{"paper":{"title":"Solving the Shortest Vector Problem in $2^n$ Time via Discrete Gaussian Sampling","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, Oded Regev","submitted_at":"2014-12-26T21:36:03Z","abstract_excerpt":"We give a randomized $2^{n+o(n)}$-time and space algorithm for solving the Shortest Vector Problem (SVP) 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 (STOC 2010, SIAM J. Comp. 2013).\n  In fact, we give a conceptually simple algorithm that solves the (in our opinion, even more interesting) problem of discrete Gaussian sampling (DGS). More specifically, we show how to sample $2^{n/2}$ vectors from the discrete Gaussian distribution at any param"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7994","kind":"arxiv","version":5},"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"}