Welcome to the resource topic for 2020/057
Title:
On the smoothing parameter and last minimum of random orthogonal lattices
Authors: Elena Kirshanova, Huyen Nguyen, Damien Stehlé, Alexandre Wallet
Abstract:Let X \in {\mathbb{Z}}^{n \times m}, with each entry independently and identically distributed from an integer Gaussian distribution. We consider the orthogonal lattice \Lambda^\perp(X) of X, i.e., the set of vectors \mathbf{v} \in {\mathbb{Z}}^m such that X \mathbf{v}= \mathbf{0}. In this work, we prove probabilistic upper bounds on the smoothing parameter and the (m-n)-th minimum of \Lambda^\perp(X). These bounds improve and the techniques build upon prior works of Agrawal, Gentry, Halevi and Sahai [Asiacrypt’13], and of Aggarwal and Regev [Chicago J. Theoret. Comput. Sci.'16].
ePrint: https://eprint.iacr.org/2020/057
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