By Topic

The shortest vector in a lattice is hard to approximate to within some constant

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Micciancio, D. ; Lab. for Comput. Sci., MIT, Cambridge, MA, USA

We show the shortest vector problem in the l2 norm is NP-hard (for randomized reductions) to approximate within any constant factor less than √2. We also give a deterministic reduction under a reasonable number theoretic conjecture. Analogous results hold in any lp norm (p⩾1). In proving our NP-hardness result, we give an alternative construction satisfying Ajtai's probabilistic variant of Sauer's lemma, that greatly simplifies Ajtai's original proof

Published in:

Foundations of Computer Science, 1998. Proceedings. 39th Annual Symposium on

Date of Conference:

8-11 Nov 1998