{
  "abstract": "Most of the known (Almost) Perfect Nonlinear functions over an arbitrary finite field Fp have the lowest possible algebraic degree (2) and can be represented by Dembowski-Ostrom (DO) polynomials. We define Generalized DO (GDO) polynomials as homogeneous polynomials of algebraic degree p over finite fields with characteristic p . We illustrate the similarities between DO and GDO polynomials when studied through generalized derivatives. We also discuss the differential uniformity and Walsh coefficients of GDO functions. Our main contribution is to use this framework in order to propose several new classes of Generalized Almost Perfect Nonlinear (GAPN) functions of algebraic degree p , the lowest possible over the finite field Fp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Noureddine El-Asri"
    },
    {
      "name": "Valentin Suder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40jn2q5x8z5d7.bib",
  "cited_by": 0,
  "doi": "10.1016/j.ffa.2026.102885",
  "fulltext_url": null,
  "id": "40jn2q5x8z5d7",
  "issns": [
    "1071-5797",
    "1090-2465"
  ],
  "landing_url": "https://hal.science/hal-05758976v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7171549437",
  "pdf_url": "https://hal.science/hal-05758976/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/40jn2q5x8z5d7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
      "native_id": "hal-05758976",
      "source": "hal",
      "url": "https://hal.science/hal-05758976v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "New GAPN functions with the lowest possible algebraic degree",
  "title_text": "New GAPN functions with the lowest possible algebraic degree",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:37Z",
  "url": "https://research.draconitic.com/paper/40jn2q5x8z5d7",
  "venue": "Finite Fields and Their Applications",
  "versions": []
}