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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.01451 |
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| _version_ | 1866917385356705792 |
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| author | Hair, Isaac M Sahai, Amit |
| author_facet | Hair, Isaac M Sahai, Amit |
| contents | We show that, assuming NP $\not\subseteq$ $\cap_{δ> 0}$DTIME$\left(\exp{n^δ}\right)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01451 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deterministic Hardness of Approximation For SVP in all Finite $\ell_p$ Norms Hair, Isaac M Sahai, Amit Computational Complexity We show that, assuming NP $\not\subseteq$ $\cap_{δ> 0}$DTIME$\left(\exp{n^δ}\right)$, 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. |
| title | Deterministic Hardness of Approximation For SVP in all Finite $\ell_p$ Norms |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2604.01451 |