Binary Quadratic Forms

An Algorithmic Approach
2007
ISBN: 978-3-540-46367-2
Verlag: Springer

Buch, Englisch, 318 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 670 g

Reihe: Algorithms and Computation in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Buchmann, Johannes

Vollmer, Ulrich

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Kryptologie, Informationssicherheit
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

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.