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On the Solvability of Byzantine-tolerant Reliable Communication in Dynamic Networks

Silvia Bonomi, Giovanni Farina, Sébastien Tixeuil

TL;DR

This work investigates the necessary and sufficient conditions for reliable communication in dynamic networks, where the network topology evolves over time despite the presence of a limited number of Byzantine faulty processes that may behave arbitrarily.

Abstract

A reliable communication primitive guarantees the delivery, integrity, and authorship of messages exchanged between correct processes of a distributed system. We investigate the necessary and sufficient conditions for reliable communication in dynamic networks, where the network topology evolves over time despite the presence of a limited number of Byzantine faulty processes that may behave arbitrarily (i.e., in the globally bounded Byzantine failure model). We identify classes of dynamic networks where such conditions are satisfied, and extend our analysis to message losses, local computation with unbounded finite delay, and authenticated messages.

On the Solvability of Byzantine-tolerant Reliable Communication in Dynamic Networks

TL;DR

This work investigates the necessary and sufficient conditions for reliable communication in dynamic networks, where the network topology evolves over time despite the presence of a limited number of Byzantine faulty processes that may behave arbitrarily.

Abstract

A reliable communication primitive guarantees the delivery, integrity, and authorship of messages exchanged between correct processes of a distributed system. We investigate the necessary and sufficient conditions for reliable communication in dynamic networks, where the network topology evolves over time despite the presence of a limited number of Byzantine faulty processes that may behave arbitrarily (i.e., in the globally bounded Byzantine failure model). We identify classes of dynamic networks where such conditions are satisfied, and extend our analysis to message losses, local computation with unbounded finite delay, and authenticated messages.

Paper Structure

This paper contains 18 sections, 22 theorems, 2 equations, 3 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Graphs and Evolving Graphs
  4. System Model and Problem Statement
  5. Solvability Conditions
  6. Classes of Evolving Graphs
  7. Authenticated Links
  8. Authenticated messages
  9. On the complexity of verifying class membership
  10. Conclusion
  13. Maurer et al. DBLP:conf/srds/MaurerTD15 Reliable Communication Results
  14. Intermediate Results and Missing Proofs
  15. Authenticated Links
  16. ...and 3 more sections

Key Result

theorem 1

The reliable communication problem can be solved, starting at time $j$, from a defined source $p_s$ to a fixed target $p_t$, in the perfect authenticated links and synchronous computation setting, if and only if $\mathcal{G}_{[j,*]} \in \mathcal{J}_{(s,t,2f+1)}$.

Figures (3)

  • Figure 1: An evolving graph example.
  • Figure 2: A spatial temporal subgraph of the evolving graph in Figure \ref{['fig:tvg_example']}
  • Figure 3: Relations between classes of evolving graphs. The classes and relations presented in this work are depicted in square bold blue, dashed edges represent the inclusion relation of a spatial subgraph. In the red circle is the minimal class of evolving graphs where the any-to-any reliable communication problem is solvable at any time under all the settings considered.

Theorems & Definitions (58)

  • definition 1: Journey DBLP:conf/srds/MaurerTD15
  • definition 2: Set $\Sigma(\mathcal{G},p_s,p_t)$ of node sets between two vertices DBLP:conf/srds/MaurerTD15
  • definition 3: Hitting set DBLP:books/fm/GareyJ79
  • definition 4: Minimum Hitting Set DBLP:books/fm/GareyJ79 and MinCut DBLP:conf/srds/MaurerTD15
  • definition 5: Dynamic minimum cut size $k$ between two nodes and $p_s \rightsquigarrow_k p_t$ DBLP:conf/srds/MaurerTD15
  • definition 6: Class $\mathcal{J}_{(s,t)}$ - Temporal Reachability
  • definition 7: Class $\mathcal{TC}$ - Temporal Connectivity
  • definition 8: Class $\mathcal{J}^\mathcal{R}_{(s,t)}$ - Recurrent Reachability
  • definition 9: Class $\mathcal{TC}^\mathcal{R}$ - Recurrent temporal connectivity
  • definition 10: Class $\mathcal{C^*}$ - Always-connected snapshots, or 1-interval connectivity
  • ...and 48 more