{
  "id": "ag10-lwe-small-gaussian",
  "categoryId": "lwe-gaussian-algebraic-history",
  "paperId": "arora-ge2010-eccc",
  "year": 2011,
  "date": "2010-12-13",
  "datePrecision": "day",
  "time": {
    "coefficient": null,
    "expression": "2^{Õ(n^{2ε})}, for αq=n^ε and fixed ε<1/2"
  },
  "space": {
    "coefficient": null,
    "expression": "Exponential-size linearization; no numerical space coefficient extracted."
  },
  "tags": [
    "small Gaussian error",
    "provable",
    "oracle samples"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Subexponential only in the stated small-error regime. Date is the checked ECCC revision, preceding ICALP 2011.",
  "extra": {
    "parameters": "Prime q=q(n) with q ≫ (αq log n)²; αq=n^ε, fixed 0≤ε<1/2.",
    "noise": "Source Gaussian Ψ_α over GF(q), width parameter αq.",
    "secret": "Arbitrary fixed u∈GF(q)^n.",
    "samples": "Oracle access; 2^{Õ(n^{2ε})} samples allowed, not a linear-sample claim.",
    "objective": "Recover the full secret.",
    "model": "Classical randomized polynomial-system linearization; polynomial input-size factors implicit.",
    "assumptions": "Theorem for the specified Gaussian distribution and modulus regime.",
    "success": "High probability as in Theorems 3.1 and 3.3."
  },
  "evidence": {
    "url": "https://eccc.weizmann.ac.il/report/2010/066/revision/1/download",
    "locator": "§3, Theorem 3.1, p. 8; construction and Theorem 3.3",
    "sourceVersion": "ECCC TR10-066 revision 1, 13 December 2010"
  }
}