What Can Verifiable Decapsulation Tests Certify? Pass Bounds and Fault-Recognition Limits for FO-Based KEMs
About
Black-box tests for Fujisaki-Okamoto decapsulation observe the sampled execution seen by the harness, whereas the reencryption computation itself is visible only through the values that reach final key derivation. We study confirmation-code-augmented KEM variants under an honest-reference harness in which the reference encapsulation fixes a hidden final-key point $\langle good,B,W\rangle$, with $W$ the confirmation witness. For a $q$-localized system under test, acceptance is bounded by honest correctness error, adversarial aliasing, final-key freshness defects, a hit on the localized suffix list $Q_G(B)$, and $2^{-\kappa}$. A one-query construction from any predictor of $W$ matches this bound up to the fresh-key coincidence term, so the list-hit event is the black-box obstruction measured by the harness. The list-hit term is bounded either by a cUP-faithful harness certificate, which transfers source confirmation-code unpredictability with a $q$-loss, or by an average conditional min-entropy bound, with separate RawEnt and TailEnt hypotheses for short diagnostic and truncation-tail codes. The same model proves a dependency-cone lower bound for non-certification claims. When the black-box observation of an honest-support harness factors through the confirmation-observable final-key target, every operation outside the support-active cone has a coupled erasure implementation with the same transcript distribution; over any implementation class containing that erasure, soundness and completeness errors of an execution certifier satisfy $\alpha+\beta\ge 1$. The ML-KEM and HQC case studies distinguish theorem-covered positive rows, finite-catalog artifact rows, and non-certification rows that carry a cone-inactivity certificate. The security of the standard KEM lines is the construction-level security supplied by the cited source analyses.