Algorithmic number theory : lattices, number fields, curves and cryptography /
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作 者：edited by J.P. Buhler, P. Stevenhagen.
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ISBN：9780521808545
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简介
The advent of computers and especially sophisticated algorithms has gradually led to the emergence of algorithmic and number theory as a distinct field, after centuries of their submergence into other disciplines. Reflecting the wide used algorithmic and number theory in computer science, cryptography, and medicine, these 20 survey articles cover such topics as the Pell equation, basic algorithms and number theory, the quadratic sieve, primary testing algorithms, lattices, elliptic curves, number theory as an element of computational theory (and beyond), discrete logarithms, the effects of the number field sieve on discreet logarithms, finite fields, reducing the lattice basis to examine univariate polynomials, computing Arakelov class groups, computational class field theory, the algorithm theory of zeta functions over finite fields, congruent number problems and their variants, and an introduction to computing modular forms using modular symbols. Annotation 漏2009 Book News, Inc., Portland, OR (booknews.com)
目录
1 Solving Pell's equation Hendrik Lenstra
2 Basic algorithms in number theory Joe Buhler and Stan Wagon
3 Elliptic curves Bjorn Poonen
4 The arithmetic of number rings Peter Stevenhagen
5 Fast multiplication and applications Dan Bernstein
6 Primality testing Rene Schoof
7 Smooth numbers: computational number theory and beyond Andrew Granville
8 Smooth numbers and the quadratic sieve Carl Pomerance
9 The number field sieve Peter Stevenhagen
10 Elementary thoughts on discrete logarithms Carl Pomerance
11 The impact of the number field sieve on the discrete logarithm problem in finite fields Oliver Schirokauer
12 Lattices Hendrik Lenstra
13 Reducing lattices to find small-height values of univariate polynomials Dan Bernstein
14 Protecting communications against forgery Dan Bernstein
15 Computing Arakelov class groups Rene Schoof
16 Computational class field theory Henri Cohen and Peter Stevenhagen
17 Zeta functions over finite fields Daqing Wan
18 Counting points on varieties over finite fields Alan Lauder and Daqing Wan
19 How to get your hands on modular forms using modular symbols William Stein
20 Congruent number problems in dimension one and two Jaap Top and Noriko Yui
2 Basic algorithms in number theory Joe Buhler and Stan Wagon
3 Elliptic curves Bjorn Poonen
4 The arithmetic of number rings Peter Stevenhagen
5 Fast multiplication and applications Dan Bernstein
6 Primality testing Rene Schoof
7 Smooth numbers: computational number theory and beyond Andrew Granville
8 Smooth numbers and the quadratic sieve Carl Pomerance
9 The number field sieve Peter Stevenhagen
10 Elementary thoughts on discrete logarithms Carl Pomerance
11 The impact of the number field sieve on the discrete logarithm problem in finite fields Oliver Schirokauer
12 Lattices Hendrik Lenstra
13 Reducing lattices to find small-height values of univariate polynomials Dan Bernstein
14 Protecting communications against forgery Dan Bernstein
15 Computing Arakelov class groups Rene Schoof
16 Computational class field theory Henri Cohen and Peter Stevenhagen
17 Zeta functions over finite fields Daqing Wan
18 Counting points on varieties over finite fields Alan Lauder and Daqing Wan
19 How to get your hands on modular forms using modular symbols William Stein
20 Congruent number problems in dimension one and two Jaap Top and Noriko Yui
Algorithmic number theory : lattices, number fields, curves and cryptography /
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