Paper 2026/2228
Adelic reduction of module lattices
Abstract
We give a strict generalization of the LLL algorithm over number fields, based on the reduction theory of $\mathrm{GL}(n)$ over the adele ring of a number field. Our algorithm is free of heuristics, with rigorous bounds on output quality and complexity. As a consequence, we obtain a hierarchy of reductions from module-(H)SVP to ideal-HSVP, an example of which has runtime and approximation factors subexponential in the field degree. More importantly, we uncover a close connection between structured lattice reduction and a Diophantine approximation over number fields.
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- Keywords
- lattice reductionmodule lattices
- Contact author(s)
- seungki math @ gmail com
- History
- 2026-09-27: approved
- 2026-09-26: received
- See all versions
- Short URL
- https://ia.cr/2026/2228
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2026/2228,
author = {Henry Bambury and Seungki Kim and Changmin Lee and Phong Q. Nguyen},
title = {Adelic reduction of module lattices},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2228},
year = {2026},
url = {https://eprint.iacr.org/2026/2228}
}
