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BCM-Broadcast: A Byzantine-Tolerant Causal Broadcast Algorithm for Distributed Mobile Systems

Leila NamvariTazehkand, Saied Pashazadeh, Ali Ebnenasir

TL;DR

BCM-Broadcast addresses causal broadcast in distributed mobile systems with Byzantine nodes by introducing a hierarchical, three-layer architecture that interplays Byzantine failure management, causal delivery management, and mobility management. Built on BR-Broadcast and C-Broadcast primitives, it proves a set of properties (validity, integrity, termination, causality, safety) and demonstrates linear message complexity, with safety probability analyzed via a Poisson-process model under mobility. The paper substantiates correctness through theoretical proofs and an execution scenario, showing causal order preservation across handoffs. It also outlines concrete directions for future work, including fully mobile architectures and dynamic, multi-fault environments to broaden the applicability of the BCM-Broadcast framework.

Abstract

This paper presents an algorithm, called BCM-Broadcast, for the implementation of causal broadcast in distributed mobile systems in the presence of Byzantine failures. The BCM-Broadcast algorithm simultaneously focuses on three critical challenges in distributed systems: Byzantine failures, Causality, and Mobility. We first present a hierarchical architecture for BCM-Broadcast. Then, we define twelve properties for BCM-Broadcast, including validity, integrity, termination, and causality. We then show that BCM-Broadcast satisfies all these properties. We also prove the safety of BCM-Broadcast; i.e., no healthy process delivers a message from any Byzantine process, assuming that the number of Byzantine processes is less than a third of the total number of mobile nodes. Subsequently, we show that the message complexity of BCM-Broadcast is linear. Finally, using the Poisson process, we analyze the probability of the violation of the safety condition under different mobility scenarios.

BCM-Broadcast: A Byzantine-Tolerant Causal Broadcast Algorithm for Distributed Mobile Systems

TL;DR

BCM-Broadcast addresses causal broadcast in distributed mobile systems with Byzantine nodes by introducing a hierarchical, three-layer architecture that interplays Byzantine failure management, causal delivery management, and mobility management. Built on BR-Broadcast and C-Broadcast primitives, it proves a set of properties (validity, integrity, termination, causality, safety) and demonstrates linear message complexity, with safety probability analyzed via a Poisson-process model under mobility. The paper substantiates correctness through theoretical proofs and an execution scenario, showing causal order preservation across handoffs. It also outlines concrete directions for future work, including fully mobile architectures and dynamic, multi-fault environments to broaden the applicability of the BCM-Broadcast framework.

Abstract

This paper presents an algorithm, called BCM-Broadcast, for the implementation of causal broadcast in distributed mobile systems in the presence of Byzantine failures. The BCM-Broadcast algorithm simultaneously focuses on three critical challenges in distributed systems: Byzantine failures, Causality, and Mobility. We first present a hierarchical architecture for BCM-Broadcast. Then, we define twelve properties for BCM-Broadcast, including validity, integrity, termination, and causality. We then show that BCM-Broadcast satisfies all these properties. We also prove the safety of BCM-Broadcast; i.e., no healthy process delivers a message from any Byzantine process, assuming that the number of Byzantine processes is less than a third of the total number of mobile nodes. Subsequently, we show that the message complexity of BCM-Broadcast is linear. Finally, using the Poisson process, we analyze the probability of the violation of the safety condition under different mobility scenarios.
Paper Structure (17 sections, 27 theorems, 9 equations, 7 figures, 1 table, 8 algorithms)

This paper contains 17 sections, 27 theorems, 9 equations, 7 figures, 1 table, 8 algorithms.

Table of Contents

  1. Introduction
  2. Basic Concepts
  3. Distributed Mobile System
  4. Basic Definitions
  5. Defining the Properties of BCM-Broadcast
  6. BCM-Broadcast: The Proposed Algorithm
  7. Data Structures
  8. BCM-Broadcast Layers
  9. Byzantine Failure Management
  10. Causal Delivery Management
  11. Mobility Management
  12. The BCM-Broadcast Algorithm
  13. An Execution Scenario
  14. Correctness of the BCM-Broadcast Algorithm
  15. Stochastic Analysis of the t-Condition
  16. ...and 2 more sections

Key Result

Lemma 5.1

If an MSS $s_j$ bcm-Sbroadcasts a message $m$, it bcm-Sdelivers $m$.

Figures (7)

  • Figure 1: A distributed mobile system
  • Figure 2: The hierarchical architecture
  • Figure 3: The steps of handoff of $h_i$ from $s_j$ to $s_k$
  • Figure 4: The layers of the BCM-Broadcast algorithm
  • Figure 5: The relationship between the operations in different layers
  • ...and 2 more figures

Theorems & Definitions (32)

  • Definition 2.1: Handoff
  • Definition 2.2: Byzantine Failure
  • Definition 2.3: BR-Broadcast for mobile systems
  • Definition 2.4: C-Broadcast
  • Definition 3.1: BCM-Broadcast
  • Lemma 5.1
  • Theorem 5.2
  • Theorem 5.3
  • Lemma 5.4
  • Lemma 5.5
  • ...and 22 more