The Hardness of the Closest Vector Problem With Preprocessing Over$ell_infty$Norm

We show that the closest vector problem with preprocessing (CVPP) over
$ell_infty$
norm
$(hboxCVPP_infty)$
is NP-hard. The result is obtained by the reduction from the subset sum problem with preprocessing to
$hbox CVPP_infty$
. The reduction also shows the NP-hardness of
$hbox CVP_infty$
, which is much simpler than all previously known proofs. In addition, we also give a direct reduction from exact 3-sets cover problem to
$hbox CVPP_infty$
.