{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CU7RWXFBE5HBCJJR25XPWWKJE3","short_pith_number":"pith:CU7RWXFB","schema_version":"1.0","canonical_sha256":"153f1b5ca1274e112531d76efb594926fcf99adb4ae602e1d4e69c393ef2aead","source":{"kind":"arxiv","id":"1806.05709","version":2},"attestation_state":"computed","paper":{"title":"Ramanujan graphs in cryptography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.CO"],"primary_cat":"math.NT","authors_text":"Anamaria Costache, Anna Pusk\\'as, Brooke Feigon, Kristin Lauter, Maike Massierer","submitted_at":"2018-06-14T19:16:04Z","abstract_excerpt":"In this paper we study the security of a proposal for Post-Quantum Cryptography from both a number theoretic and cryptographic perspective. Charles-Goren-Lauter in 2006 [CGL06] proposed two hash functions based on the hardness of finding paths in Ramanujan graphs. One is based on Lubotzky-Phillips-Sarnak (LPS) graphs and the other one is based on Supersingular Isogeny Graphs. A 2008 paper by Petit-Lauter-Quisquater breaks the hash function based on LPS graphs. On the Supersingular Isogeny Graphs proposal, recent work has continued to build cryptographic applications on the hardness of finding "},"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":"1806.05709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-14T19:16:04Z","cross_cats_sorted":["cs.CR","math.CO"],"title_canon_sha256":"da39cc83f873d277e180e4ffca7796d56f9c0eb0847df1c7f427a522d68cd91b","abstract_canon_sha256":"9aa1170b54a2406e3f0602373ea92f1075f79c39e3f559de661b2cbb33b1e86d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:08.582828Z","signature_b64":"RF0PuUhOuei6byTQmHCIZMH1SnhOsluoCSxKWVZrTgjVLtIpT94Hwekzxj5GjdSJk+1H2MVVaZ+DASGoI0GbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"153f1b5ca1274e112531d76efb594926fcf99adb4ae602e1d4e69c393ef2aead","last_reissued_at":"2026-05-17T23:58:08.582186Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:08.582186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramanujan graphs in cryptography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.CO"],"primary_cat":"math.NT","authors_text":"Anamaria Costache, Anna Pusk\\'as, Brooke Feigon, Kristin Lauter, Maike Massierer","submitted_at":"2018-06-14T19:16:04Z","abstract_excerpt":"In this paper we study the security of a proposal for Post-Quantum Cryptography from both a number theoretic and cryptographic perspective. Charles-Goren-Lauter in 2006 [CGL06] proposed two hash functions based on the hardness of finding paths in Ramanujan graphs. One is based on Lubotzky-Phillips-Sarnak (LPS) graphs and the other one is based on Supersingular Isogeny Graphs. A 2008 paper by Petit-Lauter-Quisquater breaks the hash function based on LPS graphs. On the Supersingular Isogeny Graphs proposal, recent work has continued to build cryptographic applications on the hardness of finding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05709","kind":"arxiv","version":2},"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":"1806.05709","created_at":"2026-05-17T23:58:08.582288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.05709v2","created_at":"2026-05-17T23:58:08.582288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05709","created_at":"2026-05-17T23:58:08.582288+00:00"},{"alias_kind":"pith_short_12","alias_value":"CU7RWXFBE5HB","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"CU7RWXFBE5HBCJJR","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"CU7RWXFB","created_at":"2026-05-18T12:32:19.392346+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/CU7RWXFBE5HBCJJR25XPWWKJE3","json":"https://pith.science/pith/CU7RWXFBE5HBCJJR25XPWWKJE3.json","graph_json":"https://pith.science/api/pith-number/CU7RWXFBE5HBCJJR25XPWWKJE3/graph.json","events_json":"https://pith.science/api/pith-number/CU7RWXFBE5HBCJJR25XPWWKJE3/events.json","paper":"https://pith.science/paper/CU7RWXFB"},"agent_actions":{"view_html":"https://pith.science/pith/CU7RWXFBE5HBCJJR25XPWWKJE3","download_json":"https://pith.science/pith/CU7RWXFBE5HBCJJR25XPWWKJE3.json","view_paper":"https://pith.science/paper/CU7RWXFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.05709&json=true","fetch_graph":"https://pith.science/api/pith-number/CU7RWXFBE5HBCJJR25XPWWKJE3/graph.json","fetch_events":"https://pith.science/api/pith-number/CU7RWXFBE5HBCJJR25XPWWKJE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CU7RWXFBE5HBCJJR25XPWWKJE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CU7RWXFBE5HBCJJR25XPWWKJE3/action/storage_attestation","attest_author":"https://pith.science/pith/CU7RWXFBE5HBCJJR25XPWWKJE3/action/author_attestation","sign_citation":"https://pith.science/pith/CU7RWXFBE5HBCJJR25XPWWKJE3/action/citation_signature","submit_replication":"https://pith.science/pith/CU7RWXFBE5HBCJJR25XPWWKJE3/action/replication_record"}},"created_at":"2026-05-17T23:58:08.582288+00:00","updated_at":"2026-05-17T23:58:08.582288+00:00"}