Defense Against Shortest Path Attacks

TL;DR

This paper proposes a game-theoretic defense mechanism to protect shortest path computations in networks from malicious manipulation, balancing security and user experience through heuristic and linear programming solutions.

Contribution

It introduces a novel Stackelberg game model for defending shortest path integrity and develops heuristic algorithms and linear programming relaxations for practical implementation.

Findings

Defense methods often reach the lower bound of defender's cost.

Heuristic solutions effectively balance attack prevention and path accuracy.

Approaches are validated on synthetic and real network data.

Abstract

Identifying shortest paths between nodes in a network is an important task in many applications. Recent work has shown that a malicious actor can manipulate a graph to make traffic between two nodes of interest follow their target path. In this paper, we develop a defense against such attacks by modifying the edge weights that users observe. The defender must balance inhibiting the attacker against any negative effects on benign users. Specifically, the defender's goals are: (a) recommend the shortest paths to users, (b) make the lengths of the shortest paths in the published graph close to those of the same paths in the true graph, and (c) minimize the probability of an attack. We formulate the defense as a Stackelberg game in which the defender is the leader and the attacker is the follower. We also consider a zero-sum version of the game in which the defender's goal is to minimize cost while achieving the minimum possible attack probability. We show that the defense problem is NP-hard and propose heuristic solutions for both the zero-sum and non-zero-sum settings. By relaxing some constraints of the original problem, we formulate a linear program for local optimization around a feasible point. We present defense results with both synthetic and real networks and show that our methods often reach the lower bound of the defender's cost.