Optimizing windowed arithmetic for quantum attacks against RSA-2048 - Luongo, Alessandro; Narasimhachar, Varun; Sireesh, Adithya (2025 62nd ACM/IEEE Design Automation Conference (DAC), 2025)
Windowed arithmetic is a technique for reducing the cost of quantum arithmetic circuits with space-time trade-offs using memory queries to precomputed tables. It can reduce the asymptotic cost of modular exponentiation from \mathcal{O}\left(n^{2}\right) to \mathcal{O}\left(n^{2} / \log ^{2} n\right) operations, resulting in the current state-of-the-art compilations of quantum attacks against modern cryptography. We introduce several optimizations to windowed arithmetic. Notably, we effect an approximate 50 % reduction in the costs of uncomputing memory lookups in quantum factoring applications. We validate our optimizations by improving the gate count of quantum attacks against public-key cryptography by 1.5 % to 3.4 %, depending on the key size. We also enable a 16 % runtime reduction at the cost of a 12 % increase in qubit count. Our techniques can be used to reduce the complexity of not only factoring algorithms but also a wide range of quantum algorithms that rely on windowed arithmetic.