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Proximal Byzantine Consensus

Roy Shadmon, Daniel Spencer, Owen Arden

TL;DR

This work tackles approximate consensus in distributed edge systems subject to Byzantine faults and noisy networks. It proposes proximal Byzantine consensus (PC), a probabilistic method that infers the most likely ideal output given observed non-faulty values and provides an interval guarantee around the decision with a specified confidence. Compared to convex-hull-based Vector Consensus (VC), PC delivers significantly lower error and stronger attack containment, with formal run-time and security bounds. The approach shows particular strength in higher dimensions, suggesting practical impact for robust, real-time decision-making in edge computing environments.

Abstract

Distributed control systems require high reliability and availability guarantees despite often being deployed at the edge of network infrastructure. Edge computing resources are less secure and less reliable than centralized resources in data centers. Replication and consensus protocols improve robustness to network faults and crashed or corrupted nodes, but these volatile environments can cause non-faulty nodes to temporarily diverge, increasing the time needed for replicas to converge on a consensus value, and give Byzantine attackers too much influence over the convergence process. This paper proposes proximal Byzantine consensus, a new approximate consensus protocol where clients use statistical models of streaming computations to decide a consensus value. In addition, it provides an interval around the decision value and the probability that the true (non-faulty, noise-free) value falls within this interval. Proximal consensus (PC) tolerates unreliable network conditions, Byzantine behavior, and other sources of noise that cause honest replica states to diverge. We evaluate our approach for scalar values, and compare PC simulations against a vector consensus (VC) protocol simulation. Our simulations demonstrate that consensus values selected by PC have lower error and are more robust against Byzantine attacks. We formally characterize the security guarantees against Byzantine attacks and demonstrate attacker influence is bound with high probability. Additionally, an informal complexity analysis suggests PC scales better to higher dimensions than convex hull-based protocols such as VC.

Proximal Byzantine Consensus

TL;DR

This work tackles approximate consensus in distributed edge systems subject to Byzantine faults and noisy networks. It proposes proximal Byzantine consensus (PC), a probabilistic method that infers the most likely ideal output given observed non-faulty values and provides an interval guarantee around the decision with a specified confidence. Compared to convex-hull-based Vector Consensus (VC), PC delivers significantly lower error and stronger attack containment, with formal run-time and security bounds. The approach shows particular strength in higher dimensions, suggesting practical impact for robust, real-time decision-making in edge computing environments.

Abstract

Distributed control systems require high reliability and availability guarantees despite often being deployed at the edge of network infrastructure. Edge computing resources are less secure and less reliable than centralized resources in data centers. Replication and consensus protocols improve robustness to network faults and crashed or corrupted nodes, but these volatile environments can cause non-faulty nodes to temporarily diverge, increasing the time needed for replicas to converge on a consensus value, and give Byzantine attackers too much influence over the convergence process. This paper proposes proximal Byzantine consensus, a new approximate consensus protocol where clients use statistical models of streaming computations to decide a consensus value. In addition, it provides an interval around the decision value and the probability that the true (non-faulty, noise-free) value falls within this interval. Proximal consensus (PC) tolerates unreliable network conditions, Byzantine behavior, and other sources of noise that cause honest replica states to diverge. We evaluate our approach for scalar values, and compare PC simulations against a vector consensus (VC) protocol simulation. Our simulations demonstrate that consensus values selected by PC have lower error and are more robust against Byzantine attacks. We formally characterize the security guarantees against Byzantine attacks and demonstrate attacker influence is bound with high probability. Additionally, an informal complexity analysis suggests PC scales better to higher dimensions than convex hull-based protocols such as VC.
Paper Structure (15 sections, 27 equations, 4 figures, 3 algorithms)

This paper contains 15 sections, 27 equations, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Proximal Byzantine Consensus
  3. System design and threat model
  4. One-shot proximal consensus
  5. Coordinated proximal consensus
  6. System model
  7. Network model
  8. Threat model
  9. Consensus as probability maximization
  10. Computing a proximal consensus
  11. Run-time complexity
  12. Security guarantees against adversaries
  13. Evaluation
  14. Related Work
  15. Conclusion

Figures (4)

  • Figure 1: Tverberg consensus selects points within the convex hull of non-faulty replicas. Proximal consensus selects points most likely to have been produced by non-faulty replicas.
  • Figure 2: System Architecture for a fault-tolerant data pipeline.
  • Figure 3: Counting the number of tails flipped.
  • Figure 4: Evaluation results comparing the accuracy of PC and VC, as well as the PI and convex hull, respectively.

Theorems & Definitions (4)

  • Definition 2.1: Proximal Byzantine Consensus Problem
  • Definition 4.1: Proximal consensus of $Q$
  • Definition 4.2: Conditional Probability
  • Definition 4.3: Effective attacks