An LLL algorithm with symmetries
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916590697578496 |
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| author | Romano, Beth Thorne, Jack A. |
| author_facet | Romano, Beth Thorne, Jack A. |
| contents | We give a generalisation of the Lenstra-Lenstra-Lovász (LLL) lattice-reduction algorithm that is valid for an arbitrary (split, semisimple) reductive group $G$. This can be regarded as `lattice reduction with symmetries'. We make this algorithm explicit for the classical groups $G = \mathrm{Sp}_{2g}$, $\mathrm{SO}_{2g}$, and for the exceptional group $G = G_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An LLL algorithm with symmetries Romano, Beth Thorne, Jack A. Number Theory We give a generalisation of the Lenstra-Lenstra-Lovász (LLL) lattice-reduction algorithm that is valid for an arbitrary (split, semisimple) reductive group $G$. This can be regarded as `lattice reduction with symmetries'. We make this algorithm explicit for the classical groups $G = \mathrm{Sp}_{2g}$, $\mathrm{SO}_{2g}$, and for the exceptional group $G = G_2$. |
| title | An LLL algorithm with symmetries |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.07012 |