Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: ℤ-lattice

Sortuj według:

Ogranicz wyniki do:

Dual Lattice of ℤ-module Lattice

100%

Futa Y., Shidama Y.

Formalized Mathematics

2017

tom 25

nr 2

157-169

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].

Lattice of ℤ-module

100%

Futa Y., Shidama Y.

Formalized Mathematics

2016

tom 24

nr 1

49-68

In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9].

Ograniczanie wyników

2 Formalized Mathematics

2 Futa Y.

2 Shidama Y.

1 2017

1 2016

Wyniki wyszukiwania

Dual Lattice of ℤ-module Lattice

Lattice of ℤ-module