  We show the first dimension-preserving search-to-decision reductions for
approximate SVP and CVP. In particular, for any $\gamma \leq 1 + O(\log n/n)$,
we obtain an efficient dimension-preserving reduction from $\gamma^{O(n/\log
n)}$-SVP to $\gamma$-GapSVP and an efficient dimension-preserving reduction
from $\gamma^{O(n)}$-CVP to $\gamma$-GapCVP. These results generalize the known
equivalences of the search and decision versions of these problems in the exact
case when $\gamma = 1$. For SVP, we actually obtain something slightly stronger
than a search-to-decision reduction---we reduce $\gamma^{O(n/\log n)}$-SVP to
$\gamma$-unique SVP, a potentially easier problem than $\gamma$-GapSVP.
