Algorithmic number theory : lattices, number fields, curves and cryptography
Author(s)
Bibliographic Information
Algorithmic number theory : lattices, number fields, curves and cryptography
(Mathematical Sciences Research Institute publications, 44)
Cambridge University Press, 2011, c2008
- : pbk
Available at 1 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references
Originally published: 2008
Description and Table of Contents
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 cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.
Table of Contents
- 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.
by "Nielsen BookData"