{"paper":{"title":"Arithmetic of split Kummer surfaces: Montgomery endomorphism of Edwards products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Kohel","submitted_at":"2016-01-14T17:41:30Z","abstract_excerpt":"Let $E$ be an elliptic curve, $\\mathcal{K}_1$ its Kummer curve $E/\\{\\pm1\\}$, $E^2$ its square product, and $\\mathcal{K}_2$ the split Kummer surface $E^2/\\{\\pm1\\}$. The addition law on $E^2$ gives a large endomorphism ring, which induce endomorphisms of $\\mathcal{K}_2$. With a view to the practical applications to scalar multiplication on $\\mathcal{K}_1$, we study the explicit arithmetic of $\\mathcal{K}_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03680","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":""},"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"}