{
  "id": "2102.02605",
  "version": "v1",
  "published": "2021-02-04T13:38:45.000Z",
  "updated": "2021-02-04T13:38:45.000Z",
  "title": "Linear complexity of some sequences derived from hyperelliptic curves of genus 2",
  "authors": [
    "Vishnupriya Anupindi",
    "László Mérai"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "For a given hyperelliptic curve $C$ over a finite field with Jacobian $J_C$, we consider the hyperelliptic analogue of the congruential generator defined by $W_n=W_{n-1}+D$ for $n\\geq 1$ and $D,W_0\\in J_C$. We show that curves of genus 2 produce sequences with large linear complexity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-04T13:38:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G20",
      "11K45",
      "11T71"
    ],
    "keywords": [
      "hyperelliptic curve",
      "large linear complexity",
      "congruential generator",
      "finite field",
      "hyperelliptic analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}