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].
@article{bwmeta1.element.doi-10_2478_v10037-012-0007-z,
author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama},
title = {Z-modules},
journal = {Formalized Mathematics},
volume = {20},
year = {2012},
pages = {47-59},
zbl = {1276.94012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0007-z}
}
Yuichi Futa; Hiroyuki Okazaki; Yasunari Shidama. Z-modules. Formalized Mathematics, Tome 20 (2012) pp. 47-59. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0007-z/
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