  We consider the problem of encoding a deterministic source sequence (a.k.a.\
individual sequence) for the degraded wiretap channel by means of an encoder
and decoder that can both be implemented as finite--state machines. Our first
main result is a necessary condition for both reliable and secure transmission
in terms of the given source sequence, the bandwidth expansion factor, the
secrecy capacity, the number of states of the encoder and the number of states
of the decoder. Equivalently, this necessary condition can be presented as a
converse bound (i.e., a lower bound) on the smallest achievable bandwidth
expansion factor. The bound is asymptotically achievable by Lempel-Ziv
compression followed by good channel coding for the wiretap channel. Given that
the lower bound is saturated, we also derive a lower bound on the minimum
necessary rate of purely random bits needed for local randomness at the encoder
in order to meet the security constraint. This bound too is achieved by the
same achievability scheme. Finally, we extend the main results to the case
where the legitimate decoder has access to a side information sequence, which
is another individual sequence that may be related to the source sequence, and
a noisy version of the side information sequence leaks to the wiretapper.
