Random Integer Lattice Generation via the Hermite Normal Form

Lattices used in cryptography are integer lattices. Defining and generating a “random integer lattice” are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the rand...

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Detalles Bibliográficos
Autores principales: Hu, Gengran, You, Lin, Li, Liang, Hu, Liqin, Wang, Hui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8620907/
https://www.ncbi.nlm.nih.gov/pubmed/34828207
http://dx.doi.org/10.3390/e23111509
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author Hu, Gengran
You, Lin
Li, Liang
Hu, Liqin
Wang, Hui
author_facet Hu, Gengran
You, Lin
Li, Liang
Hu, Liqin
Wang, Hui
author_sort Hu, Gengran
collection PubMed
description Lattices used in cryptography are integer lattices. Defining and generating a “random integer lattice” are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the random integer lattice given by G. Hu et al. and present an improved generation algorithm for it via the Hermite normal form. It can be proven that with probability ≥0.99, this algorithm outputs an n-dim random integer lattice within [Formula: see text] operations.
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spelling pubmed-86209072021-11-27 Random Integer Lattice Generation via the Hermite Normal Form Hu, Gengran You, Lin Li, Liang Hu, Liqin Wang, Hui Entropy (Basel) Article Lattices used in cryptography are integer lattices. Defining and generating a “random integer lattice” are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the random integer lattice given by G. Hu et al. and present an improved generation algorithm for it via the Hermite normal form. It can be proven that with probability ≥0.99, this algorithm outputs an n-dim random integer lattice within [Formula: see text] operations. MDPI 2021-11-14 /pmc/articles/PMC8620907/ /pubmed/34828207 http://dx.doi.org/10.3390/e23111509 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Hu, Gengran
You, Lin
Li, Liang
Hu, Liqin
Wang, Hui
Random Integer Lattice Generation via the Hermite Normal Form
title Random Integer Lattice Generation via the Hermite Normal Form
title_full Random Integer Lattice Generation via the Hermite Normal Form
title_fullStr Random Integer Lattice Generation via the Hermite Normal Form
title_full_unstemmed Random Integer Lattice Generation via the Hermite Normal Form
title_short Random Integer Lattice Generation via the Hermite Normal Form
title_sort random integer lattice generation via the hermite normal form
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8620907/
https://www.ncbi.nlm.nih.gov/pubmed/34828207
http://dx.doi.org/10.3390/e23111509
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