Algorithmic Number Theory Lattices, Number Fields, Curves and Cryptography

Name: Algorithmic Number Theory Lattices, Number Fields, Curves and Cryptography
Price: 96.38 USD
Availability: InStock
ISBN: 9780521808545

ISBN-10: 0521808545

ISBN-13: 9780521808545

Edition: 2008

Authors: J. P. Buhler, Peter Stevenhagen, P. Stevenhagen, P. Stevenhagen

List price: $206.00

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Description:

Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that…

Book details

List price: $206.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 10/20/2008
Binding: Hardcover
Pages: 664
Size: 6.14" wide x 9.21" long x 1.46" tall
Weight: 2.266
Language: English




Solving Pell's equation




Basic algorithms in number theory




Elliptic curves




The arithmetic of number rings




Fast multiplication and applications




Primality testing




Smooth numbers: computational number theory and beyond




Smooth numbers and the quadratic sieve




The number field sieve




Elementary thoughts on discrete logarithms




The impact of the number field sieve on the discrete logarithm problem in finite fields




Lattices




Reducing lattices to find small-height values of univariate polynomials




Protecting communications against forgery




Computing Arakelov class groups




Computational class field theory




Zeta functions over finite fields




Counting points on varieties over finite fields




How to get your hands on modular forms using modular symbols




Congruent number problems in dimension one and two