{"paper":{"title":"Finding Primitive Elements in Finite Fields of Small Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DM","authors_text":"Anand Kumar Narayanan, Ming-Deh Huang","submitted_at":"2013-04-03T23:08:51Z","abstract_excerpt":"We describe a deterministic algorithm for finding a generating element of the multiplicative group of the finite field $\\mathbb{F}_{p^n}$ where $p$ is a prime. In time polynomial in $p$ and $n$, the algorithm either outputs an element that is provably a generator or declares that it has failed in finding one. The algorithm relies on a relation generation technique in Joux's heuristically $L(1/4)$-method for discrete logarithm computation. Based on a heuristic assumption, the algorithm does succeed in finding a generator. For the special case when the order of $p$ in $(\\mathbb{Z}/n\\mathbb{Z})^\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1206","kind":"arxiv","version":4},"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"}