A new bound for the orthogonality defect of HKZ reduced lattices
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Published version
Author(s)
Porter, Christian
Dable-Heath, Edmund
Ling, Cong
Type
Journal Article
Abstract
Hermite–Korkin–Zolotarev (HKZ) reduction is an important notion of lattice reduction which plays a significant role in number theory (particularly the geometry of numbers), and more recently in coding theory and post-quantum cryptography. In this work, we determine a sharp upper bound on the orthogonality defect of HKZ reduced bases up to dimension 3. Using this result, we determine a general upper bound for the orthogonality defect of HKZ reduced bases of arbitrary rank. This upper bound is sharper than existing bounds in literature, such as the one determined by Lagarias, Lenstra and Schnorr [3].
Date Issued
2024-09
Date Acceptance
2024-06-23
Citation
Research in Number Theory, 2024, 10 (3)
ISSN
2363-9555
Publisher
Springer
Journal / Book Title
Research in Number Theory
Volume
10
Issue
3
Copyright Statement
© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://link.springer.com/article/10.1007/s40993-024-00554-1
Subjects
Geometry of Numbers
Lattices
Mathematics
Physical Sciences
Quadratic Forms
Reduction Theory
Science & Technology
Publication Status
Published
Article Number
65
Date Publish Online
2024-07-09