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http://hdl.handle.net/11320/6283
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Pole DC | Wartość | Język |
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dc.contributor.author | Futa, Yuichi | - |
dc.contributor.author | Shidama, Yasunari | - |
dc.date.accessioned | 2018-02-08T08:10:31Z | - |
dc.date.available | 2018-02-08T08:10:31Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Formalized Mathematics, Volume 25, Issue 2, Pages 157–169 | - |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.uri | http://hdl.handle.net/11320/6283 | - |
dc.description.abstract | SummaryIn 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]. | - |
dc.language.iso | en | - |
dc.publisher | DeGruyter Open | - |
dc.subject | ℤ-lattice | - |
dc.subject | dual lattice of ℤ-lattice | - |
dc.subject | dual basis of ℤ-lattice | - |
dc.title | Dual Lattice of ℤ-module Lattice | - |
dc.type | Article | - |
dc.identifier.doi | 10.1515/forma-2017-0015 | - |
dc.description.Affiliation | Futa Yuichi - Tokyo University of Technology, Tokyo, Japan | - |
dc.description.Affiliation | Shidama Yasunari - Shinshu University, Nagano, Japan | - |
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dc.identifier.eissn | 1898-9934 | - |
dc.description.volume | 25 | - |
dc.description.issue | 2 | - |
dc.description.firstpage | 157 | - |
dc.description.lastpage | 169 | - |
dc.identifier.citation2 | Formalized Mathematics | - |
Występuje w kolekcji(ach): | Formalized Mathematics, 2017, Volume 25, Issue 2 |
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