{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YD4HUHISLN7XK2RL67FQENZNRM","short_pith_number":"pith:YD4HUHIS","schema_version":"1.0","canonical_sha256":"c0f87a1d125b7f756a2bf7cb02372d8b05aaaecb4251288d82a7355238937c16","source":{"kind":"arxiv","id":"2607.13816","version":1},"attestation_state":"computed","paper":{"title":"Quantum Algorithm for Elliptic Curve Discrete Logarithms with Space-Efficient Point Addition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.DS"],"primary_cat":"quant-ph","authors_text":"Han Luo, Jingquan Luo, Lvzhou Li, Tongyang Li, Xiaoming Sun, Yuexin Su, Ziruo Wang, Ziyi Yang","submitted_at":"2026-07-15T13:25:00Z","abstract_excerpt":"The Elliptic Curve Discrete Logarithm Problem (ECDLP) is a fundamental problem in cryptography, and reducing the resource requirements of quantum algorithms for solving ECDLP is an important goal. In this work, we present a space-efficient quantum algorithm for solving the ECDLP over prime fields, achieving an implementation with only $3n+6\\lfloor \\log_2 n \\rfloor+O(1)$ logical qubits and $919n^3/\\log_2 n+O(n^2)$ Toffoli gates, where $n$ is the bit-length of the prime. For a 256-bit prime-field curve, our construction requires only 835 logical qubits, reducing the previous best estimates of 10"},"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":"2607.13816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-15T13:25:00Z","cross_cats_sorted":["cs.CR","cs.DS"],"title_canon_sha256":"65dfcb1b8a4ce85ada3498481d1322c3d1c4be10b920da141a8ee09b22131710","abstract_canon_sha256":"881466e8b1cab2ed58c32b7584c56f7783c03f55c5055159c8f70a1f7e6dc8db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:23:07.933332Z","signature_b64":"dsMJAGZv157lTcfPJYNKymteWc0wZTL05/n4X8uelxV8vu0DQis54RPefBIzhKr8FUg1jlkSGivXkdtBqMNsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0f87a1d125b7f756a2bf7cb02372d8b05aaaecb4251288d82a7355238937c16","last_reissued_at":"2026-07-16T01:23:07.932460Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:23:07.932460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Algorithm for Elliptic Curve Discrete Logarithms with Space-Efficient Point Addition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.DS"],"primary_cat":"quant-ph","authors_text":"Han Luo, Jingquan Luo, Lvzhou Li, Tongyang Li, Xiaoming Sun, Yuexin Su, Ziruo Wang, Ziyi Yang","submitted_at":"2026-07-15T13:25:00Z","abstract_excerpt":"The Elliptic Curve Discrete Logarithm Problem (ECDLP) is a fundamental problem in cryptography, and reducing the resource requirements of quantum algorithms for solving ECDLP is an important goal. In this work, we present a space-efficient quantum algorithm for solving the ECDLP over prime fields, achieving an implementation with only $3n+6\\lfloor \\log_2 n \\rfloor+O(1)$ logical qubits and $919n^3/\\log_2 n+O(n^2)$ Toffoli gates, where $n$ is the bit-length of the prime. For a 256-bit prime-field curve, our construction requires only 835 logical qubits, reducing the previous best estimates of 10"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13816","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13816/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.13816","created_at":"2026-07-16T01:23:07.932905+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.13816v1","created_at":"2026-07-16T01:23:07.932905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13816","created_at":"2026-07-16T01:23:07.932905+00:00"},{"alias_kind":"pith_short_12","alias_value":"YD4HUHISLN7X","created_at":"2026-07-16T01:23:07.932905+00:00"},{"alias_kind":"pith_short_16","alias_value":"YD4HUHISLN7XK2RL","created_at":"2026-07-16T01:23:07.932905+00:00"},{"alias_kind":"pith_short_8","alias_value":"YD4HUHIS","created_at":"2026-07-16T01:23:07.932905+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/YD4HUHISLN7XK2RL67FQENZNRM","json":"https://pith.science/pith/YD4HUHISLN7XK2RL67FQENZNRM.json","graph_json":"https://pith.science/api/pith-number/YD4HUHISLN7XK2RL67FQENZNRM/graph.json","events_json":"https://pith.science/api/pith-number/YD4HUHISLN7XK2RL67FQENZNRM/events.json","paper":"https://pith.science/paper/YD4HUHIS"},"agent_actions":{"view_html":"https://pith.science/pith/YD4HUHISLN7XK2RL67FQENZNRM","download_json":"https://pith.science/pith/YD4HUHISLN7XK2RL67FQENZNRM.json","view_paper":"https://pith.science/paper/YD4HUHIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.13816&json=true","fetch_graph":"https://pith.science/api/pith-number/YD4HUHISLN7XK2RL67FQENZNRM/graph.json","fetch_events":"https://pith.science/api/pith-number/YD4HUHISLN7XK2RL67FQENZNRM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YD4HUHISLN7XK2RL67FQENZNRM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YD4HUHISLN7XK2RL67FQENZNRM/action/storage_attestation","attest_author":"https://pith.science/pith/YD4HUHISLN7XK2RL67FQENZNRM/action/author_attestation","sign_citation":"https://pith.science/pith/YD4HUHISLN7XK2RL67FQENZNRM/action/citation_signature","submit_replication":"https://pith.science/pith/YD4HUHISLN7XK2RL67FQENZNRM/action/replication_record"}},"created_at":"2026-07-16T01:23:07.932905+00:00","updated_at":"2026-07-16T01:23:07.932905+00:00"}