{
  "id": "pollard78-generic",
  "categoryId": "dlog-generic-classical",
  "paperId": "pollard78",
  "date": "1978-07-31",
  "datePrecision": "month",
  "time": {
    "coefficient": 0.5,
    "expression": "O(sqrt(r)) expected group operations"
  },
  "space": {
    "coefficient": null,
    "expression": "O(1) group elements"
  },
  "tags": [
    "random-walk heuristic"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Rho’s square-root running time uses a random-walk/random-function heuristic; storage is a constant number of group elements. The original paper formulates index computation modulo p; the generic group-operation formulation is its standard representation-independent specialization.",
  "extra": {
    "coefficientExact": "1/2",
    "parameter": "r is the prime subgroup order, not the finite-field cardinality."
  },
  "evidence": {
    "url": "https://www.ams.org/mcom/1978-32-143/S0025-5718-1978-0491431-9/S0025-5718-1978-0491431-9.pdf",
    "locator": "Rho method section",
    "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
  }
}