{"paper":{"title":"(Gap/S)ETH Hardness of SVP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Divesh Aggarwal, Noah Stephens-Davidowitz","submitted_at":"2017-12-04T07:50:40Z","abstract_excerpt":"$ \\newcommand{\\problem}[1]{\\ensuremath{\\mathrm{#1}} } \\newcommand{\\SVP}{\\problem{SVP}} \\newcommand{\\ensuremath}[1]{#1} $We prove the following quantitative hardness results for the Shortest Vector Problem in the $\\ell_p$ norm ($\\SVP_p$), where $n$ is the rank of the input lattice.\n  $\\bullet$ For \"almost all\" $p > p_0 \\approx 2.1397$, there no $2^{n/C_p}$-time algorithm for $\\SVP_p$ for some explicit constant $C_p > 0$ unless the (randomized) Strong Exponential Time Hypothesis (SETH) is false.\n  $\\bullet$ For any $p > 2$, there is no $2^{o(n)}$-time algorithm for $\\SVP_p$ unless the (randomize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00942","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"}