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2011 | 19 | 1 | 61-64
Tytuł artykułu

Formalization of Integral Linear Space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article, we formalize integral linear spaces, that is a linear space with integer coefficients. Integral linear spaces are necessary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm that outputs short lattice base and cryptographic systems with lattice [8].
Słowa kluczowe
Wydawca
Rocznik
Tom
19
Numer
1
Strony
61-64
Opis fizyczny
Daty
wydano
2011-01-01
online
2011-07-18
Twórcy
autor
  • Shinshu University, Nagano, Japan
  • Shinshu University, Nagano, Japan
  • Shinshu University, Nagano, Japan
Bibliografia
  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [4] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [5] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23-28, 2003.
  • [6] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  • [7] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
  • [8] Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective (the international series in engineering and computer science). 2002.
  • [9] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • [10] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
  • [11] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [12] Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.
  • [13] Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics, 1(3):581-588, 1990.
  • [14] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [16] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [17] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-011-0010-9
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