On the smoothing parameter and last minimum of random orthogonal lattices

Elena Kirshanova; Huyen Nguyen; Damien Stehlé; Alexandre Wallet

Paper 2020/057

On the smoothing parameter and last minimum of random orthogonal lattices

Elena Kirshanova, Huyen Nguyen, Damien Stehlé, and Alexandre Wallet

Abstract

Let , with each entry independently and identically distributed from an integer Gaussian distribution. We consider the orthogonal lattice of , i.e., the set of vectors such that . In this work, we prove probabilistic upper bounds on the smoothing parameter and the -th minimum of . 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].

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Designs, Codes and Cryptography
DOI: 10.1007/s10623-020-00719-w
Keywords: random lattices last minimum smoothing parameter lattice-based cryptography lattices and convex bodies
Contact author(s): elenakirshanova @ gmail com
damien stehle @ gmail com
nthuyen math @ gmail com
wallet alexandre @ gmail com
History: 2020-01-21: received
Short URL: https://ia.cr/2020/057
License: CC BY

BibTeX

@misc{cryptoeprint:2020/057,
      author = {Elena Kirshanova and Huyen Nguyen and Damien Stehlé and Alexandre Wallet},
      title = {On the smoothing parameter and last minimum of random orthogonal lattices},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/057},
      year = {2020},
      doi = {10.1007/s10623-020-00719-w},
      url = {https://eprint.iacr.org/2020/057}
}