Free ℤ-module

• Autorzy: Yuichi Futa , Hiroyuki Okazaki , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2012
• Tom: 20
• Numer: 4
• Strony: 275-280

Daty

wydano

2012-12-01

online

2013-02-02

Twórcy

autor

Yuichi Futa

• Shinshu University, Nagano, Japan

autor

Hiroyuki Okazaki

• Shinshu University, Nagano, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

Bibliografia

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Identyfikatory

DOI

10.2478/v10037-012-0033-x