{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RED72YWP23SS3AZYXDPW2P67TA","short_pith_number":"pith:RED72YWP","canonical_record":{"source":{"id":"1806.02536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-06-07T07:10:01Z","cross_cats_sorted":[],"title_canon_sha256":"b1c7865f4033bd72a93fcb3d9fb592a394ed017787a37a44f99979a7fb14086c","abstract_canon_sha256":"43d9c222ab67b8046db452a29546da49490595db9ed83c8dcbccd3dfac72c9bf"},"schema_version":"1.0"},"canonical_sha256":"8907fd62cfd6e52d8338b8df6d3fdf9812be8b51c6174136ea07205d1b15940c","source":{"kind":"arxiv","id":"1806.02536","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02536","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02536v1","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02536","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"RED72YWP23SS","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RED72YWP23SS3AZY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RED72YWP","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RED72YWP23SS3AZYXDPW2P67TA","target":"record","payload":{"canonical_record":{"source":{"id":"1806.02536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-06-07T07:10:01Z","cross_cats_sorted":[],"title_canon_sha256":"b1c7865f4033bd72a93fcb3d9fb592a394ed017787a37a44f99979a7fb14086c","abstract_canon_sha256":"43d9c222ab67b8046db452a29546da49490595db9ed83c8dcbccd3dfac72c9bf"},"schema_version":"1.0"},"canonical_sha256":"8907fd62cfd6e52d8338b8df6d3fdf9812be8b51c6174136ea07205d1b15940c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:56.506155Z","signature_b64":"H3WsJy7c4nibZaQvDt7/WY2gCgZYGR2Q8/b/5tkM6ST0Mh4UTSSc7N2WoeB49gnqkPahaZ8qdu/PoInSZ4RBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8907fd62cfd6e52d8338b8df6d3fdf9812be8b51c6174136ea07205d1b15940c","last_reissued_at":"2026-05-18T00:13:56.505514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:56.505514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.02536","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WL9h/5K40+zO/r8n2TXoUvnVLuSN1gnd+KWIufHgLTl5b1w8gmdbG76eS9+8Ke0iFGSzpVAd/b5v7dgr7aXfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:50:01.483149Z"},"content_sha256":"ce857e932db6f38c9550ace548e2cd59774a62a73dd56b645265010f0e3de2ff","schema_version":"1.0","event_id":"sha256:ce857e932db6f38c9550ace548e2cd59774a62a73dd56b645265010f0e3de2ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RED72YWP23SS3AZYXDPW2P67TA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the near prime-order MNT curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Chik How Tan, Duc-Phong Le, Nadia El Mrabet, Safia Haloui","submitted_at":"2018-06-07T07:10:01Z","abstract_excerpt":"In their seminar paper, Miyaji, Nakabayashi and Takano introduced the first method to construct families of prime-order elliptic curves with small embedding degrees, namely k = 3, 4, and 6. These curves, so-called MNT curves, were then extended by Scott and Barreto, and also Galbraith, McKee and Valenca to near prime-order curves with the same embedding degrees. In this paper, we extend the method of Scott and Barreto to introduce an explicit and simple algorithm that is able to generate all families of MNT curves with any given cofactor. Furthermore, we analyze the number of potential familie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02536","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W5IVdcNgd3tac8PosD9A+3cjPAIfm9bWUWtitgNq11kExUaY8YYTGGbk5jcv5QGgz+U6KrhIOW+roO+cV3AlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:50:01.483821Z"},"content_sha256":"1a093615e30d792ecbedc2648e801709256a201cce1e51cab1c6d2af88269b6d","schema_version":"1.0","event_id":"sha256:1a093615e30d792ecbedc2648e801709256a201cce1e51cab1c6d2af88269b6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RED72YWP23SS3AZYXDPW2P67TA/bundle.json","state_url":"https://pith.science/pith/RED72YWP23SS3AZYXDPW2P67TA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RED72YWP23SS3AZYXDPW2P67TA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T07:50:01Z","links":{"resolver":"https://pith.science/pith/RED72YWP23SS3AZYXDPW2P67TA","bundle":"https://pith.science/pith/RED72YWP23SS3AZYXDPW2P67TA/bundle.json","state":"https://pith.science/pith/RED72YWP23SS3AZYXDPW2P67TA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RED72YWP23SS3AZYXDPW2P67TA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RED72YWP23SS3AZYXDPW2P67TA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"43d9c222ab67b8046db452a29546da49490595db9ed83c8dcbccd3dfac72c9bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-06-07T07:10:01Z","title_canon_sha256":"b1c7865f4033bd72a93fcb3d9fb592a394ed017787a37a44f99979a7fb14086c"},"schema_version":"1.0","source":{"id":"1806.02536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02536","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02536v1","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02536","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"RED72YWP23SS","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RED72YWP23SS3AZY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RED72YWP","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:1a093615e30d792ecbedc2648e801709256a201cce1e51cab1c6d2af88269b6d","target":"graph","created_at":"2026-05-18T00:13:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In their seminar paper, Miyaji, Nakabayashi and Takano introduced the first method to construct families of prime-order elliptic curves with small embedding degrees, namely k = 3, 4, and 6. These curves, so-called MNT curves, were then extended by Scott and Barreto, and also Galbraith, McKee and Valenca to near prime-order curves with the same embedding degrees. In this paper, we extend the method of Scott and Barreto to introduce an explicit and simple algorithm that is able to generate all families of MNT curves with any given cofactor. Furthermore, we analyze the number of potential familie","authors_text":"Chik How Tan, Duc-Phong Le, Nadia El Mrabet, Safia Haloui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-06-07T07:10:01Z","title":"On the near prime-order MNT curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02536","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ce857e932db6f38c9550ace548e2cd59774a62a73dd56b645265010f0e3de2ff","target":"record","created_at":"2026-05-18T00:13:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"43d9c222ab67b8046db452a29546da49490595db9ed83c8dcbccd3dfac72c9bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-06-07T07:10:01Z","title_canon_sha256":"b1c7865f4033bd72a93fcb3d9fb592a394ed017787a37a44f99979a7fb14086c"},"schema_version":"1.0","source":{"id":"1806.02536","kind":"arxiv","version":1}},"canonical_sha256":"8907fd62cfd6e52d8338b8df6d3fdf9812be8b51c6174136ea07205d1b15940c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8907fd62cfd6e52d8338b8df6d3fdf9812be8b51c6174136ea07205d1b15940c","first_computed_at":"2026-05-18T00:13:56.505514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:56.505514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H3WsJy7c4nibZaQvDt7/WY2gCgZYGR2Q8/b/5tkM6ST0Mh4UTSSc7N2WoeB49gnqkPahaZ8qdu/PoInSZ4RBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:56.506155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce857e932db6f38c9550ace548e2cd59774a62a73dd56b645265010f0e3de2ff","sha256:1a093615e30d792ecbedc2648e801709256a201cce1e51cab1c6d2af88269b6d"],"state_sha256":"caca309efd479eb71142726bd2e27a6de4a659f9135262846d8d262ccd96fed0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38gnoOv6qIeCgQzbEm6WrLsT6LkZdH0cHd0aCrZZkbM4EgWtLVS5CuZmWTOzn+alP14IRWjdCLRhA4yfnnjUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:50:01.487350Z","bundle_sha256":"2f37bda5b8ecf3bb9a730402b22e3ef612f501926c75fdace31180759ecbc0ce"}}