  We consider a covert communication scenario where a transmitter wishes to
communicate simultaneously to two legitimate receivers while ensuring that the
communication is not detected by an adversary, the warden. The legitimate
receivers and the adversary observe the transmission from the transmitter via a
three-user discrete or Gaussian memoryless broadcast channel. We focus on the
case where the "no-input" symbol is not redundant, i.e., the output
distribution at the warden induced by the no-input symbol is not a mixture of
the output distributions induced by other input symbols, so that the covert
communication is governed by the square root law, i.e., at most
$\Theta(\sqrt{n})$ bits can be transmitted over $n$ channel uses. We show that
for such a setting, a simple time-division strategy achieves the optimal
throughputs for a non-trivial class of broadcast channels; this is not true for
communicating over broadcast channels without the covert communication
constraint. Our result implies that a code that uses two separate optimal
point-to-point codes each designed for the constituent channels and each used
for a fraction of the time is optimal in the sense that it achieves the best
constants of the $\sqrt{n}$-scaling for the throughputs. Our proof strategy
combines several elements in the network information theory literature,
including concave envelope representations of the capacity regions of broadcast
channels and El Gamal's outer bound for more capable broadcast channels.
