{"paper":{"title":"On the relation generation method of Joux for computing discrete logarithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.NT"],"primary_cat":"cs.CC","authors_text":"Anand Kumar Narayanan, Ming-Deh Huang","submitted_at":"2013-12-05T20:31:28Z","abstract_excerpt":"In \\cite{joux}, Joux devised an algorithm to compute discrete logarithms between elements in a certain subset of the multiplicative group of an extension of the finite field $\\mathbb{F}_{p^n}$ in time polynomial in $p$ and $n$. Shortly after, Barbulescu, Gaudry, Joux and Thome \\cite{bgjt} proposed a descent algorithm that in $(p n)^{\\mathcal{O}(\\log n)}$ time projects an arbitrary element in $\\mathbb{F}_{p^n}^\\times$ as a product of powers of elements in the aforementioned subset. Together, these two algorithms yield a quasi-polynomial time algorithm for computing discrete logarithms in finite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1674","kind":"arxiv","version":2},"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"}