  We consider a scenario in which $K$ transmitters attempt to communicate
covert messages reliably to a legitimate receiver over a discrete memoryless
MAC while simultaneously escaping detection from an adversary who observes
their communication through another discrete memoryless MAC. We assume that
each transmitter may use a secret key that is shared only between itself and
the legitimate receiver. We show that each of the $K$ transmitters can transmit
on the order of $\sqrt{n}$ reliable and covert bits per $n$ channel uses,
exceeding which, the warden will be able to detect the communication. We
identify the optimal pre-constants of the scaling, which leads to a complete
characterization of the covert capacity region of the $K$-user binary-input
MAC. We show that, asymptotically, all sum-rate constraints are inactive unlike
the traditional MAC capacity region. We also characterize the channel
conditions that have to be satisfied for the transmitters to operate without a
secret key.
