Scientists have successfully formalized the Shor's algorithm family within the Lean proof assistant, marking a significant milestone for machine-checked quantum cryptanalysis. This work employs an "agentic" approach, where software agents analyze sources, generate Lean code, and repair proofs, with human review of the scientific claims and machine verification of the resulting formal proofs. The formalization lays the mathematical foundations for analyzing quantum attacks in two key cryptographic settings: a 2048-bit modulus for RSA-2048 and the standardized elliptic curve over a 256-bit prime field (P-256).

The formalization spans from quantum algorithms for order finding to reversible quantum circuits for modular and elliptic-curve arithmetic. Drawing upon previous work published in Quantum and ASIACRYPT, the team has formalized the logical resource estimates for RSA-2048 and P-256, respectively, and has provided additional estimates for the classical operations required. This advancement is crucial for understanding the computational requirements of quantum attacks on current cryptographic systems.

This development represents an important step towards AI-assisted design and verification of quantum algorithms. The ability to rigorously formalize and verify quantum algorithms, especially those with security implications, is essential as quantum computing matures. These results are expected to pave the way for broader machine-checked quantum cryptanalysis, enhancing confidence in the security assessments of post-quantum cryptographic systems.