[
  {
    "id": "bkw-hkm-nlogn-plain-q2s1",
    "categoryId": "bkw-q2-s1-nlogn",
    "paperId": "hkm2015-asymptotic",
    "date": "2018-12-31",
    "datePrecision": "year",
    "year": 2018,
    "time": {
      "coefficient": 1,
      "expression": "2^{(2/[2(2−1)]+o(1)) n}"
    },
    "space": {
      "coefficient": 1,
      "expression": "2^{(2/[2(2−1)]+o(1)) n}"
    },
    "tags": [
      "classical",
      "provable",
      "LWE",
      "BKW"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Parameter substitution in the checked analysis; no priority claim for the underlying algorithm.",
    "extra": {
      "samples": "Θ(n log n) original samples",
      "model": "q exponent 2; Gaussian-width exponent 1; the strict theorem inequalities hold",
      "formula": "2/[2(2−1)]"
    },
    "evidence": {
      "url": "https://elenakirshanova.github.io/Papers/on_the_asymptotic_complexity.pdf",
      "locator": "Theorem 11, first display",
      "sourceVersion": "Undated 30-page author manuscript checked 2026-11-08; journal 86(1), 2018; original 2015 preprint not version-compared"
    }
  },
  {
    "id": "bkw-hkm-nlogn-coded-q2s1",
    "categoryId": "bkw-q2-s1-nlogn",
    "paperId": "hkm2015-asymptotic",
    "date": "2018-12-31",
    "datePrecision": "year",
    "year": 2018,
    "time": {
      "coefficient": 0.7213475204444817,
      "expression": "2^{(1/[2 ln(2)]+o(1)) n}"
    },
    "space": {
      "coefficient": 0.7213475204444817,
      "expression": "2^{(1/[2 ln(2)]+o(1)) n}"
    },
    "tags": [
      "classical",
      "provable",
      "LWE",
      "BKW"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Parameter substitution in the checked analysis; no priority claim for the underlying algorithm.",
    "extra": {
      "samples": "Θ(n log n) original samples",
      "model": "q exponent 2; Gaussian-width exponent 1; the strict theorem inequalities hold",
      "formula": "1/[2 ln(2)]"
    },
    "evidence": {
      "url": "https://elenakirshanova.github.io/Papers/on_the_asymptotic_complexity.pdf",
      "locator": "Theorem 11, first display",
      "sourceVersion": "Undated 30-page author manuscript checked 2026-11-08; journal 86(1), 2018; original 2015 preprint not version-compared"
    }
  }
]