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  "path": "/abs/2604.01451v1",
  "publishedAt": "2026-04-03T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Isaac M Hair",
    "Amit Sahai"
  ],
  "textContent": "**Authors:** Isaac M Hair, Amit Sahai\n\nWe 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"
}