{"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"}