Author

Lucas Lévy

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Preprint Sep 2026

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

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 f...

Jie-Yi Long, Theodore Pender, Zhao-Feng Huang et al. · 0 citations

Preprint Sep 2026

ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor's Algorithm

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...

Jie-Yi Long, Theodore Pender, Zhao-Feng Huang et al. · 0 citations

Preprint Aug 2026

Beyond Optimal Rates in Stochastic Optimization: Trajectory-Adaptive Stopping Rules

This work treats the evolving SGD trajectory as a sequential experiment whose observations provide evidence about the unknown optimization error, and develops new recursive confidence-sequence techniques and a general time-uniform empirical Bernstein inequality for adapted processes with time-varying conditional means...

Liviu Aolaritei, Lucas Lévy, Francis R. Bach et al. · 0 citations