{
  "abstract": "This paper investigates the $c$-differential uniformity of power functions over finite fields, an important class of cryptographic functions with favorable differential properties. Specifically, for finite fields $\\mathbb{F}_q$ satisfying $q-1=en$ with $e\\ge 3$ and $e\\mid n$, we prove that there exists $c\\in\\mathbb{F}_q\\setminus\\{0,1,ε,\\dots,ε^{e-1}\\}$, where $ε$ is an $e$-th primitive root of unity in $\\mathbb{F}_q^*$, the constructed power functions $f(x)=x^{ln+1}$ with $1\\le l\\le e-1$ and $\\gcd(l,e)=1$ satisfy the upper bound $Δ(f,c)\\le e$, provided that certain cyclotomic conditions hold. We show that our conditions are mild; namely, such power functions can be constructed over infinitely many extension fields $\\mathbb{F}_q$ of $\\mathbb{F}_p$ for any given $e\\ge 3$ and prime $p$ with $p\\nmid e$. Furthermore, based on the Weil bound for multiplicative character sums, we prove that the obtained upper bound is tight for sufficiently large $q$, demonstrating the optimality of our results. We also analyze the special case $c=-1$ and derive simplified explicit conditions. In particular, we explicitly characterize the admissible parameters for the case $e=3$ and present concrete function examples for practical validation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22763",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhiye Yang"
    },
    {
      "name": "Yan Wang"
    },
    {
      "name": "Keqin Feng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ay4qekg02qkj9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22763",
  "fulltext_url": null,
  "id": "ay4qekg02qkj9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22763",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7214053730",
  "pdf_url": "https://arxiv.org/pdf/2609.22763",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ay4qekg02qkj9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22763",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22763"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "New Construction of Power Functions with Low c-Differential Uniformity over Finite Fields",
  "title_text": "New Construction of Power Functions with Low c-Differential Uniformity over Finite Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/ay4qekg02qkj9",
  "venue": "arXiv",
  "versions": []
}