Private evaluation of invariant equations

Determine whether the invariant equations governing physical telemetry can themselves be evaluated privately, without disclosing the invariant coefficients or aspects of plant topology to the federated-learning coordinator.

Background

The PA-FL Lite circuit hides the raw telemetry batch but embeds the invariant coefficients, offsets, and tolerances as public circuit constants. Consequently, the coordinator can learn aspects of the plant's topology even though it cannot inspect individual sensor readings.

The paper identifies private evaluation of the invariant equations as unresolved. Solving this problem would preserve both telemetry confidentiality and the confidentiality of the physical relationships used to validate client data.

References

And while ZK conceals the raw telemetry batch, the public verification circuit embeds the invariant coefficients, disclosing aspects of plant topology to the coordinator. This leaves open whether the invariant equations themselves can be evaluated privately.

— Physics-Attested Federated Learning: Securing Collaborative Anomaly Detection in Critical Water Infrastructure  (2609.34804 - Nijsse et al., 28 Sep 2026) in Section 6, Limitations