  Information leakage can have dramatic consequences on systems security. Among
harmful information leaks, the timing information leakage occurs whenever an
attacker successfully deduces confidential internal information. In this work,
we consider that the attacker has access (only) to the system execution time.
We address the following timed opacity problem: given a timed system, a private
location and a final location, synthesize the execution times from the initial
location to the final location for which one cannot deduce whether the system
went through the private location. We also consider the full timed opacity
problem, asking whether the system is opaque for all execution times. We show
that these problems are decidable for timed automata (TAs) but become
undecidable when one adds parameters, yielding parametric timed automata
(PTAs). We identify a subclass with some decidability results. We then devise
an algorithm for synthesizing PTAs parameter valuations guaranteeing that the
resulting TA is opaque. We finally show that our method can also apply to
program analysis.
