Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition

@misc{long2026efficient,
  title = {{Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition}},
  author = {Jieyi Long and Theodore Pender and Zhao Huang and Manuel B. Santos and Samrendra Kumar Singh and Bartosz Naskręcki and BitWonka and Pierre-Luc Dallaire-Demers and Francesco Giannicola and Ruben M. L. Paschoarelli and Oli Freuler and Jackie Chia-Hsun Lee and Vasily Gnuchev and Gopi Kannappan and John Boyer and Xavier Butler and Akash Balasubramani and Jordan Newman and Bereket Dereje and Alexander Hertlein and Robert Kodra and Lucas Levy and Shaan Patel and JT Rose and Matt Zweil and Okechukwu Wisdom and Tarek El-Eter and Edison Lee and Michael Dong and Alan Li and Anto Joseph and Duy Nguyen and Gajesh Naik and Gautham Anant and Soubhik Deb and Justin Drake},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28882},
  eprint = {2609.28882},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28882},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition
AU  - Jieyi Long
AU  - Theodore Pender
AU  - Zhao Huang
AU  - Manuel B. Santos
AU  - Samrendra Kumar Singh
AU  - Bartosz Naskręcki
AU  - BitWonka
AU  - Pierre-Luc Dallaire-Demers
AU  - Francesco Giannicola
AU  - Ruben M. L. Paschoarelli
AU  - Oli Freuler
AU  - Jackie Chia-Hsun Lee
AU  - Vasily Gnuchev
AU  - Gopi Kannappan
AU  - John Boyer
AU  - Xavier Butler
AU  - Akash Balasubramani
AU  - Jordan Newman
AU  - Bereket Dereje
AU  - Alexander Hertlein
AU  - Robert Kodra
AU  - Lucas Levy
AU  - Shaan Patel
AU  - JT Rose
AU  - Matt Zweil
AU  - Okechukwu Wisdom
AU  - Tarek El-Eter
AU  - Edison Lee
AU  - Michael Dong
AU  - Alan Li
AU  - Anto Joseph
AU  - Duy Nguyen
AU  - Gajesh Naik
AU  - Gautham Anant
AU  - Soubhik Deb
AU  - Justin Drake
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.28882
UR  - https://arxiv.org/abs/2609.28882
AB  - 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.
ER  -