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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Autores principales:	Gengran Hu, Lin You, Liang Li, Liqin Hu, Hui Wang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	random integer lattice Hermite normal form generation algorithm Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/197f0c17bb274ab68213184da3831b2e
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id	oai:doaj.org-article:197f0c17bb274ab68213184da3831b2e
record_format	dspace
spelling	oai:doaj.org-article:197f0c17bb274ab68213184da3831b2e2021-11-25T17:30:22ZRandom Integer Lattice Generation via the Hermite Normal Form10.3390/e231115091099-4300https://doaj.org/article/197f0c17bb274ab68213184da3831b2e2021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1509https://doaj.org/toc/1099-4300Lattices 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 <i>n</i>-dim random integer lattice within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> operations.Gengran HuLin YouLiang LiLiqin HuHui WangMDPI AGarticlerandom integer latticeHermite normal formgeneration algorithmScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1509, p 1509 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	random integer lattice Hermite normal form generation algorithm Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	random integer lattice Hermite normal form generation algorithm Science Q Astrophysics QB460-466 Physics QC1-999 Gengran Hu Lin You Liang Li Liqin Hu Hui Wang Random Integer Lattice Generation via the Hermite Normal Form
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 <i>n</i>-dim random integer lattice within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> operations.
format	article
author	Gengran Hu Lin You Liang Li Liqin Hu Hui Wang
author_facet	Gengran Hu Lin You Liang Li Liqin Hu Hui Wang
author_sort	Gengran Hu
title	Random Integer Lattice Generation via the Hermite Normal Form
title_short	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_sort	random integer lattice generation via the hermite normal form
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/197f0c17bb274ab68213184da3831b2e
work_keys_str_mv	AT gengranhu randomintegerlatticegenerationviathehermitenormalform AT linyou randomintegerlatticegenerationviathehermitenormalform AT liangli randomintegerlatticegenerationviathehermitenormalform AT liqinhu randomintegerlatticegenerationviathehermitenormalform AT huiwang randomintegerlatticegenerationviathehermitenormalform
_version_	1718412271421489152

Random Integer Lattice Generation via the Hermite Normal Form

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