{"paper":{"title":"On the Lattice Smoothing Parameter Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chris Peikert, Daniel Dadush, Feng-Hao Liu, Kai-Min Chung","submitted_at":"2014-12-26T19:50:58Z","abstract_excerpt":"The smoothing parameter $\\eta_{\\epsilon}(\\mathcal{L})$ of a Euclidean lattice $\\mathcal{L}$, introduced by Micciancio and Regev (FOCS'04; SICOMP'07), is (informally) the smallest amount of Gaussian noise that \"smooths out\" the discrete structure of $\\mathcal{L}$ (up to error $\\epsilon$). It plays a central role in the best known worst-case/average-case reductions for lattice problems, a wealth of lattice-based cryptographic constructions, and (implicitly) the tightest known transference theorems for fundamental lattice quantities.\n  In this work we initiate a study of the complexity of approxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7979","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"}