We prove that the closest
vector problem with preprocessing (CVPP) is NP-hard to approximate
within any factor less than *sqrt{5/3}*. More
specifically, we show that there exists a reduction from an
NP-hard problem to the approximate closest vector problem such
that the lattice depends only on the size of the original problem,
and the specific instance is encoded solely in the target
vector. It follows that there are lattices for which the closest
vector problem cannot be approximated within factors *gamma
< sqrt{5/3}* in polynomial time, no matter how the lattice
is represented, unless NP is equal to P (or NP is contained in
P/poly, in case of nonuniform sequences of lattices). The result
easily extends to any *L _{p}* norm, for