Module lattices and their shortest vectors
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912647945912320 |
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| author | Gargava, Nihar Serban, Vlad Viazovska, Maryna Viglino, Ilaria |
| author_facet | Gargava, Nihar Serban, Vlad Viazovska, Maryna Viglino, Ilaria |
| contents | We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.15275v2 to establish improved results for the variance of the number of lattice vectors of bounded Euclidean norm in a random module lattice. We then derive tight probabilistic bounds for the shortest vector lengths for several notions of random module lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Module lattices and their shortest vectors Gargava, Nihar Serban, Vlad Viazovska, Maryna Viglino, Ilaria Number Theory Information Theory 11H06 (Primary) 11H50, 68R01, 94B75 (Secondary) We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.15275v2 to establish improved results for the variance of the number of lattice vectors of bounded Euclidean norm in a random module lattice. We then derive tight probabilistic bounds for the shortest vector lengths for several notions of random module lattice. |
| title | Module lattices and their shortest vectors |
| topic | Number Theory Information Theory 11H06 (Primary) 11H50, 68R01, 94B75 (Secondary) |
| url | https://arxiv.org/abs/2510.12893 |