{
  "id": "albrecht17-dual-amortized",
  "categoryId": "lwe-dual-lattice-models",
  "paperId": "albrecht2017-dual-small-secret",
  "year": 2017,
  "date": "2017-05-18",
  "datePrecision": "day",
  "time": {
    "coefficient": null,
    "expression": "T_BKZ(m,β) + M·[T_rerandomize(m) + T_BKZ(m,β′)], with β′≤β"
  },
  "space": {
    "coefficient": null,
    "expression": "Reduced basis plus M short dual vectors, if stored."
  },
  "tags": [
    "dual",
    "amortization",
    "heuristic",
    "fixed samples"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Reuses an expensive reduced basis to generate many shorter dual relations. The claimed reduction relies on relations being sufficiently short and sufficiently random; fixed-sample correlations remain a heuristic.",
  "extra": {
    "parameters": "Fix n,q, Gaussian width αq, lattice dimension m, block sizes β,β′ and required relation count M.",
    "noise": "Discrete Gaussian width αq.",
    "secret": "General LWE secret; this amortization does not require a short secret.",
    "samples": "Works on the available LWE matrix; reuses it, unlike fully independent fresh-sample amplification.",
    "objective": "Decision-LWE with amplified distinguishing advantage.",
    "model": "One BKZ-β preprocessing followed by sparse unimodular rerandomization and cheaper BKZ-β′; source instantiation β′=2.",
    "assumptions": "Cheap rerandomization yields short, adequately random relations; dependence can be ignored in the statistical test.",
    "success": "Target advantage determines M; source estimates use dual-vector norm inflation by a factor of two."
  },
  "evidence": {
    "url": "https://github.com/malb/publications/blob/2fc91ddbe45e21d7c337bfc658e4fd8926dd887c/on-dual-attacks-against-small-secret-lwe/small-sparse-secret.tex",
    "locator": "Section Amortising costs, Algorithm 1 and its Heuristic paragraph",
    "sourceVersion": "Author TeX commit 2fc91ddbe45e21d7c337bfc658e4fd8926dd887c, 18 May 2017; associated ePrint last revised 6 May 2017"
  }
}