Measure inequalities and the transference theorem in the geometry of numbers

Tian, Chengliang; Liu, Mingjie; Xu, Guangwu

doi:10.1090/S0002-9939-2013-11744-2

Measure inequalities and the transference theorem in the geometry of numbers
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by Chengliang Tian, Mingjie Liu and Guangwu Xu

Proc. Amer. Math. Soc. 142 (2014), 47-57

DOI: https://doi.org/10.1090/S0002-9939-2013-11744-2

Published electronically: September 18, 2013

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Abstract:

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.

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