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Nature

Quantum-enhanced Markov chain Monte Carlo

David Layden, Guglielmo Mazzola, Ryan V. Mishmash, Mário Motta, Paweł Wocjan, Jin-Sung Kim, Sarah Sheldon

Published Jul 12, 2023• 84 citations
Publisher
DOI
10.1038/s41586-023-06095-4

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This paper presents a novel framework for enhancing the quantum resistance of NTRUEncrypt using Markov Chain Monte Carlo (MCMC) methods. We establish formal bounds on sampling efficiency and provide security reductions to lattice problems, bridging theoretical guarantees with practical implementations. Key contributions include: a new methodology for exploring private key vulnerabilities while maintaining quantum resistance, provable mixing time bounds for high-dimensional lattices, and concrete metrics linking MCMC parameters to lattice hardness assumptions. Numerical experiments validate our approach, demonstrating improved security guarantees and computational efficiency. These findings advance the theoretical understanding and practical adoption of NTRU- Encrypt in the post-quantum era.