Effective module lattices and their shortest vectors
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918161263099904 |
|---|---|
| author | Gargava, Nihar Serban, Vlad Viazovska, Maryna Viglino, Ilaria |
| author_facet | Gargava, Nihar Serban, Vlad Viazovska, Maryna Viglino, Ilaria |
| contents | We prove tight probabilistic bounds for the shortest vectors in module lattices over number fields using the results of arXiv:2308.15275. Moreover, establishing asymptotic formulae for counts of fixed rank matrices with algebraic integer entries and bounded Euclidean length, we prove an approximate Rogers integral formula for discrete sets of module lattices obtained from lifts of algebraic codes. This in turn implies that the moment estimates of arXiv:2308.15275 as well as the aforementioned bounds on the shortest vector also carry through for large enough discrete sets of module lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective 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 prove tight probabilistic bounds for the shortest vectors in module lattices over number fields using the results of arXiv:2308.15275. Moreover, establishing asymptotic formulae for counts of fixed rank matrices with algebraic integer entries and bounded Euclidean length, we prove an approximate Rogers integral formula for discrete sets of module lattices obtained from lifts of algebraic codes. This in turn implies that the moment estimates of arXiv:2308.15275 as well as the aforementioned bounds on the shortest vector also carry through for large enough discrete sets of module lattices. |
| title | Effective module lattices and their shortest vectors |
| topic | Number Theory Information Theory 11H06 (Primary) 11H50, 68R01, 94B75 (Secondary) |
| url | https://arxiv.org/abs/2402.10305 |