  In this paper, the probability of Eve the Eavesdropper's correct decision is
considered both in the Gaussian and Rayleigh fading wiretap channels when using
lattice codes for the transmission.
  First, it is proved that the secrecy function determining Eve's performance
attains its maximum at y=1 on all known extremal even unimodular lattices. This
is a special case of a conjecture by Belfiore and Sol\'e. Further, a very
simple method to verify or disprove the conjecture on any given unimodular
lattice is given.
  Second, preliminary analysis on the behavior of Eve's probability of correct
decision in the fast fading wiretap channel is provided. More specifically, we
compute the truncated inverse norm power sum factors in Eve's probability
expression. The analysis reveals a performance-secrecy-complexity tradeoff:
relaxing on the legitimate user's performance can significantly increase the
security of transmission. The confusion experienced by the eavesdropper may be
further increased by using skewed lattices, but at the cost of increased
complexity.
