[
  {
    "id": "wz11-ecdlp",
    "categoryId": "ecdlp-classical-lowspace",
    "paperId": "wz11",
    "date": "2011-01-05",
    "datePrecision": "day",
    "time": {
      "coefficient": 0.5,
      "expression": "r^{1/2+o(1)} expected group operations"
    },
    "space": {
      "coefficient": null,
      "expression": "Low-storage random walk; constant-size local state (plus distinguished-point storage for parallel variants)"
    },
    "tags": [
      "negation map",
      "random-walk heuristic"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "A rho/negation-map method for ordinary prime-order elliptic-curve subgroups. It addresses fruitless cycles and approaches a sqrt(2) speedup, which changes the multiplicative constant but leaves the leading exponent 1/2. The random-walk model remains heuristic.",
    "extra": {
      "coefficientExact": "1/2"
    },
    "evidence": {
      "url": "https://eprint.iacr.org/2011/008",
      "locator": "Abstract; rho analysis",
      "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
    }
  }
]