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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
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Volume 20, Issue 4 (Dec 2012)

Issues

Free ℤ-module

Yuichi Futa / Hiroyuki Okazaki / Yasunari Shidama
Published Online: 2013-02-02 | DOI: https://doi.org/10.2478/v10037-012-0033-x

Summary

In this article we formalize a free ℤ-module and its rank. We formally prove that for a free finite rank ℤ-module V , the number of elements in its basis, that is a rank of the ℤ-module, is constant regardless of the selection of its basis. ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [15]. Some theorems in this article are described by translating theorems in [21] and [8] into theorems of Z-module.

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About the article

This work was supported by JSPS KAKENHI 21240001 and 22300285.


Published Online: 2013-02-02

Published in Print: 2012-12-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0033-x.

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