Behavior-Level Authorization Leakage in Trusted Authorization Services: Evaluating the Attribution Gap under Finite Observation with Stochastic Activation

Even when authorization information is hidden at the credential or access-control protocol layer, system behavior that depends on authorization state can itself become a side channel for authorization-state inference. This paper introduces the Trusted Authorization Service (TAS) as an architectural goal that enables legitimate users to verify their own authorization state through a trusted path while limiting unnecessary state inference by external observers through ordinary system behavior. This work does not implement or prove a complete TAS protocol or its security properties. Instead, as one problem within the behavioral privacy layer required by TAS, we evaluate through synthetic simulation how the activation timing of authorization-dependent control affects authorization-state attribution under finite observation. Each trial is fixed as either Authorized or Unauthorized. In Unauthorized trials, a performance degradation of magnitude \(d\) appears after an activation time \(τ\). Immediate activation is used as the baseline and compared with Exponential and Log-normal stochastic activation. A model-informed passive observer estimates the Authorized/Unauthorized state from the observed performance series. Absolute attribution performance is evaluated using balanced accuracy \(Vₐₜₜᵣ\) and ROC-AUC, while the reduction relative to the Immediate baseline is defined as the Attribution Gap. Under representative conditions with Moderate Natural Variation, \(d=0.02\), and a 7-day observation horizon, Immediate activation yielded \(Vₐₜₜᵣ≈0.99\) and ROC-AUC \(≈1.00\), whereas Exponential activation reduced them to approximately 0.57 and 0.60, and Log-normal activation to approximately 0.51 and 0.52. As the observation horizon increased to 30 and 90 days, attribution performance recovered and the Attribution Gap narrowed. An additional experiment that maintained the same sampling frequency as the 7-day condition while increasing the number of observations also showed a narrowing of the Gap, indicating that the effect could not be explained solely by reduced sampling density under a fixed observation count. These results suggest that, in the synthetic, model-matched, passive-observer setting considered here, stochastic activation does not make authorization state permanently unidentifiable, but can increase the cost of authorization-state attribution under finite observation. This motivates evaluating TAS behavioral privacy not as a static hidden/not-hidden property, but as an inference-resistance problem conditioned on the observer’s finite observation horizon, sampling budget, and inference capability.