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Mathematics - Algebra | Binary Quadratic Forms - An Algorithmic Approach

Binary Quadratic Forms

An Algorithmic Approach

Buchmann, Johannes, Vollmer, Ulrich

2007, XIV, 318 p.

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  • Author is a world leader in number theory
  • Uniquely focuses on the algorithmic aspects of the theory
  • Requires only basic mathematical knowledge

The book deals with algorithmic problems related to binary quadratic forms, such as finding the representations of an integer by a form with integer coefficients, finding the minimum of a form with real coefficients and deciding equivalence of two forms.

In order to solve those problems, 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. It requires only basic mathematical knowledge.

Content Level » Research

Keywords » Number theory - algebra - algebraic number theory - algorithmic number theory - algorithms - cryptography - quadratic forms

Related subjects » Algebra - Number Theory and Discrete Mathematics - Security and Cryptology - Theoretical Computer Science

Table of contents 

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.

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