Enforcement of K-Step Opacity with Edit Functions

Opacity is an information flow property for dynamic systems describing plausible deniability, that is whether an eavesdropper can deduce that "secret" behavior has occurred. In particular, K-step opacity considers secret actions that have occurred within the last K-steps in the past. We consider the problem of K-step opacity enforcement over automata using obfuscation. We present a general framework for K-step opacity enforcement and transform the problem of enforcing K-step opacity to enforcing current-state opacity. We can then apply existing obfuscation synthesis methods for current-state opacity to K-step opacity. We demonstrate this approach by enforcing privacy in the context of a novel contact tracing model.