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Ensuring System-Level Protection against Eavesdropping Adversaries in Distributed Dynamical Systems

Dipankar Maity, Van Sy Mai

TL;DR

This work proves that state-of-the-art distributed algorithms, which rely on communicating the agents’ states, are vulnerable in that the final states can be perfectly estimated by any adversary including those with arbitrarily small eavesdropping success probability.

Abstract

In this work, we address the objective of protecting the states of a distributed dynamical system from eavesdropping adversaries. We prove that state-of-the-art distributed algorithms, which rely on communicating the agents' states, are vulnerable in that the final states can be perfectly estimated by any adversary including those with arbitrarily small eavesdropping success probability. While existing literature typically adds an extra layer of protection, such as encryption or differential privacy techniques, we demonstrate the emergence of a fundamental protection quotient in distributed systems when innovation signals are communicated instead of the agents' states.

Ensuring System-Level Protection against Eavesdropping Adversaries in Distributed Dynamical Systems

TL;DR

This work proves that state-of-the-art distributed algorithms, which rely on communicating the agents’ states, are vulnerable in that the final states can be perfectly estimated by any adversary including those with arbitrarily small eavesdropping success probability.

Abstract

In this work, we address the objective of protecting the states of a distributed dynamical system from eavesdropping adversaries. We prove that state-of-the-art distributed algorithms, which rely on communicating the agents' states, are vulnerable in that the final states can be perfectly estimated by any adversary including those with arbitrarily small eavesdropping success probability. While existing literature typically adds an extra layer of protection, such as encryption or differential privacy techniques, we demonstrate the emergence of a fundamental protection quotient in distributed systems when innovation signals are communicated instead of the agents' states.
Paper Structure (19 sections, 6 theorems, 45 equations, 4 figures, 2 algorithms)

This paper contains 19 sections, 6 theorems, 45 equations, 4 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Agent Dynamic Model and Assumption
  4. Eavesdropping Adversaries
  5. $\epsilon$-Protection Against Adversaries
  6. Innovation-shared Communication
  7. System-Level Protection Analysis
  8. State-based Communication
  9. Innovation-based communications
  10. The case $b=0$
  11. The case $b=1$
  12. Application to Distributed Optimization
  13. Optimization with Innovation Communication
  14. Simulation Results
  15. Conclusion
  16. ...and 4 more sections

Key Result

Theorem 1

The state of the agent is $0$-protected if $m_t = x_t$.

Figures (4)

  • Figure 1: Problem setup
  • Figure 2: Exact protection and lower bound in \ref{['eq_protection_LB']} with $\eta=1$.
  • Figure 3: The state trajectory of the first agent.
  • Figure 4: Convergence speed vs. protection from Theorem \ref{['thm_protection_infinite_horizon']} by varying $\alpha$ and $x_0$.

Theorems & Definitions (14)

  • Definition 1
  • Remark 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 2
  • Corollary 1
  • proof
  • Corollary 2
  • ...and 4 more