{
  "id": "bgpw16-binary-error-n256",
  "categoryId": "lwe-binary-error-hybrid-models",
  "paperId": "buchmann-goepfert-player-wunderer2016-hybrid",
  "year": 2016,
  "date": "2016-04-13",
  "datePrecision": "day",
  "time": {
    "coefficient": null,
    "expression": "Approximately 2^85 bit operations for (n,m,q)=(256,512,256)"
  },
  "space": {
    "coefficient": null,
    "expression": "No numerical space estimate extracted."
  },
  "tags": [
    "finite instance",
    "binary error",
    "hybrid",
    "historical estimate"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Source Table 1’s concrete hybrid estimate, including the paper’s basis-reduction model. Its empirical LP-based BKZ estimate was later criticized; keep this as historical finite-instance evidence, without an asymptotic cn coefficient.",
  "extra": {
    "parameters": "Fixed finite instance n=256, m=512, q=256; no q(n) asymptotic family asserted.",
    "noise": "Independent uniform binary errors.",
    "secret": "Independent uniform binary secret.",
    "samples": "At most 512=2n samples.",
    "objective": "Recover the secret / valid error.",
    "model": "Historical bit-operation estimate; source Table 1, row V. BKZ model is the empirical Eq. (1).",
    "assumptions": "Hybrid collision heuristics, basis-profile model and historical lattice-reduction estimator.",
    "success": "As estimated in the paper’s attack/parameter optimization."
  },
  "evidence": {
    "url": "https://download.hrz.tu-darmstadt.de/media/FB20/Dekanat/Publikationen/Crossing/hybrid_attack.pdf",
    "locator": "Abstract; §4, Table 1, row V, PDF p. 15; Eq. (1) for the historical BKZ estimator",
    "sourceVersion": "Author-hosted AFRICACRYPT 2016 manuscript; ePrint revision 13 April 2016"
  }
}