[
  {
    "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"
    }
  }
]