{"paper":{"title":"Fast Computation of Isomorphisms Between Finite Fields Using Elliptic Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NT"],"primary_cat":"cs.DS","authors_text":"Anand Kumar Narayanan","submitted_at":"2016-04-11T19:11:02Z","abstract_excerpt":"We propose a randomized algorithm to compute isomorphisms between finite fields using elliptic curves. To compute an isomorphism between two fields of cardinality $q^n$, our algorithm takes $$n^{1+o(1)} \\log^{1+o(1)}q + \\max_{\\ell} \\left(\\ell^{n_\\ell + 1+o(1)} \\log^{2+o(1)} q + O(\\ell \\log^5q)\\right)$$ time, where $\\ell$ runs through primes dividing $n$ but not $q(q-1)$ and $n_\\ell$ denotes the highest power of $\\ell$ dividing $n$. Prior to this work, the best known run time dependence on $n$ was quadratic. Our run time dependence on $n$ is at worst quadratic but is subquadratic if $n$ has no "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03072","kind":"arxiv","version":3},"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"}