{
  "id": "rnsl17-ecc-prime",
  "categoryId": "ecdlp-prime-quantum",
  "paperId": "rnsl17",
  "date": "2017-06-21",
  "datePrecision": "day",
  "time": {
    "coefficient": null,
    "expression": "At most 448 n^3 log₂(n) + 4090 n^3 logical Toffoli gates"
  },
  "space": {
    "coefficient": null,
    "expression": "At most 9n + 2 ceil(log₂ n) + 10 logical qubits"
  },
  "tags": [
    "logical Toffoli gates",
    "logical qubits"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Resource estimate for a specific quantum circuit over an n-bit prime field. Counts logical gates and qubits; excludes physical error correction. This is a proved circuit bound rather than a measured quantum attack.",
  "extra": {},
  "evidence": {
    "url": "https://eprint.iacr.org/2017/598",
    "locator": "Abstract",
    "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
  }
}