Buffered control for opacity in timed automata

2026-06-26

AI Summary

This work addresses the enforcement of opacity in timed automata under buffered observations—defined as sequences of actions together with the integer parts of their timestamps—by dynamically controlling the enabling of actions. It introduces, for the first time, a formal model of controllable opacity under buffered observations and establishes that full opacity and weak opacity are equivalent in this setting. While the existence of a control strategy is undecidable in general, the problem becomes decidable under two natural restrictions: when the controller’s switching frequency is bounded, or when all controllable actions are both observable and distinguishable. For these decidable cases, tight computational complexity bounds are provided.

Abstract

Timed automata are an extension of finite automata that can measure and react to the passage of time, handling real-time constraints by using clocks. The timed opacity problem, where an attacker attempts to infer from observed actions and timestamps whether a secret location was visited, was shown undecidable for timed automata. Execution-time opacity is a decidable though limited setting in which the attacker attempts to detect whether the secret location was visited, by only relying on the run duration. Here, we significantly extend this setting, by allowing the attacker to observe all observable actions, in the right order though with only the integral parts of their timestamps, which we call buffered observations. We consider the controlled setting, in which we aim at dynamically defining a sequence of sets of enabled actions ensuring opacity with buffered observations. We first prove the inter-reducibility of full opacity (observations must not leak the visit of the secret location) and weak opacity (the attacker might prove that the location was not visited, but not that it was visited) in this new controlled setting. Then, we prove the undecidability of the problem of existence of a sequential control strategy ensuring opacity under buffered observations. Finally and most importantly, we prove that decidability is retrieved in two independent cases, with their tight theoretical complexities, with and without control. These two assumptions express realistic limitations of the controller. The first case is when the strategy of the controller changes at most an a priori fixed number of times per time unit, which is not a strong practical assumption. The second case is when all controllable actions are observable and distinguishable by an attacker.

Problem

• timed automata
• opacity
• buffered observations
• control
• secret location

Innovation

• buffered observations
• timed opacity
• control strategy
• decidability
• timed automata