{"paper":{"title":"Cover attacks for elliptic curves with prime order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.CR","authors_text":"Song Tian","submitted_at":"2020-12-13T22:41:08Z","abstract_excerpt":"We give a new approach to the elliptic curve discrete logarithm problem over cubic extension fields $\\mathbb{F}_{q^3}$. It is based on a transfer: First an $\\mathbb{F}_q$-rational $(\\ell,\\ell,\\ell)$-isogeny from the Weil restriction of the elliptic curve under consideration with respect to $\\mathbb{F}_{q^3}/\\mathbb{F}_q$ to the Jacobian variety of a genus three curve over $\\mathbb{F}_q$ is applied and then the problem is solved in the Jacobian via the index-calculus attacks. Although using no covering maps in the construction of the desired homomorphism, this method is, in a sense, a kind of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.07173","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.07173/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}