{"paper":{"title":"Computing Individual Discrete Logarithms Faster in GF$(p^n)$ with the NFS-DL Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CR","authors_text":"Aurore Guillevic (GRACE, LIX)","submitted_at":"2015-05-28T06:12:59Z","abstract_excerpt":"The Number Field Sieve (NFS) algorithm is the best known method to compute discrete logarithms (DL) in finite fields $\\mathbb{F}\\_{p^n}$, with $p$ medium to large and $n \\geq 1$ small. This algorithm comprises four steps: polynomial selection, relation collection, linear algebra and finally, individual logarithm computation. The first step outputs two polynomials defining two number fields, and a map from the polynomial ring over the integers modulo each of these polynomials to $\\mathbb{F}\\_{p^n}$. After the relation collection and linear algebra phases, the (virtual) logarithm of a subset of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07553","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"}