{
  "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"
  }
}