{
  "abstract": "The mapping $ χ_n:\\mathbb{F}_2^n \\to \\mathbb{F}_2^n$ defined by $y=χ_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\\le u, v, w<n$ and $a_i\\in \\mathbb{F}_2$, $1\\le i\\le n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19548",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiutao Feng"
    },
    {
      "name": "Qiang Wang"
    },
    {
      "name": "Jingyi Yu"
    },
    {
      "name": "Anpeng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dh11h5t4fbgq7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19548",
  "fulltext_url": null,
  "id": "dh11h5t4fbgq7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19548",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7213610169",
  "pdf_url": "https://arxiv.org/pdf/2609.19548",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dh11h5t4fbgq7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.19548",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19548"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "A generalization of the map $χ$",
  "title_text": "A generalization of the map χ",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dh11h5t4fbgq7",
  "venue": "arXiv",
  "versions": []
}