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

arXiv:2609.28882 · quant-ph · Submitted 2026-09-24 · Read on arXiv

quant-ph

Submitted: 2026-09-24

Updated: 2026-09-24

Code: https://github.com/Layr-Labs/ecdsafail-challenge

Project page: https://ecdsa.fail

Terminology

• Ablation — 5× in this paper · explained in 1 episode
• Adaptation — 5× in this paper · explained in 1 episode
• Benchmark — 4× in this paper · explained in 2 episodes
• Quantum Circuits — 4× in this paper · explained in 2 episodes
• AI Agents — 3× in this paper · explained in 2 episodes
• Alternation — 3× in this paper · explained in 1 episode
• Decode — 3× in this paper · explained in 2 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Ablation Studies — 1× in this paper · explained in 1 episode
• Accuracy — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Allocator — 1× in this paper · explained in 1 episode
• Provenance — 1× in this paper · explained in 3 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes

Sources

• A Simple Proof that Toffoli and Hadamard are Quantum Universal
• Securing Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations
• Windowed quantum arithmetic
• Optimized quantum implementation of elliptic curve arithmetic over binary fields
• Verifiable Quantum Advantage via Optimized DQI Circuits
• How to compute a 256-bit elliptic curve private key with only 50 million Toffoli gates
• A Vision for Auto Research with LLM Agents
• ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor's Algorithm
• AlphaEvolve: A coding agent for scientific and algorithmic discovery
• Improved reversible and quantum circuits for Karatsuba-based integer multiplication
• Quantum resource estimates for computing elliptic curve discrete logarithms
• Quantum Circuit Optimization with AlphaTensor
• Optimized Point Addition Circuits for Elliptic Curve Discrete Logarithms

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