Module lattices and their shortest vectors

Nihar Gargava; Vlad Serban; Maryna Viazovska; Ilaria Viglino

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arXiv · 2510.12893

Module lattices and their shortest vectors

Nihar Gargava·Vlad Serban·Maryna Viazovska·Ilaria Viglino

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Abstract

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.

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Nihar Gargava, Vlad Serban, Maryna Viazovska, Ilaria Viglino. 2025-10-14. Module lattices and their shortest vectors. https://arxiv.org/abs/2510.12893

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