[
  {
    "id": "peikert10-dgs-parallel-online",
    "categoryId": "dgs-operator-width-online",
    "paperId": "peikert-2010-gaussian",
    "year": 2010,
    "date": "2010-12-31",
    "datePrecision": "year",
    "time": {
      "coefficient": null,
      "expression": "O(n^2) online real operations; O(n^2/P) per processor"
    },
    "space": {
      "coefficient": null,
      "expression": "Offline matrices and fresh perturbation vector"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "trapdoor",
      "parallel",
      "offline online",
      "shifted DGS"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The scalar width is controlled by the largest singular value, not the longest Gram–Schmidt vector. Publication year is known; the detailed theorem was checked in the 2011 full author version.",
    "extra": {
      "width": "Covariance Sigma > r^2 B B^T, r=omega(sqrt(log n)); spherical sufficient condition s > r s_1(B)",
      "preprocessing": "Matrix factorization/inversion and one fresh continuous-Gaussian perturbation before each query",
      "output": "One sample on L+c, arbitrary real shift c",
      "error": "Negligible statistical distance",
      "model": "Theorem 4.2: P <= n^2 processors; O(n^2/P) sufficiently precise real operations per processor"
    },
    "evidence": {
      "url": "https://web.eecs.umich.edu/~cpeikert/pubs/pargauss.pdf",
      "locator": "Algorithm 1 and Theorem 4.2, printed pp. 11–12",
      "sourceVersion": "CRYPTO 2010 paper; checked full author version dated 13 April 2011"
    }
  }
]