## Z-modules

In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].

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## Z-modules

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*Formalized Mathematics*, 2017, Volume 25, Number 2

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Yuichi Futa / Hiroyuki Okazaki / Yasunari Shidama

In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].

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**Published Online**: 2012-09-12

**Published in Print**: 2012-01-01

**Citation Information: **Formalized Mathematics, Volume 20, Issue 1, Pages 47–59, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0007-z.

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Yuichi Futa and Yasunari Shidama

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