Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

Reports tagged with Computational Problems in Integer Lattices:
TR97-031 | 9th September 1997
Oded Goldreich

On the Limits of Non-Approximability of Lattice Problems

Revisions: 2

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 >>>

TR99-002 | 22nd January 1999
Oded Goldreich, Daniele Micciancio, Shmuel Safra and Jean-Pierre Seifert.

Approximating shortest lattice vectors is not harder than approximating closest lattice vectors.

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 >>>

ISSN 1433-8092 | Imprint