{
  "id": "2307.09491",
  "version": "v1",
  "published": "2023-07-18T11:22:53.000Z",
  "updated": "2023-07-18T11:22:53.000Z",
  "title": "Root Extraction in Finite Abelian $p$-Groups",
  "authors": [
    "M. S. Srinath"
  ],
  "comment": "This work appeared as a chapter in the author's Ph.D. thesis, titled Isogeny-based Quantum Resistant Undeniable Blind Signature and Authenticated Encryption Schemes, 2018",
  "categories": [
    "math.GR"
  ],
  "abstract": "We formulate a problem called Generalized Root Extraction in finite Abelian groups that have more than one generator. We then study this problem for the specific case of the torsion subgroups of elliptic curves. We give a necessary and sufficient condition for the existence of a solution. We also present an algorithm to find a solution. Our algorithm easily generalizes to Abelian groups of prime power order having a specific structure. We then discuss a variant of this problem called Simultaneous Root Extraction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-18T11:22:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20-08",
      "20K01",
      "14H52"
    ],
    "keywords": [
      "finite abelian groups",
      "prime power order",
      "specific structure",
      "simultaneous root extraction",
      "specific case"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}