Adelic reduction of module lattices
Henry Bambury, Seungki Kim, Changmin Lee, Phong Q. Nguyen
Source abstract
We give a strict generalization of the LLL algorithm over number fields, based on the reduction theory of $\GL(n)$ 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.
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