{
  "abstract": "Supersingular abelian surfaces are essential in isogeny-based cryptography. Despite this, we have no efficient algorithm to verify if a given abelian surface is supersingular. In this work, we initiate this research topic by giving an efficient Monte Carlo algorithm to verify if an abelian surface over $\\mathbb{F}_p$ is supersingular in $O(\\log p)$ with negligible failure probability, and an efficient conclusive algorithm if the order is smooth. We derive this algorithm by a careful analysis on the structure of supersingular Jacobians over $\\mathbb{F}_p$. Furthermore, we derive efficient algorithms to verify if an abelian variety of any dimension is minimal or maximal, and to verify if a Jacobian of any dimension is superspecial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01924",
  "author_total": 3,
  "authors": [
    {
      "name": "Maria Corte-Real Santos"
    },
    {
      "name": "Gioella Lorenzon"
    },
    {
      "name": "Krijn Reijnders"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a0mbxmk6wgqp3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01924",
  "fulltext_url": null,
  "id": "a0mbxmk6wgqp3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01924",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CR"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "1710|Cryptography and Residue Arithmetic"
    ]
  ],
  "openalex": "W7216103401",
  "pdf_url": "https://arxiv.org/pdf/2610.01924",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a0mbxmk6wgqp3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01924",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01924"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Supersingularity and Superspeciality Verification of Abelian Surfaces",
  "title_text": "Supersingularity and Superspeciality Verification of Abelian Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/a0mbxmk6wgqp3",
  "venue": "arXiv",
  "versions": []
}