A Note on Banaszczyk's Inequality
The paper improves Banaszczyk's inequality, providing a significantly better tail estimate for the discrete Gaussian measure on a lattice, which has applications in analyzing dual attacks against the LWE problem.
Abstract
More Like ThisBanaszczyk'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.