ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor's Algorithm
Abstract
We propose Open Autoresearch, a paradigm in which humans and AI agents publish evaluator-verified improvements to a public leaderboard. We instantiate it in ECDSA.Fail, optimizing reversible secp256k1 point-addition circuits, a bottleneck in Shor's algorithm for elliptic-curve cryptography. The benchmark minimizes the spacetime-inspired score S=Q× T, where Q is peak logical qubit width and T is average executed Toffoli count. Participants reduced S by 86.1%. At the data cutoff (26 July 2026), the best-scoring circuit uses 1,151 qubits and 1,299,453 average executed Toffoli gates, giving Q× T≈1.496 billion. This is more than 50% below Google's published point-addition score thresholds (arXiv:2603.28846), under different accounting conventions. Because the benchmark supplies one addend classically, we construct a coherent windowed-addition-compatible variant implementing the single-call interface required by windowed Shor. It uses 1,162 qubits and 1,684,161 average executed Toffoli gates. On 100,000 random inputs, its empirical success probability is p̂=0.99809, giving Q× T/p̂≈1.961 billion under an independently rerunnable per-call sensitivity model, not a full-Shor success estimate. Its qubit and Toffoli counts lie below Google's published thresholds and Schrottenloher's reported operating points (arXiv:2606.02235), although differing interfaces, accounting conventions, and validation scope preclude formal dominance. After the cutoff, the score was further reduced to 1.259 billion, while a separate low-width circuit reached 813 qubits. The public record shows AI agents complementing human judgment, providing evidence for open autoresearch on efficiently evaluable, machine-checkable objectives.
Related
- Quantum Algorithm for Elliptic Curve Discrete Logarithms with Space-Efficient Point Addition
- Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition
- Toward Efficient End-to-End Quantum Elliptic PDE Solvers: a Multilevel Correction Algorithm for Direct Observable Estimation
- Encoded reversible addition in constant Toffoli depth
- Age-targeted failure in evolving networks with addition and deletion of vertices
BibTeX
@misc{long2026ecdsafail,
title = {{ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor's Algorithm}},
author = {Jieyi Long and Theodore Pender and Zhao Huang and Manuel B. Santos and Samrendra Kumar Singh and Bartosz Naskręcki and Bit Wonka 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 Gajesh Naik and Gautham Anant and Soubhik Deb and Justin Drake},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09582},
eprint = {2609.09582},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09582},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor's Algorithm
AU - Jieyi Long
AU - Theodore Pender
AU - Zhao Huang
AU - Manuel B. Santos
AU - Samrendra Kumar Singh
AU - Bartosz Naskręcki
AU - Bit Wonka
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 - Gajesh Naik
AU - Gautham Anant
AU - Soubhik Deb
AU - Justin Drake
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.09582
UR - https://arxiv.org/abs/2609.09582
AB - We propose Open Autoresearch, a paradigm in which humans and AI agents publish evaluator-verified improvements to a public leaderboard. We instantiate it in ECDSA.Fail, optimizing reversible secp256k1 point-addition circuits, a bottleneck in Shor's algorithm for elliptic-curve cryptography. The benchmark minimizes the spacetime-inspired score S=Q× T, where Q is peak logical qubit width and T is average executed Toffoli count. Participants reduced S by 86.1%. At the data cutoff (26 July 2026), the best-scoring circuit uses 1,151 qubits and 1,299,453 average executed Toffoli gates, giving Q× T≈1.496 billion. This is more than 50% below Google's published point-addition score thresholds (arXiv:2603.28846), under different accounting conventions. Because the benchmark supplies one addend classically, we construct a coherent windowed-addition-compatible variant implementing the single-call interface required by windowed Shor. It uses 1,162 qubits and 1,684,161 average executed Toffoli gates. On 100,000 random inputs, its empirical success probability is p̂=0.99809, giving Q× T/p̂≈1.961 billion under an independently rerunnable per-call sensitivity model, not a full-Shor success estimate. Its qubit and Toffoli counts lie below Google's published thresholds and Schrottenloher's reported operating points (arXiv:2606.02235), although differing interfaces, accounting conventions, and validation scope preclude formal dominance. After the cutoff, the score was further reduced to 1.259 billion, while a separate low-width circuit reached 813 qubits. The public record shows AI agents complementing human judgment, providing evidence for open autoresearch on efficiently evaluable, machine-checkable objectives.
ER -