{
  "id": "bkw-plain-regev",
  "categoryId": "bkw-regev",
  "paperId": "paper-87fab2296b57",
  "year": 2012,
  "date": "2012-11-11",
  "time": {
    "coefficient": 1,
    "expression": "2^{n+o(n)}"
  },
  "space": {
    "coefficient": 1,
    "expression": "2^{n+o(n)}"
  },
  "tags": [
    "classical",
    "heuristic",
    "LWE",
    "BKW",
    "Regev regime",
    "unlimited samples",
    "unstructured"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Decision-LWE specialization of the original free-depth corollary: choose a≈2 log₂n and b=n/a. Then q^b=2^{n+o(n)} and m=exp(O(n/log₂⁴n))=2^{o(n)}. The simplified Search-LWE Theorem 1 fixes a≈log₂n and instead gives coefficient 2; do not conflate the two statements.",
  "extra": {
    "samples": "2^{n+o(n)} fresh samples",
    "model": "Original Decision-LWE corollary; expectation and distribution assumptions as in the source",
    "schedule": "Exact block cancellation",
    "access": "Classical tables",
    "variant": "Decision-LWE",
    "formula": "a≈2 log₂n, b=n/a; q^b=2^{n+o(n)}",
    "success": "Constant target distinguishing advantage; polynomial amplification permitted"
  },
  "evidence": {
    "url": "https://eprint.iacr.org/2012/636.pdf",
    "locator": "Corollary 1, pp. 2–3; Corollary 3, Equations (15)–(18); distinguish simplified Search-LWE Theorem 1",
    "sourceVersion": "ePrint 2012/636 PDF checked 2026-11-08; original version not separately diffed"
  }
}