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

被引：41
|
作者：
Micciancio, D [1 ]
机构：
[1] MIT, Comp Sci Lab, Cambridge, MA 02139 USA
来源：
39TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS | 1998年
关键词：
D O I：
10.1109/SFCS.1998.743432
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
We show the shortest vector problem in the l(2) norm is NP-hard (for randomized reductions) to approximate within any constant factor less than root 2. We also give a deterministic reduction under a reasonable number theoretic conjecture. Analogous results hold in any l(p) norm (p greater than or equal to 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.
引用
收藏
页码：92 / 98
页数：3
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