{
  "id": "gs11-ordinary",
  "categoryId": "ordinary-isogeny-classical",
  "paperId": "gs11-isogeny",
  "date": "2011-05-31",
  "datePrecision": "day",
  "time": {
    "coefficient": 0.25,
    "expression": "O~(q^{1/4})"
  },
  "space": {
    "coefficient": null,
    "expression": "Not stated in the checked source"
  },
  "tags": [],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "The ordinary horizontal-isogeny random-walk method has q^{1/4} scale; this work improves practical constants, not that exponent. The paper reports an approximately 14-fold speedup on a 160-bit prime field.",
  "extra": {
    "scale-evidence": "CJS Section 1 describes Galbraith–Stolbunov as fourth-root q",
    "primary-source": "https://arxiv.org/abs/1105.6331"
  },
  "evidence": {
    "url": "https://arxiv.org/pdf/1012.4019",
    "locator": "Abstract; asymptotic scale also stated in CJS Section 1",
    "sourceVersion": "Checked 2026-11-08; see linked source version/date"
  }
}