{
  "id": "0709.2704",
  "version": "v1",
  "published": "2007-09-17T19:27:14.000Z",
  "updated": "2007-09-17T19:27:14.000Z",
  "title": "On RSA Moduli with Almost Half of the Bits Prescribed",
  "authors": [
    "Sidney W. Graham",
    "Igor E. Shparlinski"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that using character sum estimates due to H. Iwaniec leads to an improvement of recent results about the distribution and finding RSA moduli $M=pl$, where $p$ and $l$ are primes, with prescribed bit patterns. We are now able to specify about $n$ bits instead of about $n/2$ bits as in the previous work. We also show that the same result of H. Iwaniec can be used to obtain an unconditional version of a combinatorial result of W. de Launey and D. Gordon that was originally derived under the Extended Riemann Hypothesis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-17T19:27:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "11L40",
      "11N25",
      "94A60"
    ],
    "keywords": [
      "character sum estimates",
      "extended riemann hypothesis",
      "combinatorial result",
      "unconditional version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2704G"
    }
  }
}