{
  "abstract": "The Learning With Errors (LWE) problem, introduced by Regev in 2005, is central to modern cryptography and post-quantum security. The algorithms to solve the search version of the problem, Search-LWE, can be broadly categorised into algebraic, combinatorial and lattice-based. In this work we propose a new algebraic algorithm for the Search-LWE problem. At a high level, the algorithm combines linear-algebraic techniques with S-polynomial-based methods from Groebner basis computation. We provide a direct complexity analysis of our algorithm, avoiding semi-regularity assumptions and complexity bounds derived from the degree of regularity. Our algorithm achieves a polynomial improvement in complexity over prior results that use Groebner basis methods to solve Search-LWE.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29977",
  "author_total": 3,
  "authors": [
    {
      "name": "Luca Campa"
    },
    {
      "name": "Massimo Fumiani"
    },
    {
      "name": "Arnab Roy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/daz6ppvwb5vct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29977",
  "fulltext_url": null,
  "id": "daz6ppvwb5vct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29977",
  "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.CR"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "1702|Cryptography and Data Security"
    ]
  ],
  "openalex": "W7204903675",
  "pdf_url": "https://arxiv.org/pdf/2608.29977",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/daz6ppvwb5vct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29977",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29977"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A New Algebraic Algorithm for LWE",
  "title_text": "A New Algebraic Algorithm for LWE",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/daz6ppvwb5vct",
  "venue": "arXiv",
  "versions": []
}