{
  "abstract": "The Shortest Vector Problem (SVP) is the computational foundation of lattice-based cryptography, and its hardness on structured lattices directly impacts the security of NIST-standardized schemes such as Kyber and Dilithium. This paper investigates the SVP on anti-circulant lattices, studies the algebraic structure underlying the polynomial ring Z[x]/(xn+1), and reveals a fundamental distinction from their circulant counterparts. Using the convex body restriction strategy, we prove that for n≤3, every SVP solution has coefficients in {0,±1} unconditionally, and for n=4,5,6, explicit coefficient bounds hold under mild conditions on the lattice parameters. For higher dimensions up to n=50, experiments with an exact SVP show that with probability ≥95%, there exists an SVP solution with coefficients in {0,±1}, and with probability ≥97%, and there exists one with coefficients in {0,±1,±2}. All experiments are computed with the exact SVP, without using any approximation algorithm as the primary oracle.",
  "abstract_shown": true,
  "affiliations": [
    "School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China",
    "Zhejiang Provincial Key Laboratory of Sensitive Data Security and Confidentiality Governance, Hangzhou Dianzi University, Hangzhou 310018, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Gengran Hu",
      "orcid": "0000-0002-3061-2388"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rxb108zvvv10.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15110802",
  "fulltext_url": null,
  "id": "1rxb108zvvv10",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/11/802",
  "language": null,
  "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": [
    [
      "openalex",
      "1702|Cryptography and Data Security"
    ]
  ],
  "openalex": "W7224095241",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/1rxb108zvvv10.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15110802",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/11/802"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "On the SVP for Anti-Circulant Lattices",
  "title_text": "On the SVP for Anti-Circulant Lattices",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/1rxb108zvvv10",
  "venue": "Axioms",
  "versions": []
}