Lecture Notes in Mathematics

The Development of the Number Field Sieve

Editors: Lenstra, Arjen K., Lenstra, Hendrik W.Jr. (Eds.)

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About this book

The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.

Table of contents (7 chapters)

  • The number field sieve: An annotated bibliography

    Lenstra, H. W.

    Pages 1-3

  • Factoring with cubic integers

    Pollard, J. M.

    Pages 4-10

  • The number field sieve

    Lenstra, A. K. (et al.)

    Pages 11-42

  • The lattice sieve

    Pollard, J. M.

    Pages 43-49

  • Factoring integers with the number field sieve

    Buhler, J. P. (et al.)

    Pages 50-94

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-47892-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-57013-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Development of the Number Field Sieve
Editors
  • Arjen K. Lenstra
  • Hendrik W.Jr. Lenstra
Series Title
Lecture Notes in Mathematics
Series Volume
1554
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47892-8
DOI
10.1007/BFb0091534
Softcover ISBN
978-3-540-57013-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 140
Topics