{
  "abstract": "We study reversible secp256k1 point-addition circuits developed through ECDSA.Fail for Shor's elliptic-curve discrete-logarithm algorithm. Two complementary constructions improve record-and-replay GCD arithmetic: Jump-2 groups binary-GCD steps and compresses their decisions using base-5 encoding, while ping-pong uses fixed register alternation and one-bit decisions to avoid full-width comparisons and data-dependent swaps. Fused replay combines doubling and signed addition into one modular correction. Both constructions support quantum-addressed window selection with measurement-based lookup cleanup. We compare three circuits on 100,000 fresh inputs across nine lookup-table configurations. A separately tested repair uses 1,419 qubits and 1.356 million mean executed Toffolis, with no detected failures on another 100,000 inputs. Structured supported-input counterexamples remain, so these tests do not establish all-input correctness. We also provide conditional coherent-error analysis and reversible safegcd comparisons. Under the stated window allowance, repaired-circuit resources lie below Google's low-gate caps and Schrottenloher's low-gate estimates, but differing accounting and correctness evidence preclude formal dominance. The results concern individual window-selected additions, not complete Shor computations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28882",
  "author_total": 36,
  "authors": [
    {
      "name": "Jieyi Long"
    },
    {
      "name": "Theodore Pender"
    },
    {
      "name": "Zhao Huang"
    },
    {
      "name": "Manuel B. Santos"
    },
    {
      "name": "Samrendra Kumar Singh"
    },
    {
      "name": "Bartosz Naskręcki"
    },
    {
      "name": "BitWonka"
    },
    {
      "name": "Pierre-Luc Dallaire-Demers"
    },
    {
      "name": "Francesco Giannicola"
    },
    {
      "name": "Ruben M. L. Paschoarelli"
    },
    {
      "name": "Oli Freuler"
    },
    {
      "name": "Jackie Chia-Hsun Lee"
    },
    {
      "name": "Vasily Gnuchev"
    },
    {
      "name": "Gopi Kannappan"
    },
    {
      "name": "John Boyer"
    },
    {
      "name": "Xavier Butler"
    },
    {
      "name": "Akash Balasubramani"
    },
    {
      "name": "Jordan Newman"
    },
    {
      "name": "Bereket Dereje"
    },
    {
      "name": "Alexander Hertlein"
    },
    {
      "name": "Robert Kodra"
    },
    {
      "name": "Lucas Levy"
    },
    {
      "name": "Shaan Patel"
    },
    {
      "name": "JT Rose"
    },
    {
      "name": "Matt Zweil"
    },
    {
      "name": "Okechukwu Wisdom"
    },
    {
      "name": "Tarek El-Eter"
    },
    {
      "name": "Edison Lee"
    },
    {
      "name": "Michael Dong"
    },
    {
      "name": "Alan Li"
    },
    {
      "name": "Anto Joseph"
    },
    {
      "name": "Duy Nguyen"
    },
    {
      "name": "Gajesh Naik"
    },
    {
      "name": "Gautham Anant"
    },
    {
      "name": "Soubhik Deb"
    },
    {
      "name": "Justin Drake"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0c759p8datrp6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28882",
  "fulltext_url": null,
  "id": "0c759p8datrp6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28882",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214399396",
  "pdf_url": "https://arxiv.org/pdf/2609.28882",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0c759p8datrp6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.28882",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28882"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition",
  "title_text": "Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/0c759p8datrp6",
  "venue": "arXiv",
  "versions": []
}