Skip to content
Open global navigation

Cambridge University Press

AcademicLocation selectorSearch toggleMain navigation toggle
Cart
Register Sign in Wishlist

Algorithmic Number Theory
Lattices, Number Fields, Curves and Cryptography

$68.00

Part of Mathematical Sciences Research Institute Publications

Dan Berstein, Dan Boneh, Joe Buhler, Henri Cohen, Cynthia Dwork, Andrew Granville, Hendrik Lenstra, Andrew Odlyzko, Carl Pomerance, Bjorn Poonen, Oliver Schirokauer, Rene Schoof, Jeffrey Shallit, William Stein, Peter Stevenhagen, Stan Wagon, Daqing Wan, Noriko Yui
View all contributors
  • Date Published: July 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521208338

$68.00
Paperback

Add to cart Add to wishlist

Other available formats:
Hardback


Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
About the Authors
  • 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.

    • Introduction aimed at beginning graduate students
    • Extensive coverage by a large body of experts
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: July 2011
    • format: Paperback
    • isbn: 9780521208338
    • length: 664 pages
    • dimensions: 234 x 156 x 34 mm
    • weight: 0.92kg
    • availability: Available
  • 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.

  • Editors

    J.P. Buhler, Reed College, Oregon

    P. Stevenhagen, Universiteit Leiden

    Contributors

    Dan Berstein, Dan Boneh, Joe Buhler, Henri Cohen, Cynthia Dwork, Andrew Granville, Hendrik Lenstra, Andrew Odlyzko, Carl Pomerance, Bjorn Poonen, Oliver Schirokauer, Rene Schoof, Jeffrey Shallit, William Stein, Peter Stevenhagen, Stan Wagon, Daqing Wan, Noriko Yui

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

You are now leaving the Cambridge University Press website, your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Find content that relates to you

© Cambridge University Press 2014

Back to top

Are you sure you want to delete your account?

This cannot be undone.

Cancel Delete

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×