Shor’s Algorithm Formalized in Lean for RSA-2048 and P-256

Researchers use AI-assisted Lean formalization to machine-check foundations and resource estimates for quantum attacks on RSA-2048 and P-256.

TL;DR — A new paper uses AI-assisted Lean theorem proving to formalize foundations and logical resource estimates for Shor-related quantum attacks on RSA-2048 and P-256. It is a step toward machine-checked quantum cryptanalysis, not evidence of a practical break.

Background: why Shor's algorithm matters

Shor’s algorithm is a central result in quantum computing because, on a sufficiently large fault-tolerant quantum computer, it could solve problems that underpin major public-key cryptosystems, including RSA and elliptic-curve cryptography.

RSA-2048 refers to RSA with a 2048-bit modulus. P-256 is a standardized elliptic curve over a 256-bit prime field and is widely used in security protocols. Both remain secure against known classical attacks at their intended security levels, but both are important benchmarks for quantum cryptanalysis.

The paper, “Building Shor’s Algorithm in Lean: An Agentic Formalization of Quantum Attacks on RSA-2048 and P-256,” does not report a practical break. It formalizes the reasoning used to analyze quantum attacks against these targets.

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