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From Symmetric to Asymmetric Asynchronous Byzantine Consensus

Christian Cachin, Luca Zanolini

TL;DR

This work addresses asynchronous Byzantine consensus under asymmetric trust, where each process may select its own fault-prone assumptions. Building on the PODC-14 randomized, signature-free approach, the authors diagnose a liveness fault, propose minimal fixes that preserve simplicity, and extend the protocol to asymmetric quorums using a common coin. They introduce the maximal guild concept and show how to achieve asymmetric strong Byzantine consensus with $O(1)$ rounds in expectation, suitable for blockchain-style environments. The results provide a rigorous framework for subjective trust in consensus, combining asymmetric quorums, common coins, and kernel-based progress within a principled guild structure. The work has practical implications for scalable, trust-flexible distributed systems and outlines directions for dynamic membership and cryptographic instantiations.

Abstract

Consensus is arguably one of the most important notions in distributed computing. Among asynchronous, randomized, and signature-free implementations, the protocols of Mostéfaoui et al. (PODC 2014 and JACM 2015) represent a landmark result, which has been extended later and taken up in practical systems. The protocols achieve optimal resilience and takes, in expectation, only a constant expected number of rounds of quadratic message complexity. Randomization is provided through a common-coin primitive. In traditional consensus protocols, all involved processes adhere to a global, symmetric failure model, typically only defined by bounds on the number of faulty processes. Motivated by applications to blockchains, however, more flexible trust assumptions have recently been considered. In particular, with asymmetric trust, a process is free to choose which other processes it trusts and which ones might collude against it. This paper revisits the optimal asynchronous protocol of Mostéfaoui et al. and shows how to realize it with asymmetric trust. The paper starts by pointing out in detail why some versions of this protocol may violate liveness. Then it proposes a fix for the protocol that does not affect its properties, but lets it regain the simplicity of its original version (PODC 2014). At the same time, the paper shows how to realize randomized signature-free asynchronous Byzantine consensus with asymmetric quorums. This results in an optimal consensus protocol with subjective, asymmetric trust and constant expected running time. It is suitable for applications to blockchains, for instance.

From Symmetric to Asymmetric Asynchronous Byzantine Consensus

TL;DR

This work addresses asynchronous Byzantine consensus under asymmetric trust, where each process may select its own fault-prone assumptions. Building on the PODC-14 randomized, signature-free approach, the authors diagnose a liveness fault, propose minimal fixes that preserve simplicity, and extend the protocol to asymmetric quorums using a common coin. They introduce the maximal guild concept and show how to achieve asymmetric strong Byzantine consensus with rounds in expectation, suitable for blockchain-style environments. The results provide a rigorous framework for subjective trust in consensus, combining asymmetric quorums, common coins, and kernel-based progress within a principled guild structure. The work has practical implications for scalable, trust-flexible distributed systems and outlines directions for dynamic membership and cryptographic instantiations.

Abstract

Consensus is arguably one of the most important notions in distributed computing. Among asynchronous, randomized, and signature-free implementations, the protocols of Mostéfaoui et al. (PODC 2014 and JACM 2015) represent a landmark result, which has been extended later and taken up in practical systems. The protocols achieve optimal resilience and takes, in expectation, only a constant expected number of rounds of quadratic message complexity. Randomization is provided through a common-coin primitive. In traditional consensus protocols, all involved processes adhere to a global, symmetric failure model, typically only defined by bounds on the number of faulty processes. Motivated by applications to blockchains, however, more flexible trust assumptions have recently been considered. In particular, with asymmetric trust, a process is free to choose which other processes it trusts and which ones might collude against it. This paper revisits the optimal asynchronous protocol of Mostéfaoui et al. and shows how to realize it with asymmetric trust. The paper starts by pointing out in detail why some versions of this protocol may violate liveness. Then it proposes a fix for the protocol that does not affect its properties, but lets it regain the simplicity of its original version (PODC 2014). At the same time, the paper shows how to realize randomized signature-free asynchronous Byzantine consensus with asymmetric quorums. This results in an optimal consensus protocol with subjective, asymmetric trust and constant expected running time. It is suitable for applications to blockchains, for instance.

Paper Structure

This paper contains 16 sections, 9 theorems, 6 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related work
  3. System model and preliminaries
  4. System model
  5. Byzantine quorum systems
  6. Revisiting signature-free asynchronous Byzantine consensus
  7. Binary-value broadcast
  8. Randomized consensus
  9. A liveness problem
  10. Fixing the problem
  11. Asymmetric trust
  12. On the importance of a guild in a protocol.
  13. Asymmetric randomized Byzantine consensus
  14. Asymmetric binary validated broadcast
  15. Asymmetric randomized consensus
  16. ...and 1 more sections

Key Result

Lemma 1

Let $\mathcal{F}$ be a fail-prone system. A Byzantine quorum system for $\mathcal{F}$ exists if and only if $Q^3(\mathcal{F}\xspace)$. In particular, if $Q^3(\mathcal{F}\xspace)$ holds, then $\overline{\mathcal{F}\xspace}$, the bijective complement of $\mathcal{F}$, is a Byzantine quorum system call

Figures (1)

  • Figure 1: The execution of Algorithm \ref{['alg:rbv-consensus']}, where processes $p_1$ and $p_3$ execute line \ref{['algrbc:uponb']} with $B=\{0,1\}$.

Theorems & Definitions (32)

  • Definition 1: Fail-prone system
  • Definition 2: Symmetric Byzantine quorum system
  • Definition 3: $Q^3$-condition DBLP:journals/dc/MalkhiR98DBLP:journals/joc/HirtM00
  • Lemma 1: Quorum system existence DBLP:journals/dc/MalkhiR98
  • Definition 4: Kernel system
  • Lemma 2
  • proof
  • Definition 5: Binary validated broadcast
  • Definition 6: Strong Byzantine consensus
  • Definition 7: Common coin
  • ...and 22 more