{
  "abstract": "For a monic irreducible $f \\in \\mathbb{Z}[x]$ of degree $n$ and an integer $c$, we study the palindromic transform $F(x) = x^n f(x + x^{-1} + c)$, which produces a polynomial of degree $2n$. We give a discriminant formula $\\operatorname{disc}(F) = f(c+2)f(c-2)\\operatorname{disc}(f)^2$, sufficient conditions for the irreducibility of $F$, and a criterion showing that $F$ is monogenic when $f$ is monogenic and $f(c+2)f(c-2)$ is squarefree, together with a matching non-monogenicity criterion. Iterating the transform yields monogenic number fields of degree $2^k n$ from a fixed base polynomial. As an explicit example, we construct a monogenic field of degree 512 from $x^4 + x + 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22374",
  "author_total": 3,
  "authors": [
    {
      "name": "Swechchha Adhikari"
    },
    {
      "name": "Daphne Plott"
    },
    {
      "name": "Parker Torgersen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zk05req9tjsh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22374",
  "fulltext_url": null,
  "id": "7zk05req9tjsh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22374",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214017719",
  "pdf_url": "https://arxiv.org/pdf/2609.22374",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zk05req9tjsh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22374",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22374"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Monogenic Fields of Cryptographic Size",
  "title_text": "Monogenic Fields of Cryptographic Size",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/7zk05req9tjsh",
  "venue": "arXiv",
  "versions": []
}