Secure Distributed Hypothesis Testing

2026-05-28

AI Summary

This work establishes the impossibility of secure distributed hypothesis testing under the standard model and, for the first time, formally demonstrates this fundamental limitation. To circumvent this barrier, the authors propose a novel protocol leveraging one-bit shared keys among clients and Private Simultaneous Messages (PSM). Their approach first symmetrizes the test distribution into a canonical form via key-based transformations, achieving information-theoretic perfect security for simple hypothesis classes. For general finite hypothesis classes over finite domains, they reduce the problem to standard hypothesis testing through a PSM-based construction, thereby preserving information-theoretic security while attaining polynomial communication complexity and key length.

Abstract

In distributed hypothesis testing, a central server performs hypothesis testing based on information received from distributed sensors/clients. We study a secure variant of this problem in which the central server determines the hypothesis class of an underlying distribution without learning any additional information about the distribution itself. We prove that, in its standard form, this is impossible to achieve, even for simple and highly restricted cases. To bypass this impossibility, we augment the model with a shared secret key available to clients but hidden from the server. We show that a single-bit secret key enables perfectly secure testing for simple classes by reducing the test distributions to a symmetric, canonical instance. Finally, for arbitrary hypothesis classes over finite domains, we establish a reduction to standard hypothesis testing using Private Simultaneous Messages (PSM) protocols, achieving polynomial communication and key lengths.

Problem

• Secure Distributed Hypothesis Testing
• Privacy
• Shared Secret Key
• Hypothesis Classes
• Information-theoretic Security

Innovation

• Secure Distributed Hypothesis Testing
• Shared Secret Key
• Private Simultaneous Messages (PSM)
• Information-Theoretic Security
• Hypothesis Class Reduction