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Dual Lattice of ℤ-module Lattice Cover
Open Access
|Sep 2017

Abstract

In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [20], [10] and [19].

DOI: https://doi.org/10.1515/forma-2017-0015 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 157 - 169
Submitted on: Jun 27, 2017
Published on: Sep 23, 2017
Published by: University of Bialystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 times per year

© 2017 Yuichi Futa, Yasunari Shidama, published by University of Bialystok
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.