{
  "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"
  }
}