[
  {
    "id": "gpv08-dgs-gs-width",
    "categoryId": "dgs-basis-gs-width",
    "paperId": "gentry-peikert-vaikuntanathan-2008",
    "year": 2008,
    "date": "2008-08-25",
    "datePrecision": "day",
    "time": {
      "coefficient": null,
      "expression": "Probabilistic polynomial time"
    },
    "space": {
      "coefficient": null,
      "expression": "Polynomial space (polynomial-time algorithm)"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "trapdoor",
      "basis relative",
      "shifted DGS"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The published paper title is retained. The checked full version adds the heading “How to Use a Short Basis”. The November 2007 preliminary manuscript only states a longest-basis-vector width, so the Gram–Schmidt bound is not backdated to 2007.",
    "extra": {
      "width": "s >= ||B_tilde|| omega(sqrt(log n)); ||B_tilde||=max_i ||b_tilde_i||",
      "basis": "Any supplied lattice basis; obtaining a short basis is excluded",
      "output": "One sample from a distribution close to D_{L,s,c}, arbitrary center c",
      "error": "Statistical closeness; the proof makes it negligible with the stated superlogarithmic margin",
      "model": "Probabilistic polynomial time, sequential randomized nearest plane"
    },
    "evidence": {
      "url": "https://web.eecs.umich.edu/~cpeikert/pubs/trap_lattice.pdf",
      "locator": "Theorem 4.1, printed p. 14; §4",
      "sourceVersion": "Full author version dated 25 August 2008; STOC 2008 publication"
    }
  }
]