Building Shor's Algorithm in Lean: An Agentic Formalization of Quantum Attacks on RSA-2048 and P-256

Researchers have successfully formalized Shor's algorithm in Lean, a machine-checked library, to demonstrate the vulnerability of RSA-2048 and P-256 encryption to quantum attacks¹. This achievement leverages the capabilities of large language models and agentic systems to automate demanding formal theorem-proving tasks. By utilizing Lean, the team has created a rigorous and machine-verified proof of the algorithm's correctness, highlighting the potential risks of quantum computing to classical cryptography. The formalization of Shor's algorithm in Lean enables the exploration of quantum attacks on widely used cryptographic protocols, underscoring the need for quantum-resistant cryptography. This development has significant implications for the security of online transactions and communication, as quantum computers could potentially break current encryption standards. So what matters to practitioners is that they must begin transitioning to quantum-resistant cryptographic protocols to ensure the long-term security of their systems.