{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KPBR2POPZ2KG7TGE7X7D7QYJHP","short_pith_number":"pith:KPBR2POP","schema_version":"1.0","canonical_sha256":"53c31d3dcfce946fccc4fdfe3fc3093bdeb8a94ca183a1120c27eef2ad59d2f8","source":{"kind":"arxiv","id":"1103.0337","version":1},"attestation_state":"computed","paper":{"title":"Refinements of Miller's Algorithm over Weierstrass Curves Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chao-Liang Liu, Duc-Phong Le","submitted_at":"2011-03-02T02:50:33Z","abstract_excerpt":"In 1986 Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented. Most of them involve a choice of elliptic curves of a \\emph{special} forms to exploit a possible twist during Tate pairing computation. Other improvements involve a reduction of the number of iterations in the Miller's algorithm. For the generic case, Blake, Murty and Xu proposed three refinements to Miller's algorithm over Weierstrass curves. Though their re"},"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":"1103.0337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-03-02T02:50:33Z","cross_cats_sorted":[],"title_canon_sha256":"d46fb2f3c755505ddcc3994dff65bd2a62f9f6d20a48bef06f8aa02648056b8b","abstract_canon_sha256":"7d55a3e03aaa976012a343ac87684f787b61e3ce4344862efa2046041103485b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:35.212091Z","signature_b64":"JemzRPTuW8GrvGZIU6BWEKvmmnDpC/mm3h5z+l0DMCRJg90Hd9rj0M0b+aIQqaFkLti5QmTAaBuJAmI/cA/FBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53c31d3dcfce946fccc4fdfe3fc3093bdeb8a94ca183a1120c27eef2ad59d2f8","last_reissued_at":"2026-05-18T04:27:35.211326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:35.211326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Refinements of Miller's Algorithm over Weierstrass Curves Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chao-Liang Liu, Duc-Phong Le","submitted_at":"2011-03-02T02:50:33Z","abstract_excerpt":"In 1986 Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented. Most of them involve a choice of elliptic curves of a \\emph{special} forms to exploit a possible twist during Tate pairing computation. Other improvements involve a reduction of the number of iterations in the Miller's algorithm. For the generic case, Blake, Murty and Xu proposed three refinements to Miller's algorithm over Weierstrass curves. Though their re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0337","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":"1103.0337","created_at":"2026-05-18T04:27:35.211431+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.0337v1","created_at":"2026-05-18T04:27:35.211431+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0337","created_at":"2026-05-18T04:27:35.211431+00:00"},{"alias_kind":"pith_short_12","alias_value":"KPBR2POPZ2KG","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KPBR2POPZ2KG7TGE","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KPBR2POP","created_at":"2026-05-18T12:26:32.869790+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/KPBR2POPZ2KG7TGE7X7D7QYJHP","json":"https://pith.science/pith/KPBR2POPZ2KG7TGE7X7D7QYJHP.json","graph_json":"https://pith.science/api/pith-number/KPBR2POPZ2KG7TGE7X7D7QYJHP/graph.json","events_json":"https://pith.science/api/pith-number/KPBR2POPZ2KG7TGE7X7D7QYJHP/events.json","paper":"https://pith.science/paper/KPBR2POP"},"agent_actions":{"view_html":"https://pith.science/pith/KPBR2POPZ2KG7TGE7X7D7QYJHP","download_json":"https://pith.science/pith/KPBR2POPZ2KG7TGE7X7D7QYJHP.json","view_paper":"https://pith.science/paper/KPBR2POP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.0337&json=true","fetch_graph":"https://pith.science/api/pith-number/KPBR2POPZ2KG7TGE7X7D7QYJHP/graph.json","fetch_events":"https://pith.science/api/pith-number/KPBR2POPZ2KG7TGE7X7D7QYJHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KPBR2POPZ2KG7TGE7X7D7QYJHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KPBR2POPZ2KG7TGE7X7D7QYJHP/action/storage_attestation","attest_author":"https://pith.science/pith/KPBR2POPZ2KG7TGE7X7D7QYJHP/action/author_attestation","sign_citation":"https://pith.science/pith/KPBR2POPZ2KG7TGE7X7D7QYJHP/action/citation_signature","submit_replication":"https://pith.science/pith/KPBR2POPZ2KG7TGE7X7D7QYJHP/action/replication_record"}},"created_at":"2026-05-18T04:27:35.211431+00:00","updated_at":"2026-05-18T04:27:35.211431+00:00"}