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arXiv · 2605.10461

A Note on Banaszczyk's Inequality

Hongyuan Qu·Chengliang Tian·Guangwu Xu
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Abstract

Banaszczyk's inequality establishes a tail estimate for the discrete Gaussian measure on a lattice in $\mathbb{R}^n$. 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.

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Hongyuan Qu, Chengliang Tian, Guangwu Xu. 2026-05-11. A Note on Banaszczyk's Inequality. https://arxiv.org/abs/2605.10461

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