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Binary Quadratic Forms [electronic resource] :An Algorithmic Approach / by Johannes Buchmann, Ulrich Vollmer.

by Buchmann, Johannes [author.]; Vollmer, Ulrich [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Algorithms and Computation in Mathematics: 20Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.Description: XIV, 318 p. online resource.ISBN: 9783540463689.Subject(s): Mathematics | Data encryption (Computer science) | Computer science | Algebra | Number theory | Mathematics | Number Theory | Data Encryption | Mathematics of Computing | AlgebraDDC classification: 512.7 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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QA241-247.5 (Browse shelf) Available

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.

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.

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