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The Development of the Number Field Sieve

  • Conference proceedings
  • © 1993

Overview

Editors:
  1. Arjen K. Lenstra
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  2. Hendrik W. Lenstra
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    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (7 papers)

  1. Front Matter

    Pages i-viii
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  2. The number field sieve: An annotated bibliography

    • H. W. Lenstra Jr.
    Pages 1-3

  3. Factoring with cubic integers

    • J. M. Pollard
    Pages 4-10

  4. The number field sieve

    • A. K. Lenstra, H. W. Lenstra Jr., M. S. Manasse, J. M. Pollard
    Pages 11-42

  5. The lattice sieve

    • J. M. Pollard
    Pages 43-49

  6. Factoring integers with the number field sieve

    • J. P. Buhler, H. W. Lenstra Jr., Carl Pomerance
    Pages 50-94

  7. Computing a square root for the number field sieve

    • Jean-Marc Couveignes
    Pages 95-102

  8. A general number field sieve implementation

    • Daniel J. Bernstein, A. K. Lenstra
    Pages 103-126

  9. Back Matter

    Pages 127-131
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Keywords

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.

Bibliographic Information

  • Book Title: The Development of the Number Field Sieve

  • Editors: Arjen K. Lenstra, Hendrik W. Lenstra

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0091534

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-57013-4Published: 30 August 1993

  • eBook ISBN: 978-3-540-47892-8Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 140

  • Topics: Applications of Mathematics, Number Theory, Combinatorics

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