{
  "abstract": "We present a generalization of the Fast Fourier and fast Walsh transform algorithms to tensor products of $n$ arbitrary $q\\times q$ matrices over a commutative ring, reducing the cost of applying such a tensor product from $q^{2n}$ to $nq^{n}$ ring operations. We then give an explicit construction of square orthogonal matrices over a commutative unitary ring, starting from a prescribed first row, and specialize this construction to ${\\mathbb Z}/256{\\mathbb Z}$. Combining these two ingredients, we propose a symmetric cryptosystem in which the secret key determines~$n$ orthogonal matrices over ${\\mathbb Z}/256{\\mathbb Z}$ whose tensor product encrypts a block of $q^n$ bytes; encryption and decryption both exploit the fast tensor product algorithm. We give three examples of implementations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14782",
  "author_total": 1,
  "authors": [
    {
      "name": "Jacques Peyrière"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77z21r8w9gcx4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14782",
  "fulltext_url": null,
  "id": "77z21r8w9gcx4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14782",
  "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",
      "math.RA"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7213356449",
  "pdf_url": "https://arxiv.org/pdf/2609.14782",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77z21r8w9gcx4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14782",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14782"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fast tensor transforms and ring-valued orthogonal matrices: an application to cryptography",
  "title_text": "Fast tensor transforms and ring-valued orthogonal matrices: an application to cryptography",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/77z21r8w9gcx4",
  "venue": "arXiv",
  "versions": []
}