  Covert communication is necessary when revealing the mere existence of a
message leaks sensitive information to an attacker. Consider a network link
where an authorized transmitter Jack sends packets to an authorized receiver
Steve, and the packets visit Alice, Willie, and Bob, respectively, before they
reach Steve. Covert transmitter Alice wishes to alter the packet stream in some
way to send information to covert receiver Bob without watchful and capable
adversary Willie being able to detect the presence of the message. In our
previous works, we addressed two techniques for such covert transmission from
Alice to Bob: packet insertion and packet timing. In this paper, we consider
covert communication via bit insertion in packets with available space (e.g.,
with size less than the maximum transmission unit). We consider three
scenarios: 1) packet sizes are independent and identically distributed (i.i.d.)
with a probability mass function (pmf) whose support is a set of one bit spaced
values; 2) packet sizes are i.i.d. with a pmf whose support is arbitrary; 3)
packet sizes may be dependent. For the first and second assumptions, we show
that Alice can covertly insert $\mathcal{O}(\sqrt{n})$ bits of information in a
flow of $n$ packets; conversely, if she inserts $\omega(\sqrt{n})$ bits of
information, Willie can detect her with arbitrarily small error probability.
For the third assumption, we prove Alice can covertly insert on average
$\mathcal{O}(c(n)/\sqrt{n})$ bits in a sequence of $n$ packets, where $c(n)$ is
the average number of conditional pmf of packet sizes given the history, with a
support of at least size two.
