{
  "id": "bbhl20-ecc-binary",
  "categoryId": "ecdlp-binary-quantum",
  "paperId": "bbhl20",
  "date": "2020-10-19",
  "datePrecision": "day",
  "time": {
    "coefficient": null,
    "expression": "48n^3 + 8n^{log₂(3)+1} + 352n² log₂(n) + 512n² + O(n^{log₂(3)}) logical Toffoli gates"
  },
  "space": {
    "coefficient": null,
    "expression": "7n + floor(log₂ n) + 9 logical qubits"
  },
  "tags": [
    "logical Toffoli gates",
    "logical qubits",
    "double-and-add"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Double-and-add scalar multiplication variant over F_{2^n}. The source also provides a fixed-window variant with a logarithmic factor improvement. These are logical resource bounds, not physical attack timings.",
  "extra": {},
  "evidence": {
    "url": "https://eprint.iacr.org/2020/1296",
    "locator": "Abstract",
    "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
  }
}