# On the Performance Analysis of Binary Hypothesis Testing with Byzantine Sensors

## TL;DR

This paper analyzes how Byzantine attacks affect distributed binary hypothesis testing, proposing an optimal attack strategy that maximizes detection errors under energy constraints, supported by theoretical analysis and simulations.

## Contribution

It formulates an optimization framework for Byzantine attacks in distributed detection and derives properties of optimal attack strategies using convex and parametric optimization.

## Key findings

- Optimal attack strategies significantly increase detection error probabilities.
- The proposed coordinate descent algorithm effectively finds optimal attack solutions.
- Simulation results confirm the effectiveness of the attack strategies.

## Abstract

We investigate the impact of Byzantine attacks in distributed detection under binary hypothesis testing. It is assumed that a fraction of the transmitted sensor measurements are compromised by the injected data from a Byzantine attacker, whose purpose is to confuse the decision maker at the fusion center. From the perspective of a Byzantine attacker, under the injection energy constraint, an optimization problem is formulated to maximize the asymptotic missed detection error probability, which is based on the Kullback-Leibler divergence. The properties of the optimal attack strategy are analyzed by convex optimization and parametric optimization methods. Based on the derived theoretic results, a coordinate descent algorithm is proposed to search the optimal attack solution. Simulation examples are provided to illustrate the effectiveness of the obtained attack strategy.