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Asymmetric Distributed Trust

Orestis Alpos, Christian Cachin, Björn Tackmann, Luca Zanolini

TL;DR

This work introduces asymmetric Byzantine quorum systems to capture subjective trust in distributed settings, generalizing classical symmetric quorum models. It develops formal definitions (asymmetric fail-prone systems, guilds, cores, and kernels) and shows how memory, broadcast, and consensus protocols can be adapted to operate with process-specific trust assumptions. The paper provides two memory emulations, c-/r-broadcast primitives, and a randomized asynchronous consensus built on an asymmetric common coin, with liveness guaranteed for wise processes within a maximal guild. By tying the tolerated system to a symmetric quorum framework, it also connects asymmetric trust to existing blockchain-inspired protocols (Ripple, Stellar) and offers a pathway to robust, modular protocol design under subjective trust. The results pave the way for more complex algorithms that leverage heterogeneous trust while highlighting the role of guilds and kernels in achieving progress and safety.

Abstract

Quorum systems are a key abstraction in distributed fault-tolerant computing for capturing trust assumptions. They can be found at the core of many algorithms for implementing reliable broadcasts, shared memory, consensus and other problems. This paper introduces asymmetric Byzantine quorum systems that model subjective trust. Every process is free to choose which combinations of other processes it trusts and which ones it considers faulty. Asymmetric quorum systems strictly generalize standard Byzantine quorum systems, which have only one global trust assumption for all processes. This work also presents protocols that implement abstractions of shared memory, broadcast primitives, and a consensus protocol among processes prone to Byzantine faults and asymmetric trust. The model and protocols pave the way for realizing more elaborate algorithms with asymmetric trust.

Asymmetric Distributed Trust

TL;DR

This work introduces asymmetric Byzantine quorum systems to capture subjective trust in distributed settings, generalizing classical symmetric quorum models. It develops formal definitions (asymmetric fail-prone systems, guilds, cores, and kernels) and shows how memory, broadcast, and consensus protocols can be adapted to operate with process-specific trust assumptions. The paper provides two memory emulations, c-/r-broadcast primitives, and a randomized asynchronous consensus built on an asymmetric common coin, with liveness guaranteed for wise processes within a maximal guild. By tying the tolerated system to a symmetric quorum framework, it also connects asymmetric trust to existing blockchain-inspired protocols (Ripple, Stellar) and offers a pathway to robust, modular protocol design under subjective trust. The results pave the way for more complex algorithms that leverage heterogeneous trust while highlighting the role of guilds and kernels in achieving progress and safety.

Abstract

Quorum systems are a key abstraction in distributed fault-tolerant computing for capturing trust assumptions. They can be found at the core of many algorithms for implementing reliable broadcasts, shared memory, consensus and other problems. This paper introduces asymmetric Byzantine quorum systems that model subjective trust. Every process is free to choose which combinations of other processes it trusts and which ones it considers faulty. Asymmetric quorum systems strictly generalize standard Byzantine quorum systems, which have only one global trust assumption for all processes. This work also presents protocols that implement abstractions of shared memory, broadcast primitives, and a consensus protocol among processes prone to Byzantine faults and asymmetric trust. The model and protocols pave the way for realizing more elaborate algorithms with asymmetric trust.

Paper Structure

This paper contains 46 sections, 19 theorems, 13 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Asymmetric trust.
  3. Protocols with asymmetric quorums.
  4. Motivation.
  5. Contribution.
  6. Related work
  7. Practical systems: Ripple and Stellar.
  8. Models of asymmetric trust.
  9. Signature-free randomized consensus.
  10. System model
  11. Processes.
  12. Executions and faults.
  13. Functionalities.
  14. Links.
  15. Idealized digital signatures.
  16. ...and 31 more sections

Key Result

Lemma 1

Given a fail-prone system $\mathcal{F}$, 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.

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 (58)

  • Definition 1: Byzantine quorum system DBLP:journals/dc/MalkhiR98
  • Definition 2: $Q^3$-condition DBLP:journals/dc/MalkhiR98DBLP:journals/joc/HirtM00
  • Lemma 1
  • Definition 3: Kernel system
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Definition 4: Asymmetric Byzantine quorum system
  • Definition 5: $B^3$-condition
  • ...and 48 more