Runtime enforcement of K-step opacity

We study the enforcement of K-step opacity at runtime. In K-step opacity, the knowledge of the secret is of interest to the attacker within K steps after the secret occurs and becomes obsolete afterwards. We introduce the mechanism of runtime enforcer that is placed between the output of the system and the attacker and enforces opacity using delays. If an output event from the system violates K-step opacity, the enforcer stores the event in the memory, for the minimal number of system steps until the secret is no longer interesting to the attacker (or, K-step opacity holds again).