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In this paper, we discuss the problem of detecting general faults in distributed systems that handle confidential information. Detecting non-crash faults is difficult in this setting because, to check the behavior of a given node, we need to know its expected behavior -- but that can depend on the confidential information. Classical zero-knowledge proofs are difficult to apply because they are designed to verify functions with a fixed number of inputs, but in many distributed systems, both the size and the number of a node's "inputs" (the messages it has received from other nodes) are not known. We propose an approach that can efficiently provide zero-knowledge fault detection for certain systems. Our approach spreads the detection tasks across multiple nodes, leveraging a node's existing knowledge whenever possible. We use epistemic reasoning to infer such knowledge, and we combine classical zero-knowledge proofs with a special data structure to handle inputs of unknown size. We show how our approach can be applied to a simple example system, and we report some initial performance measurements.