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Secure Over-the-Air Computation Against Multiple Eavesdroppers using Correlated Artificial Noise

Year: 2026
Type: article
Abstract: Over-the-air (OtA) computation enables scalable analog aggregation by exploiting the superposition property of wireless channels, making it an attractive joint communication and computation paradigm for distributed sensing and learning. However, the uncoded nature of analog transmission exposes the computation result to eavesdropping, and the fundamental security limits of OtA computation against multiple cooperating adversaries remain poorly understood. In this paper, we develop an estimation-theoretic framework for analyzing the security of analog OtA computation in the presence of multiple distributed eavesdroppers that may jointly process their observations. We first derive the optimal estimator for cooperating eavesdroppers and bounds on the achievable estimation accuracy of both the legitimate receiver and the adversaries. Our analysis reveals a key insight: while random channel phase misalignment provides significant inherent MSE-security against individual eavesdroppers, this protection largely disappears once multiple eavesdroppers cooperate. Motivated by this observation, we propose a correlated artificial noise design based on zero-forcing that preserves the aggregation accuracy at the legitimate receiver while maximizing the estimation error at the cooperative eavesdroppers. Numerical results demonstrate that the proposed design substantially reduces the security advantage gained through eavesdropper cooperation and achieves security close to uncorrelated artificial-noise schemes without sacrificing computation accuracy. These results provide both a theoretical characterization of the security limits of analog OtA computation and a practical design guideline for its secure deployment in real-world wireless systems.
DOI: 10.1109/tcomm.2026.3742861
Open Access status: green
OpenAlex ID: W4416967227
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