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Dual Lattice of ℤ-module Lattice

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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].

Ograniczanie wyników

1 Formalized Mathematics

1 Futa Y.

1 Shidama Y.

1 2017

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Dual Lattice of ℤ-module Lattice