Deterministic Hardness of Approximation For SVP in all Finite $\ell_p$ Norms

Isaac M Hair; Amit Sahai

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arXiv · 2604.01451

Deterministic Hardness of Approximation For SVP in all Finite $\ell_p$ Norms

Isaac M Hair·Amit Sahai

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Abstract

We show that, assuming NP $\not\subseteq$ $\cap_{\delta > 0}$DTIME$\left(\exp{n^\delta}\right)$, the shortest vector problem for lattices of rank $n$ in any finite $\ell_p$ norm is hard to approximate within a factor of $2^{(\log n)^{1 - o(1)}}$, via a deterministic reduction. Previously, for the Euclidean case $p=2$, even hardness of the exact shortest vector problem was not known under a deterministic reduction.

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BibTeX RIS

Isaac M Hair, Amit Sahai. 2026-04-01. Deterministic Hardness of Approximation For SVP in all Finite $\ell_p$ Norms. https://arxiv.org/abs/2604.01451

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