Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
47-59
Opis fizyczny
Daty
wydano
2012-01-01
online
2012-09-12
Twórcy
autor
- Shinshu University, Nagano, Japan
autor
- Shinshu University, Nagano, Japan
autor
- Shinshu University, Nagano, Japan
Bibliografia
- Grzegorz Bancerek. Curried and uncurried functions. Formalized Mathematics, 1(3):537-541, 1990.
- Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
- Czesław Byliński. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.
- Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
- Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
- Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective (the international series in engineering and computer science). 2002.
- Christoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559-564, 2001.
- Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
- Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
- Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
- Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
- Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
- Stanisław Żukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215-222, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0007-z