The development of the number field sieve

  • Editors
  • Arjen K. Lenstra
  • Hendrik W. LenstraJr.
Conference proceedings

Part of the Lecture Notes in Mathematics book series (LNM, volume 1554)

Table of contents

  1. Front Matter
    Pages i-viii
  2. J. M. Pollard
    Pages 4-10
  3. A. K. Lenstra, H. W. Lenstra Jr., M. S. Manasse, J. M. Pollard
    Pages 11-42
  4. J. M. Pollard
    Pages 43-49
  5. J. P. Buhler, H. W. Lenstra Jr., Carl Pomerance
    Pages 50-94
  6. Jean-Marc Couveignes
    Pages 95-102
  7. Daniel J. Bernstein, A. K. Lenstra
    Pages 103-126
  8. Back Matter
    Pages 127-131

About these proceedings


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.


Algebra Algebraic Number Fields Computational Number Theory Factoring algorithm Prime Prime Numbers number theory

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57013-4
  • Online ISBN 978-3-540-47892-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site