{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IWXBUEPXKEW6WRF2SDL6GUQWHU","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":"b91e162ecac7e809b30bf728a19c71b4d4a37fc3b9407213db57aefb13b0c973","cross_cats_sorted":["cs.ET"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-06-21T06:21:39Z","title_canon_sha256":"c7dc0a5801e20e779a0f779910ce6b3cf44f1446f55de1951df777485ebd8141"},"schema_version":"1.0","source":{"id":"1706.06752","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06752","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06752v3","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06752","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"IWXBUEPXKEW6","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IWXBUEPXKEW6WRF2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IWXBUEPX","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:36b3ac41a4a73a300aca171449ddc67f18ec9f3ee3c3637118afc5bc1b72f824","target":"graph","created_at":"2026-05-18T00:31:45Z","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":"We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQ$Ui|\\rangle$. We determine circuit implementations for reversible modular arithmetic, including modular addition, multiplication and inversion, as well as reversible elliptic curve point addition. We conclude that elliptic curve discrete logarithms on an elliptic curve ","authors_text":"Kristin Lauter, Krysta M. Svore, Martin Roetteler, Michael Naehrig","cross_cats":["cs.ET"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-06-21T06:21:39Z","title":"Quantum resource estimates for computing elliptic curve discrete logarithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06752","kind":"arxiv","version":3},"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:fb705ee62db1442a4f6fc682e992f4eb7fa148d272ff35f3ec45b8ae4a113458","target":"record","created_at":"2026-05-18T00:31:45Z","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":"b91e162ecac7e809b30bf728a19c71b4d4a37fc3b9407213db57aefb13b0c973","cross_cats_sorted":["cs.ET"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-06-21T06:21:39Z","title_canon_sha256":"c7dc0a5801e20e779a0f779910ce6b3cf44f1446f55de1951df777485ebd8141"},"schema_version":"1.0","source":{"id":"1706.06752","kind":"arxiv","version":3}},"canonical_sha256":"45ae1a11f7512deb44ba90d7e352163d3f43e064eb1980dc07dbc298421ac5e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45ae1a11f7512deb44ba90d7e352163d3f43e064eb1980dc07dbc298421ac5e6","first_computed_at":"2026-05-18T00:31:45.015074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:45.015074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i2DdRdKoEtji2X0P6I8NP62Qt9XAkE5jQYuzDNvVfFfUDY1epC26GbHVTSEFX/CfZCcJC5tHZVb8thGyg08JBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:45.015655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06752","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb705ee62db1442a4f6fc682e992f4eb7fa148d272ff35f3ec45b8ae4a113458","sha256:36b3ac41a4a73a300aca171449ddc67f18ec9f3ee3c3637118afc5bc1b72f824"],"state_sha256":"d088fc0178ec449991cb1ebe67be5345299e952c61cab883e10ba1dd309971a3"}