  In this paper we review the technique to solve the CVP based on dual
HKZ-bases by J. Bloemer. The technique is based on the transference theorems
given by Banaszczyk which imply some necessary conditions on the coefficients
of the closest vectors with respect to a basis whose dual is HKZ reduced.
Recursively, starting with the last coefficient, intervals of length i can be
derived for the i-th coefficient of any closest vector. This leads to n!
candidates for closest vectors. In this paper we refine the necessary
conditions derived from the transference theorems, giving an exponential
reduction of the number of candidates. The improvement is due to the fact that
the lengths of the intervals are not independent. In the original algorithm the
candidates for a coefficient pair (a_i,a_{i+1}) correspond to the integer
points in a rectangle of volume i(i+1). In our analysis we show that the
candidates for (a_i,a_{i+1}) in fact lie in an ellipse with transverse and
conjugate diameter i+1, respectively i. This reduces the overall number of
points to be enumerated by an exponential factor of about 0.886^n. We further
show how a choice of the coefficients (a_n,...,a_{i+1}) influences the interval
from which a_i can be chosen. Numerical computations show that these
considerations allow to bound the number of points to be enumerated by n^{0.75
n} for 10 <= n <= 2000. Under the assumption that the Gaussian heuristic for
the length of the shortest nonzero vector in a lattice is tight, this number
can even be bounded by 2^{-2n} n^{n/2}.
