{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:U7ACW27F7UP6BBJP5N66XWZSV2","short_pith_number":"pith:U7ACW27F","schema_version":"1.0","canonical_sha256":"a7c02b6be5fd1fe0852feb7debdb32ae83cb9e32383b2defbabaab29e11d373f","source":{"kind":"arxiv","id":"0812.0789","version":2},"attestation_state":"computed","paper":{"title":"How long does it take to catch a wild kangaroo?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"Prasad Tetali, Ravi Montenegro","submitted_at":"2008-12-03T20:07:11Z","abstract_excerpt":"We develop probabilistic tools for upper and lower bounding the expected time until two independent random walks on $\\ZZ$ intersect each other. This leads to the first sharp analysis of a non-trivial Birthday attack, proving that Pollard's Kangaroo method solves the discrete logarithm problem $g^x=h$ on a cyclic group in expected time $(2+o(1))\\sqrt{b-a}$ for an average $x\\in_{uar}[a,b]$. Our methods also resolve a conjecture of Pollard's, by showing that the same bound holds when step sizes are generalized from powers of 2 to powers of any fixed $n$."},"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":"0812.0789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-03T20:07:11Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8b96d3c83906a903890ad9a674d7b7ec4f4ef3796346067a37450cc10b34e824","abstract_canon_sha256":"7e7d4fe4b43d03f36cdd2cec905d3d8b34240309c1fdfa6beef991ff550a42f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:51.430144Z","signature_b64":"D1hyVlA+gzj3N20DTyy6nHsf0iZlsdygiA+h68vpk+yG6hxZFUN+uM+Tlh3d7peOuYyubEqw7lChMyWcUu+WCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c02b6be5fd1fe0852feb7debdb32ae83cb9e32383b2defbabaab29e11d373f","last_reissued_at":"2026-05-18T04:36:51.429576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:51.429576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How long does it take to catch a wild kangaroo?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"Prasad Tetali, Ravi Montenegro","submitted_at":"2008-12-03T20:07:11Z","abstract_excerpt":"We develop probabilistic tools for upper and lower bounding the expected time until two independent random walks on $\\ZZ$ intersect each other. This leads to the first sharp analysis of a non-trivial Birthday attack, proving that Pollard's Kangaroo method solves the discrete logarithm problem $g^x=h$ on a cyclic group in expected time $(2+o(1))\\sqrt{b-a}$ for an average $x\\in_{uar}[a,b]$. Our methods also resolve a conjecture of Pollard's, by showing that the same bound holds when step sizes are generalized from powers of 2 to powers of any fixed $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0789","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":"0812.0789","created_at":"2026-05-18T04:36:51.429674+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.0789v2","created_at":"2026-05-18T04:36:51.429674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0789","created_at":"2026-05-18T04:36:51.429674+00:00"},{"alias_kind":"pith_short_12","alias_value":"U7ACW27F7UP6","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"U7ACW27F7UP6BBJP","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"U7ACW27F","created_at":"2026-05-18T12:25:58.018023+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/U7ACW27F7UP6BBJP5N66XWZSV2","json":"https://pith.science/pith/U7ACW27F7UP6BBJP5N66XWZSV2.json","graph_json":"https://pith.science/api/pith-number/U7ACW27F7UP6BBJP5N66XWZSV2/graph.json","events_json":"https://pith.science/api/pith-number/U7ACW27F7UP6BBJP5N66XWZSV2/events.json","paper":"https://pith.science/paper/U7ACW27F"},"agent_actions":{"view_html":"https://pith.science/pith/U7ACW27F7UP6BBJP5N66XWZSV2","download_json":"https://pith.science/pith/U7ACW27F7UP6BBJP5N66XWZSV2.json","view_paper":"https://pith.science/paper/U7ACW27F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.0789&json=true","fetch_graph":"https://pith.science/api/pith-number/U7ACW27F7UP6BBJP5N66XWZSV2/graph.json","fetch_events":"https://pith.science/api/pith-number/U7ACW27F7UP6BBJP5N66XWZSV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U7ACW27F7UP6BBJP5N66XWZSV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U7ACW27F7UP6BBJP5N66XWZSV2/action/storage_attestation","attest_author":"https://pith.science/pith/U7ACW27F7UP6BBJP5N66XWZSV2/action/author_attestation","sign_citation":"https://pith.science/pith/U7ACW27F7UP6BBJP5N66XWZSV2/action/citation_signature","submit_replication":"https://pith.science/pith/U7ACW27F7UP6BBJP5N66XWZSV2/action/replication_record"}},"created_at":"2026-05-18T04:36:51.429674+00:00","updated_at":"2026-05-18T04:36:51.429674+00:00"}