{
  "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"
  }
}