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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| Published in: | 2025 62nd ACM/IEEE Design Automation Conference (DAC) pp. 1 - 7 |
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| Format: | Conference Proceeding |
| Language: | English |
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IEEE
22.06.2025
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Luongo, Alessandro Narasimhachar, Varun Sireesh, Adithya |
| Author_xml | – sequence: 1 givenname: Alessandro surname: Luongo fullname: Luongo, Alessandro organization: Center for Quantum Technologies (CQT),Singapore – sequence: 2 givenname: Varun surname: Narasimhachar fullname: Narasimhachar, Varun organization: Agency for Science, Technology and Research (ASTAR),Singapore – sequence: 3 givenname: Adithya surname: Sireesh fullname: Sireesh, Adithya email: asireesh@ed.ac.uk organization: University of Edinburgh,Quantum Software Lab,Edinburgh,United Kingdom |
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| SubjectTerms | Arithmetic circuit optimization Costs Cryptography Design automation Logic gates modular arithmetic Optimization Public key cryptography Quantum algorithm quantum computing Qubit Runtime |
| Title | Optimizing windowed arithmetic for quantum attacks against RSA-2048 |
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