{
  "id": "lwe-kf2015-binary-linear",
  "categoryId": "lwe-binary-linear-samples",
  "paperId": "paper-e014be9a6925",
  "date": "2015-06-29",
  "datePrecision": "day",
  "year": 2015,
  "time": {
    "coefficient": 0.34657359027997264,
    "expression": "2^{(ln(2)/2+o(1)) n/log₂ log₂ n}"
  },
  "space": {
    "coefficient": null,
    "expression": "Not separately normalized"
  },
  "tags": [
    "classical",
    "provable",
    "LWE",
    "binary secret",
    "binary errors",
    "linear samples"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Decision bound for binary secret/error, q≈n², m=n. The corollary gap is Θ(log n), satisfying HKM’s stronger amplification condition.",
  "extra": {
    "samples": "n original equations",
    "model": "Uniform binary secret and errors; prime modulus q≈n²",
    "formula": "ln(2)/2 on the n/log₂log₂n scale"
  },
  "evidence": {
    "url": "https://arxiv.org/pdf/1506.02717v4",
    "locator": "Abstract; §5.2, Definition 11 and Corollary 6",
    "sourceVersion": "arXiv:1506.02717v4, 29 June 2015"
  }
}