  Security properties of real-time systems often involve reasoning about
hyper-properties, as opposed to properties of single executions or trees of
executions. These hyper-properties need to additionally be expressive enough to
reason about real-time constraints. Examples of such properties include
information flow, side channel attacks and service-level agreements. In this
paper we study computational problems related to a branching-time,
hyper-property extension of metric temporal logic (MTL) that we call HCMTL*. We
consider both the interval-based and point-based semantics of this logic. The
verification problem that we consider is to determine if a given HCMTL* formula
$\varphi$ is true in a system represented by a timed automaton. We show that
this problem is undecidable. We then show that the verification problem is
decidable if we consider executions upto a fixed time horizon $T$. Our
decidability result relies on reducing the verification problem to the truth of
an MSO formula over reals with a bounded time interval.
