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Binary Quadratic Forms : An Algorithmic Approach / by Johannes Buchmann, Ulrich Vollmer
(Algorithms and Computation in Mathematics ; 20)

データ種別 電子ブック
出版者 Berlin, Heidelberg : Springer Berlin Heidelberg
出版年 2007
本文言語 英語
大きさ XIV, 318 p : online resource

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URL 電子ブック


EB0120412

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内容注記 Binary Quadratic Forms
Equivalence of Forms
Constructing Forms
Forms, Bases, Points, and Lattices
Reduction of Positive Definite Forms
Reduction of Indefinite Forms
Multiplicative Lattices
Quadratic Number Fields
Class Groups
Infrastructure
Subexponential Algorithms
Cryptographic Applications
一般注記 This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography. A considerable part of the theory is developed for forms with real coe?cients and it is shown that forms with integer coe?cients appear in a natural way. Much of the progress of number theory has been stimulated by the study of concrete computational problems. Deep theories were developed from the classic time of Euler and Gauss onwards to this day that made the solutions ofmanyof theseproblemspossible.Algorithmicsolutionsandtheirproperties became an object of study in their own right. Thisbookintertwinestheexpositionofoneveryclassicalstrandofnumber theory with the presentation and analysis of algorithms both classical and modern which solve its motivating problems. This algorithmic approach will lead the reader, we hope, not only to an understanding of theory and solution methods, but also to an appreciation of the e?ciency with which solutions can be reached. The computer age has led to a marked advancement of algorithmic - search. On the one hand, computers make it feasible to solve very hard pr- lems such as the solution of Pell equations with large coe?cients. On the other, the application of number theory in public-key cryptography increased the urgency for establishing the complexity of several computational pr- lems: many a computer system stays only secure as long as these problems remain intractable
著者標目 *Buchmann, Johannes author
Vollmer, Ulrich author
SpringerLink (Online service)
件 名 LCSH:Mathematics
LCSH:Data encryption (Computer science)
LCSH:Computer science -- Mathematics  全ての件名で検索
LCSH:Algebra
LCSH:Number theory
FREE:Mathematics
FREE:Algebra
FREE:Number Theory
FREE:Mathematics of Computing
FREE:Data Encryption
分 類 DC23:512
巻冊次 ISBN:9783540463689 REFWLINK
ISBN 9783540463689
URL http://dx.doi.org/10.1007/978-3-540-46368-9
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