NP-hardness of SVP in Euclidean Space
Number Theory
2026-03-31 v1 Computational Complexity
Abstract
van Emde Boas (1981) conjectured that computing a shortest non-zero vector of a lattice in an Euclidean space is NP-hard. In this paper, we prove that this conjecture is true and hence de-randomize the classical randomness result of Ajtai (1998). Our proof builds on the construction of Bennet-Peifert (2023) on locally dense lattices via Reed-Solomon codes, and depends crucially on the work of Deligne on the Weil conjectures for higher dimensional varieties over finite fields.
Keywords
Cite
@article{arxiv.2603.27398,
title = {NP-hardness of SVP in Euclidean Space},
author = {Daqing Wan},
journal= {arXiv preprint arXiv:2603.27398},
year = {2026}
}
Comments
23 pages. Comments welcome!