Measure inequalities and the transference theorem in the geometry of numbers
Chengliang Tian, Mingjie Liu, Guangwu Xu · Proceedings of the American Mathematical Society · 2013
The measure inequalities of Banaszczyk have been important tools in applying discrete Gaussian measure over lattices to lattice-based cryptography. This paper presents an improvement of Banaszczyk’s inequalities and provides a concise and transparent proof. This paper also generalizes the transference theorem of Cai to general convex bodies. The bound is better than that obtained by simply generalizing the $l_2$ norm using the canonical norm inequalities.