{
  "abstract": "For any permutation of a nontrivial finite abelian group, the differential uniformity is at least two; permutations attaining this bound are called almost perfect nonlinear (APN). We construct three infinite classes of APN permutations on the cyclic group $\\mathbb{Z}_n$ using Singer cycles, binomials inducing projective permutations, and completed reciprocals combined with parity and quadratic characters. The respective domain orders are $q+1$ for prime powers $q>2$, $(3^d-1)/2$ for integers $d\\ge2$, and $2p$ for primes $p>5$ with $p\\equiv5\\pmod6$. Each class contains an infinite subclass of composite orders outside the standard forms $r-1$, $r-2$, $r-3$, and $r-4$, where $r$ is a prime power. These forms arise in the Welch--Costas, Panario--Sakzad--Stevens--Wang, and Golomb constructions. To the best of our knowledge, these are the first infinite APN constructions on $\\mathbb{Z}_n$ reported since 2011 that yield infinitely many composite orders outside these standard forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05917",
  "author_total": 1,
  "authors": [
    {
      "name": "Deng Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xr6f268f5mqr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05917",
  "fulltext_url": null,
  "id": "8xr6f268f5mqr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05917",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
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      "openalex",
      "1702|Coding theory and cryptography"
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  "openalex": "W7212016107",
  "pdf_url": "https://arxiv.org/pdf/2609.05917",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xr6f268f5mqr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05917",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05917"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Three Infinite Classes of APN Permutations on $Z_n$",
  "title_text": "Three Infinite Classes of APN Permutations on Z_n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/8xr6f268f5mqr",
  "venue": "arXiv",
  "versions": []
}