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Fundamental Limits of Routing Attack on Network Overload

Xinyu Wu, Eytan Modiano

TL;DR

The results demonstrate that the proposed algorithms can accurately quantify the risk of overload given an arbitrary set of hijacked nodes and identify the critical nodes that should be protected against routing attacks.

Abstract

We quantify the threat of network adversaries to inducing \emph{network overload} through \emph{routing attacks}, where a subset of network nodes are hijacked by an adversary. We develop routing attacks on the hijacked nodes for two objectives related to overload: \emph{no-loss throughput minimization} and \emph{loss maximization}. The first objective attempts to identify a routing attack that minimizes the network's throughput that is guaranteed to survive. We develop a polynomial-time algorithm that can output the optimal routing attack in multi-hop networks with global information on the network's topology, and an algorithm with an approximation ratio of $2$ under partial information. The second objective attempts to maximize the throughput loss. We demonstrate that this problem is NP-hard, and develop two approximation algorithms with multiplicative and additive guarantees respectively in single-hop networks. We further investigate the adversary's optimal selection of nodes to hijack that can maximize network overload. We propose a heuristic polynomial-time algorithm to solve this NP-hard problem, and prove its optimality in special cases. We validate the near-optimal performance of the proposed algorithms over a wide range of network settings. Our results demonstrate that the proposed algorithms can accurately quantify the risk of overload given an arbitrary set of hijacked nodes and identify the critical nodes that should be protected against routing attacks.

Fundamental Limits of Routing Attack on Network Overload

TL;DR

The results demonstrate that the proposed algorithms can accurately quantify the risk of overload given an arbitrary set of hijacked nodes and identify the critical nodes that should be protected against routing attacks.

Abstract

We quantify the threat of network adversaries to inducing \emph{network overload} through \emph{routing attacks}, where a subset of network nodes are hijacked by an adversary. We develop routing attacks on the hijacked nodes for two objectives related to overload: \emph{no-loss throughput minimization} and \emph{loss maximization}. The first objective attempts to identify a routing attack that minimizes the network's throughput that is guaranteed to survive. We develop a polynomial-time algorithm that can output the optimal routing attack in multi-hop networks with global information on the network's topology, and an algorithm with an approximation ratio of under partial information. The second objective attempts to maximize the throughput loss. We demonstrate that this problem is NP-hard, and develop two approximation algorithms with multiplicative and additive guarantees respectively in single-hop networks. We further investigate the adversary's optimal selection of nodes to hijack that can maximize network overload. We propose a heuristic polynomial-time algorithm to solve this NP-hard problem, and prove its optimality in special cases. We validate the near-optimal performance of the proposed algorithms over a wide range of network settings. Our results demonstrate that the proposed algorithms can accurately quantify the risk of overload given an arbitrary set of hijacked nodes and identify the critical nodes that should be protected against routing attacks.

Paper Structure

This paper contains 37 sections, 12 theorems, 13 equations, 18 figures, 3 tables, 8 algorithms.

Table of Contents

  1. Introduction
  2. Network Models and Problem Definition
  3. Network Models
  4. Multi-hop network
  5. Single-hop network
  6. Problem Definition
  7. No-Loss Throughput Minimization
  8. Problem Formulation
  9. Exact Algorithms
  10. Brute-Force under $|\mathcal{V}_A|=O(1)$
  11. MaxFlow-based Solution for General $\mathcal{V}_A$
  12. 2-Approximation Algorithm with Partial Information
  13. Practical Extensions
  14. Heuristic for Distributed Attack
  15. Constraints on Routing Attacks
  16. ...and 22 more sections

Key Result

Proposition 1

Suppose there are $P$ paths $\{Path_p\}_{p=1}^P$ of a commodity, where a fraction $\theta_p$ of the traffic takes $Path_p$. The corresponding routing matrix $\mathbf{X}$ satisfies $x_{ij} = \beta_{ij} / \sum_{k:(i,k)\in \mathcal{E}}\beta_{ik},~\forall (i,j)\in \mathcal{E}$, where $\beta_{ij} = \sum_

Figures (18)

  • Figure 1: (a) Switch network; (b) Server farm; (c) Bipartite graph (in the dashed box) with meta source $s_0$ and destination $d_0$
  • Figure 2: (a) A 6-node network with $\mathcal{V}_A=\{3\}$ and $\mathcal{V}_N = \{1,2,4,5,6\}$; (b) Optimal routing to minimize $\lambda^*$ is $(x_{34}, x_{35}) = (0,1)$: $\lambda_{OPT}^*$ is $2$ and $(5,6)$ is the first saturated link; (c) Given $\lambda=10$, the optimal routing to maximize loss is $(x_{34}, x_{35}) = (1,0)$, with maximum loss of $\lambda - c_{46} = 10 - 3 = 7$.
  • Figure 3: One of the 4 combinations must be optimal, where $\mathcal{V}_A=\{2,3\}$ serve all traffic through the highlighted links.
  • Figure 4: Example of Algorithm \ref{['Alg:optimal-metric-1-general']}. Assume that $c_{12}, c_{13}\rightarrow \infty$ which means $(1,2)$ and $(1,3)$ will not be saturated. We can calculate $MF[2] = x_{12}$, $MF[3] = 1$ since the adversarial node $2$ can route all packets to $3$, $MF[4] = x_{12} + x_{13}x_{34}$ since node $2$ can route all packets to $4$, and $MF[5] = 1$ since node $4$ can route all packets to $5$. Then we find the first saturated connected downstream link of each node in $\{2,3,4,5\}$, where the calculation in (a) and (c) follows line 5 in Algorithm \ref{['Alg:optimal-metric-1-general']} since $2,4\in \mathcal{V}_A$ with links highlighted in red, while that in (b) and (d) follows line 4 since $3,5\in \mathcal{V}_N$ highlighted in blue.
  • Figure 5: Example of running Algorithm \ref{['Alg:approximation-2']} from (a) to (c)
  • ...and 13 more figures

Theorems & Definitions (23)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3
  • proof
  • Corollary 1
  • ...and 13 more