{"paper":{"title":"Improved hardness results for unique shortest vector problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chandan Dubey, Divesh Aggarwal","submitted_at":"2011-12-07T13:58:29Z","abstract_excerpt":"We give several improvements on the known hardness of the unique shortest vector problem. - We give a deterministic reduction from the shortest vector problem to the unique shortest vector problem. As a byproduct, we get deterministic NP-hardness for unique shortest vector problem in the $\\ell_\\infty$ norm. - We give a randomized reduction from SAT to uSVP_{1+1/poly(n)}. This shows that uSVP_{1+1/poly(n)} is NP-hard under randomized reductions. - We show that if GapSVP_\\gamma \\in coNP (or coAM) then uSVP_{\\sqrt{\\gamma}} \\in coNP (coAM respectively). This simplifies previously known uSVP_{n^{1/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1564","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"}