{"paper":{"title":"Solving the Closest Vector Problem in $2^n$ Time--- The Discrete Gaussian Strikes Again!","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Daniel Dadush, Divesh Aggarwal, Noah Stephens-Davidowitz","submitted_at":"2015-04-08T14:54:39Z","abstract_excerpt":"We give a $2^{n+o(n)}$-time and space randomized algorithm for solving the exact Closest Vector Problem (CVP) on $n$-dimensional Euclidean lattices. This improves on the previous fastest algorithm, the deterministic $\\widetilde{O}(4^{n})$-time and $\\widetilde{O}(2^{n})$-space algorithm of Micciancio and Voulgaris.\n  We achieve our main result in three steps. First, we show how to modify the sampling algorithm from [ADRS15] to solve the problem of discrete Gaussian sampling over lattice shifts, $L- t$, with very low parameters. While the actual algorithm is a natural generalization of [ADRS15],"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01995","kind":"arxiv","version":2},"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"}