{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:4UGP35P355TTCKPI4577ZRX2CV","short_pith_number":"pith:4UGP35P3","schema_version":"1.0","canonical_sha256":"e50cfdf5fbef673129e8e77ffcc6fa1544c31a83aa9377e16e8dbc60defcbae0","source":{"kind":"arxiv","id":"cs/0609020","version":1},"attestation_state":"computed","paper":{"title":"Fast algorithms for computing isogenies between elliptic curves","license":"","headline":"","cross_cats":["cs.SC","math.NT"],"primary_cat":"cs.CC","authors_text":"Alin Bostan (INRIA Rocquencourt), Bruno Salvy (INRIA Rocquencourt), Eric Schost (LIX), Francois Morain (LIX, INRIA Futurs)","submitted_at":"2006-09-06T12:10:17Z","abstract_excerpt":"We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree $\\ell$ ($\\ell$ different from the characteristic) in time quasi-linear with respect to $\\ell$. This is based in particular on fast algorithms for power series expansion of the Weierstrass $\\wp$-function and related functions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"cs/0609020","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.CC","submitted_at":"2006-09-06T12:10:17Z","cross_cats_sorted":["cs.SC","math.NT"],"title_canon_sha256":"be73941ccea22ce460dec4229e04243128939c95a648875209b6b0274e0097ce","abstract_canon_sha256":"a14efcbe0a5e6d8fa552155e2b421f5a3d40eef8036c81c4158320754264abcd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:36.520215Z","signature_b64":"RyfTcsU7pJqJSM5pZbG6fpb/TEHgpiKbFPTXkFzB1UqoRS8yUYYHi6sQKWlBIClNPcmA4vboaZ1w4KjMuNjSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e50cfdf5fbef673129e8e77ffcc6fa1544c31a83aa9377e16e8dbc60defcbae0","last_reissued_at":"2026-05-18T03:20:36.519250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:36.519250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast algorithms for computing isogenies between elliptic curves","license":"","headline":"","cross_cats":["cs.SC","math.NT"],"primary_cat":"cs.CC","authors_text":"Alin Bostan (INRIA Rocquencourt), Bruno Salvy (INRIA Rocquencourt), Eric Schost (LIX), Francois Morain (LIX, INRIA Futurs)","submitted_at":"2006-09-06T12:10:17Z","abstract_excerpt":"We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree $\\ell$ ($\\ell$ different from the characteristic) in time quasi-linear with respect to $\\ell$. This is based in particular on fast algorithms for power series expansion of the Weierstrass $\\wp$-function and related functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0609020","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"cs/0609020","created_at":"2026-05-18T03:20:36.519440+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0609020v1","created_at":"2026-05-18T03:20:36.519440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0609020","created_at":"2026-05-18T03:20:36.519440+00:00"},{"alias_kind":"pith_short_12","alias_value":"4UGP35P355TT","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"4UGP35P355TTCKPI","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"4UGP35P3","created_at":"2026-05-18T12:25:53.939244+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV","json":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV.json","graph_json":"https://pith.science/api/pith-number/4UGP35P355TTCKPI4577ZRX2CV/graph.json","events_json":"https://pith.science/api/pith-number/4UGP35P355TTCKPI4577ZRX2CV/events.json","paper":"https://pith.science/paper/4UGP35P3"},"agent_actions":{"view_html":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV","download_json":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV.json","view_paper":"https://pith.science/paper/4UGP35P3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0609020&json=true","fetch_graph":"https://pith.science/api/pith-number/4UGP35P355TTCKPI4577ZRX2CV/graph.json","fetch_events":"https://pith.science/api/pith-number/4UGP35P355TTCKPI4577ZRX2CV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV/action/storage_attestation","attest_author":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV/action/author_attestation","sign_citation":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV/action/citation_signature","submit_replication":"https://pith.science/pith/4UGP35P355TTCKPI4577ZRX2CV/action/replication_record"}},"created_at":"2026-05-18T03:20:36.519440+00:00","updated_at":"2026-05-18T03:20:36.519440+00:00"}