  We consider reliable and secure communication over intersymbol interference
wiretap channels (ISI-WTCs). In particular, we first derive an achievable
secure rate for ISI-WTCs without imposing any constraints on the input
distribution. Afterwards, we focus on the setup where the input distribution of
the ISI-WTC is constrained to be a time-invariant finite-order Markov chain.
Optimizing the parameters of this Markov chain toward maximizing the achievable
secure rates is a computationally intractable problem in general, and so,
toward finding a local maximum, we propose an iterative algorithm that at every
iteration replaces the secure rate function with a suitable~surrogate function
whose maximum can be found efficiently. Although the secure rates achieved in
the unconstrained setup are potentially larger than the secure rates achieved
in the constrained setup, the latter setup has the advantage of leading to
efficient algorithms for estimating and optimizing the achievable secure rates,
and also has the benefit of being the basis of efficient coding schemes.
