Hardness of Approximating the Shortest Vector Problem in High Lp Norms

Authors:
Subhash Khot
Affiliations:
-
Venue:
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Year:
2003

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Abstract

We show that for every \varepsilon 0, there is a constant p(\varepsilon) such that for all integers p \geqslant p(\varepsilon), it is NP-hard to approximate the Shortest Vector Problem in Lp norm within factor p^{1 - \varepsilon } under randomized reductions. For large values of p, this improves the factor 2^{{1 \mathord{\left/ {\vphantom {1 p}} \right. \kern-\nulldelimiterspace} p}}- \delta hardness shown by Micciancio.