{"paper":{"title":"Tensor-based Hardness of the Shortest Vector Problem to within Almost Polynomial Factors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Ishay Haviv, Oded Regev","submitted_at":"2018-06-11T16:17:21Z","abstract_excerpt":"$ \\newcommand{\\SVP}{\\mathsf{SVP}} \\newcommand{\\NP}{\\mathsf{NP}} \\newcommand{\\RTIME}{\\mathsf{RTIME}} \\newcommand{\\RSUBEXP}{\\mathsf{RSUBEXP}} \\newcommand{\\eps}{\\epsilon} \\newcommand{\\poly}{\\mathop{\\mathrm{poly}}} $We show that unless $\\NP \\subseteq \\RTIME (2^{\\poly(\\log{n})})$, there is no polynomial-time algorithm approximating the Shortest Vector Problem ($\\SVP$) on $n$-dimensional lattices in the $\\ell_p$ norm ($1 \\leq p< \\infty$) to within a factor of $2^{(\\log{n})^{1-\\eps}}$ for any $\\eps > 0$. This improves the previous best factor of $2^{(\\log{n})^{1/2-\\eps}}$ under the same complexity as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04087","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}