[
  {
    "id": "peikert10-dgs-qary-online",
    "categoryId": "dgs-qary-online",
    "paperId": "peikert-2010-gaussian",
    "year": 2010,
    "date": "2010-12-31",
    "datePrecision": "year",
    "time": {
      "coefficient": null,
      "expression": "O(n^2) integer operations plus n randomized-rounding calls online"
    },
    "space": {
      "coefficient": null,
      "expression": "O(n^2 log q) matrix bits plus O(n log q) bits per fresh perturbation"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "q-ary",
      "trapdoor",
      "offline online",
      "parallel"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The integer arithmetic bound excludes offline preparation and fresh perturbation generation. It uses the stronger operator-norm width promise.",
    "extra": {
      "width": "s >= r(2 s_1(B)+1), r=omega(sqrt(log n)), for spherical covariance",
      "preprocessing": "Precompute inverse and perturbations; a fresh perturbation is consumed for each output",
      "output": "One sample on L+c; q Z^n contained in L contained in Z^n and c integral",
      "error": "Negligible statistical distance",
      "model": "P <= n^2 processors: O(n^2/P) integer operations and ceil(n/P) rounding calls each; arithmetic can be modulo q or q^2"
    },
    "evidence": {
      "url": "https://web.eecs.umich.edu/~cpeikert/pubs/pargauss.pdf",
      "locator": "§1.2; Algorithm 2 and Theorem 4.3, printed pp. 12–14",
      "sourceVersion": "CRYPTO 2010; full author version 13 April 2011"
    }
  }
]