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arXiv · 2603.27398

NP-hardness of SVP in Euclidean Space

Daqing Wan
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Abstract

In 1981, van Emde Boas conjectured that computing a shortest non-zero vector of a lattice in a Euclidean space is $\mathbf{NP}$-hard. In this paper, we prove this conjecture, thereby derandomizing Ajtai's classical randomized hardness result (1998). We follow the derandomization program formulated by Micciancio (1998--2014) who conjectured the existence of an efficient deterministic construction of locally dense lattices. The key is to resolve this conjecture. Our proof builds on the candidate construction via Reed-Solomon codes by Bennett and Peikert (2023), and depends crucially on Deligne's work on the Weil conjectures for higher-dimensional varieties over finite fields.

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Daqing Wan. 2026-03-28. NP-hardness of SVP in Euclidean Space. https://arxiv.org/abs/2603.27398

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