  We consider fundamental limits for communicating over a compound channel when
the state of the channel needs to be masked. Our model is closely related to an
area of study known as covert communication that is a setting in which the
transmitter wishes to communicate to legitimate receiver(s) while ensuring that
the communication is not detected by an adversary. The main contribution in our
two-state masking setup is the establishment of bounds on the throughput-key
region when the constraint that quantifies how much the states are masked is
defined to be the total variation distance between the two channel-induced
distributions. For the scenario in which the key length is infinite, we provide
sufficient conditions for when the bounds to coincide for the throughput, which
follows the square-root law. Numerical examples, including that of a Gaussian
channel, are provided to illustrate our results.
