Unique Shortest Vector Problem for max norm is NP-hard

Than Quang Khoat; Nguyen Hong Tan

Paper 2008/366

Unique Shortest Vector Problem for max norm is NP-hard

Than Quang Khoat and Nguyen Hong Tan

Abstract

The unique Shortest vector problem (uSVP) in lattice theory plays a crucial role in many public-key cryptosystems. The security of those cryptosystems bases on the hardness of uSVP. However, so far there is no proof for the proper hardness of uSVP even in its exact version. In this paper, we show that the exact version of uSVP for $\ell_\infty$ norm is NP-hard. Furthermore, many other lattice problems including unique Subspace avoiding problem, unique Closest vector problem and unique Generalized closest vector problem, for any $\ell_p$ norm, are also shown to be NP-hard.

Note: The paper deals with the hardness of some lattice problems related to some public-key cryptosystems.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Unique shortest vector problem unique closest vector problem unique subspace avoiding problem Lattice NP-hard Lattice-based cryptosystems
Contact author(s): quangkhoat @ gmail com
History: 2008-09-28: revised; 2008-08-27: received; See all versions
Short URL: https://ia.cr/2008/366
License: CC BY

BibTeX

@misc{cryptoeprint:2008/366,
      author = {Than Quang Khoat and Nguyen Hong Tan},
      title = {Unique Shortest Vector Problem for max norm is {NP}-hard},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/366},
      year = {2008},
      url = {https://eprint.iacr.org/2008/366}
}