{
  "id": "jllr20-cm-action",
  "categoryId": "cm-action-quantum-polynomial-space",
  "paperId": "jllr20",
  "date": "2020-06-14",
  "datePrecision": "day",
  "time": {
    "coefficient": null,
    "expression": "Subexponential time in log N, with N=|Cl(O)|"
  },
  "space": {
    "coefficient": null,
    "expression": "Polynomial quantum space; subexponential classical precomputation/storage"
  },
  "tags": [],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "The checked analysis assumes the class group is cyclic. It uses classical subexponential precomputation and storage, but polynomial quantum space for the online action-inversion computation. Extension to non-cyclic groups is conjectured in Section 3.1.",
  "extra": {
    "restriction": "Cyclic class group",
    "application": "CRS and CSIDH CM group-action inversion",
    "method": "BKW-like classical precomputation"
  },
  "evidence": {
    "url": "https://www.degruyterbrill.com/document/doi/10.1515/jmc-2015-0057/html",
    "locator": "Abstract; Sections 3.1 and 4.4",
    "sourceVersion": "Checked 2026-11-08; see linked source version/date"
  }
}