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This paper investigates secure distributed hypothesis testing, where a central server infers the hypothesis class of a distribution based on client data without learning the distribution itself. The authors prove that perfectly secure testing is impossible without additional assumptions. They then demonstrate that a single-bit shared secret key enables perfectly secure testing for simple hypothesis classes and provide a reduction to standard hypothesis testing using Private Simultaneous Messages (PSM) protocols for arbitrary hypothesis classes.
Even in simple cases, perfectly secure distributed hypothesis testing is impossible without a shared secret, but a single bit can be enough to restore perfect security for some classes.
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.