Johannes Buchmann, Ulrich Vollmer

Binary Quadratic Forms (eBook, PDF)

An Algorithmic Approach

• Format: PDF

Produktbeschreibung

The book deals with algorithmic problems related to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory. The book explains applications to cryptography and requires only basic mathematical knowledge. The author is a world leader in number theory.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 318
• Erscheinungstermin: 22. Juni 2007
• Englisch
• ISBN-13: 9783540463689
• Artikelnr.: 37367029

Autorenporträt

Buchmann: Professor of Computer Science and Mathematics special areas number theory, computer algebra, cryptography associate editor Journal of Cryptology Leibniz Award of the Deutsche Forschungsgemeinschaft Author of "Introduction to cryptography" UTM, translated into seven languages Member of Berlin-Brandenburg Academy of Sciences Member of Academy of Sciences and Literature, Mainz

Vollmer: Thesis and several articles on algorithms for Class Group and Regulator computation in quadratic fields.

Inhaltsangabe

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.

Rezensionen

From the reviews: "Quadratic Field Theory is the best platform for the development of a computer viewpoint. Such an idea is not dominant in earlier texts on quadratic forms ... . this book reads like a continuous program with major topics occurring as subroutines. The theory appears as 'program comments,' accompanied by numerical examples. ... An appendix explaining linear algebra (bases and matrices) helps make this work ideal as a self-contained well-motivated textbook for computer-oriented students at any level and as a reference book." (Harvey Cohn, Zentralblatt MATH, Vol. 1125 (2), 2008)