  We consider the problem of covert communication over a state-dependent
channel when the channel state is available either non-causally, causally, or
strictly causally, either at the transmitter alone or at both transmitter and
receiver. Covert communication with respect to an adversary, called "warden,"
is one in which, despite communication over the channel, the warden's
observation remains indistinguishable from an output induced by innocent
channel-input symbols. Covert communication involves fooling an adversary in
part by a proliferation of codebooks; for reliable decoding at the legitimate
receiver, the codebook uncertainty is typically removed via a shared secret key
that is unavailable to the warden. In contrast to previous work, we do not
assume the availability of a shared key at the transmitter and legitimate
receiver. Instead, shared randomness is extracted from the channel state in a
manner that keeps it secret from the warden, despite the influence of the
channel state on the warden's output. When channel state is available at the
transmitter and receiver, we derive the covert capacity region. When channel
state is only available at the transmitter, we derive inner and outer bounds on
the covert capacity. We provide examples for which the covert capacity is
positive with knowledge of channel state information but is zero without it.
