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15 January 2025 Symplectic enumeration reduction algorithm for lattice-based post-quantum cryptography NTRU
Xinjian Li, Chengtao Wang, Chaohai Xie
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Proceedings Volume 13513, The International Conference Optoelectronic Information and Optical Engineering (OIOE2024); 135132M (2025) https://doi.org/10.1117/12.3045735
Event: The International Conference Optoelectronic Information and Optical Engineering (OIOE2024), 2024, Wuhan, China
Abstract
The enumeration reduction algorithm is a practical method for solving the shortest vector problem(SVP) in lattice theory, and it plays an important role in analyzing the security of lattice-based post-quantum cryptography NTRU(Number Theory Research Unit), but there is still a problem of low efficiency for high-dimensional NTRU. Based on the symplectic properties of NTRU lattices, the new upper boundary of the initial boundary A of the enumeration reduction algorithm search space is analyzed. The new upper boundary Anew is 2.4 times smaller than the initial boundary ASchnorr of ENUM algorithm, and the number of lattice points in the initial search space is 2.4N times smaller. Symplectic enumeration lattice algorithm SENUM for NTRU lattices is proposed. A jump parameter is designed for SENUM algorithm, which improves its calculation speed and enumeration success rate. The experiment shows that with the same parameters β, SENUM algorithm can complete NTRU lattice enumeration operation within 1 hour, and Hermite factor of the output is better.
(2025) Published by SPIE. Downloading of the abstract is permitted for personal use only.
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Xinjian Li, Chengtao Wang, and Chaohai Xie "Symplectic enumeration reduction algorithm for lattice-based post-quantum cryptography NTRU", Proc. SPIE 13513, The International Conference Optoelectronic Information and Optical Engineering (OIOE2024), 135132M (15 January 2025); https://doi.org/10.1117/12.3045735
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KEYWORDS
Matrices
Quantum cryptography
Algorithms
Quantum experiments
Quantum security
Quantum computing
Genetical swarm optimization
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