We show simple constant-round interactive proof systems for
problems capturing the approximability, to within a factor of $\sqrt{n}$,
of optimization problems in integer lattices; specifically,
the closest vector problem (CVP), and the shortest vector problem (SVP).
These interactive proofs are for the ``coNP direction'';
that is, ... more >>>

We show that given oracle access to a subroutine which
returns approximate closest vectors in a lattice, one may find in
polynomial-time approximate shortest vectors in a lattice.
The level of approximation is maintained; that is, for any function
$f$, the following holds:
Suppose that the subroutine, on input a ... more >>>