Optimizing windowed arithmetic for quantum attacks against RSA-2048

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)...

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Bibliographic Details
Published in:2025 62nd ACM/IEEE Design Automation Conference (DAC) pp. 1 - 7
Main Authors: Luongo, Alessandro, Narasimhachar, Varun, Sireesh, Adithya
Format: Conference Proceeding
Language:English
Published: IEEE 22.06.2025
Subjects:
Arithmetic
circuit optimization
Costs
Cryptography
Design automation
Logic gates
modular arithmetic
Optimization
Public key cryptography
Quantum algorithm
quantum computing
Qubit
Runtime
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Summary: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.
DOI:10.1109/DAC63849.2025.11132436