We present Majorum, an ebb-and-flow construction whose dynamically available component builds on a quorum-based protocol (TOB-SVD). Under optimistic conditions, Majorum finalizes blocks in as few as three slots while requiring only a single voting phase per slot. In particular, when conditions remain favourable, each slot finalizes the next block extending the previously finalized one.
Paper Structure (17 sections, 25 theorems, 3 equations, 1 figure)

This paper contains 17 sections, 25 theorems, 3 equations, 1 figure.

Table of Contents

  1. Introduction and Related Work
  2. Technical Overview
  3. Model and Preliminary Notions
  4. System Model
  5. Security
  6. The Dynamically Available Component
  7. Recalling
  8. Probabilistically-Safe Variant
  9. Probabilistically-Safe Variant with Fast Confirmations
  10. Finality Component
  12. Conclusion
  13. Analysis of Algorithm \ref{['algo:prob-ga-fast']}
  14. Analysis of the Finality-Component
  15. Analysis of
  16. ...and 2 more sections

Key Result

lemma 1

Consider a sequence of $\kappa$ independent slots, where in each slot an honest validator is elected as proposer with probability at least $p = \frac{h_0}{n},$ where $h_0$ is the number of active honest validators and $n$ is the total number of validators. For a finite time horizon $\Tconf$, polynom

Figures (1)

  • Figure 1: An overview of the slot structure is shown, highlighting phases relevant to the fast confirmation and finalization of a proposal. A proposal $\chain$ is made in the first slot $t$ (top left) and becomes fast-confirmed within the same slot. It is then justified in slot $t+1$ and finalized in slot $t+2$. Similarly, the next proposal $\chain’$ made in slot $t+1$ is fast-confirmed once $\chain$ is justified, and it is justified once $\chain$ is finalized. This illustrates how the confirmation and finalization process is pipelined across consecutive slots.

Theorems & Definitions (59)

  • definition 1: Safe protocol
  • definition 2: Live protocol
  • definition 3: Secure protocol goldfish
  • definition 4: Dynamic Availability
  • definition 5: Reorg Resilience
  • definition 6: Accountable Safety
  • definition 7: Secure ebb-and-flow protocol
  • lemma 1
  • proof
  • lemma 2
  • ...and 49 more