A Note on Banaszczyk's Inequality
密码学与安全
2026-05-12 v1 概率论
摘要
Banaszczyk's inequality establishes a tail estimate for the discrete Gaussian measure on a lattice in . This classic result has been influential and plays an important role in lattice-based cryptography. An improvement of the inequality with a transparent proof was given by Tian, Liu and Xu. In this note, we further improve this inequality by imposing an appropriate condition, obtaining a significantly better bound. This refined inequality can be used to investigate dual attacks against the Learning With Errors (LWE) problem.
引用
@article{arxiv.2605.10461,
title = {A Note on Banaszczyk's Inequality},
author = {Hongyuan Qu and Chengliang Tian and Guangwu Xu},
journal= {arXiv preprint arXiv:2605.10461},
year = {2026}
}