{
  "abstract": "The quadratic sieve (QS) is an irregular, cache-hostile, branch-heavy integer factorization algorithm; prior GPU work accelerates individual stages of it. We present \\swname{}, a self-initializing quadratic sieve in which \\emph{every} stage --- polynomial initialization, sieving, relation post-processing, large-prime matching, \\GFtwo{} matrix construction, Block Wiedemann linear algebra and the square root --- executes on the GPU, the CPU restricted to orchestration, setup and I/O, the sieve window 99.9\\% GPU-busy with no device-wide or event synchronization and no synchronous copy. With it we factored the 512-bit RSA-155 challenge modulus end to end on GPUs: a 64$\\times$H100 sieve feeding a single-H100 \\GFtwo{} solve, 700.6~GPU-h and 242~kWh in total, 98.4\\% of it sieving. To our knowledge this is the largest integer factored by the quadratic sieve, exceeding the prior QS record RSA-150 (Buhrow, YAFU, 2025); all comparable general factorizations since 1996, RSA-155's own in 1999 included, used the number field sieve. On a single device we factor RSA-100 in 29.2~s on an H100 and 51.0~s on a consumer RTX~5070~Ti; in a controlled same-modulus measurement, with energy measured on both sides, the H100 is faster than the fastest CPU quadratic sieve, YAFU, on 96 cores of an EPYC~9655 (106--122~s), and than CADO-NFS's SIQS (292~s) and GNFS (263~s). Across four discrete GPUs (a 3.7$\\times$ range in CUDA cores) RSA-100 throughput is close to proportional to core count, memory bandwidth being a weaker predictor, and measured cost over seven benchmark factorizations from RSA-100 to RSA-155 grows as $\\LN{1/2}{1}^{1.04}$ ($R^2=0.993$). On RSA-150, the identical modulus on which the prior QS record was set, we measure 302.9~GPU-h against that run's 11{,}664 core-hours.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07126",
  "author_total": 2,
  "authors": [
    {
      "name": "Fabian Januszewski"
    },
    {
      "name": "Christoph Heinrichs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jjf8hz7ysncn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07126",
  "fulltext_url": null,
  "id": "7jjf8hz7ysncn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07126",
  "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.DC"
    ],
    [
      "arxiv",
      "cs.MS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "1710|Cryptography and Residue Arithmetic"
    ]
  ],
  "openalex": "W7220968875",
  "pdf_url": "https://arxiv.org/pdf/2610.07126",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jjf8hz7ysncn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07126",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07126"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "CUDA-MPQS: A GPU-Resident Self-Initializing Quadratic Sieve, and the Factorization of RSA-155",
  "title_text": "CUDA-MPQS: A GPU-Resident Self-Initializing Quadratic Sieve, and the Factorization of RSA-155",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/7jjf8hz7ysncn",
  "venue": "arXiv",
  "versions": []
}