{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6D5VVAXQWMQX277QUIRIPPIFID","short_pith_number":"pith:6D5VVAXQ","schema_version":"1.0","canonical_sha256":"f0fb5a82f0b3217d7ff0a22287bd0540d35ed4b9bbb96c341107e4e6234f7d1f","source":{"kind":"arxiv","id":"1605.08065","version":1},"attestation_state":"computed","paper":{"title":"Cryptographic applications of capacity theory: On the optimality of Coppersmith's method for univariate polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CR","authors_text":"Brett Hemenway, Nadia Heninger, Ted Chinburg, Zachary Scherr","submitted_at":"2016-05-25T20:38:56Z","abstract_excerpt":"We draw a new connection between Coppersmith's method for finding small solutions to polynomial congruences modulo integers and the capacity theory of adelic subsets of algebraic curves. Coppersmith's method uses lattice basis reduction to construct an auxiliary polynomial that vanishes at the desired solutions. Capacity theory provides a toolkit for proving when polynomials with certain boundedness properties do or do not exist. Using capacity theory, we prove that Coppersmith's bound for univariate polynomials is optimal in the sense that there are \\emph{no} auxiliary polynomials of the type"},"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":"1605.08065","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-05-25T20:38:56Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"77fc7d4e081a2743a9c71e8646cf75986f0297780aa63c042d4591e08242d7f9","abstract_canon_sha256":"a18912af362b2ad1bdce239498753eddb466007a71af129668d75201c943e56d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:37.257345Z","signature_b64":"Xp8lTec3X8U4bvteXTbAjtb9XhUiDvh76Y7UN1rVCg/KFBReANoik9+vBU1/7ChT5VmceFhBeCswIJBzL1IlBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0fb5a82f0b3217d7ff0a22287bd0540d35ed4b9bbb96c341107e4e6234f7d1f","last_reissued_at":"2026-05-18T01:13:37.256564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:37.256564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cryptographic applications of capacity theory: On the optimality of Coppersmith's method for univariate polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CR","authors_text":"Brett Hemenway, Nadia Heninger, Ted Chinburg, Zachary Scherr","submitted_at":"2016-05-25T20:38:56Z","abstract_excerpt":"We draw a new connection between Coppersmith's method for finding small solutions to polynomial congruences modulo integers and the capacity theory of adelic subsets of algebraic curves. Coppersmith's method uses lattice basis reduction to construct an auxiliary polynomial that vanishes at the desired solutions. Capacity theory provides a toolkit for proving when polynomials with certain boundedness properties do or do not exist. Using capacity theory, we prove that Coppersmith's bound for univariate polynomials is optimal in the sense that there are \\emph{no} auxiliary polynomials of the type"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08065","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":"1605.08065","created_at":"2026-05-18T01:13:37.256714+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.08065v1","created_at":"2026-05-18T01:13:37.256714+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08065","created_at":"2026-05-18T01:13:37.256714+00:00"},{"alias_kind":"pith_short_12","alias_value":"6D5VVAXQWMQX","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6D5VVAXQWMQX277Q","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6D5VVAXQ","created_at":"2026-05-18T12:30:01.593930+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/6D5VVAXQWMQX277QUIRIPPIFID","json":"https://pith.science/pith/6D5VVAXQWMQX277QUIRIPPIFID.json","graph_json":"https://pith.science/api/pith-number/6D5VVAXQWMQX277QUIRIPPIFID/graph.json","events_json":"https://pith.science/api/pith-number/6D5VVAXQWMQX277QUIRIPPIFID/events.json","paper":"https://pith.science/paper/6D5VVAXQ"},"agent_actions":{"view_html":"https://pith.science/pith/6D5VVAXQWMQX277QUIRIPPIFID","download_json":"https://pith.science/pith/6D5VVAXQWMQX277QUIRIPPIFID.json","view_paper":"https://pith.science/paper/6D5VVAXQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.08065&json=true","fetch_graph":"https://pith.science/api/pith-number/6D5VVAXQWMQX277QUIRIPPIFID/graph.json","fetch_events":"https://pith.science/api/pith-number/6D5VVAXQWMQX277QUIRIPPIFID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6D5VVAXQWMQX277QUIRIPPIFID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6D5VVAXQWMQX277QUIRIPPIFID/action/storage_attestation","attest_author":"https://pith.science/pith/6D5VVAXQWMQX277QUIRIPPIFID/action/author_attestation","sign_citation":"https://pith.science/pith/6D5VVAXQWMQX277QUIRIPPIFID/action/citation_signature","submit_replication":"https://pith.science/pith/6D5VVAXQWMQX277QUIRIPPIFID/action/replication_record"}},"created_at":"2026-05-18T01:13:37.256714+00:00","updated_at":"2026-05-18T01:13:37.256714+00:00"}