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A general number field sieve implementation

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

Abstract

The general number field sieve is the asymptotically fastest—and by far most complex—factoring algorithm known. We have implemented this algorithm, including five practical improvements: projective polynomials, the lattice sieve, the large prime variation, character columns, and the positive square root method. In this paper we describe our implementation and list some factorizations we obtained, including the record factorization of 2523 − 1.

Keywords

  • Direct Approach
  • Number Field
  • Number Ring
  • Algebraic Number Field
  • Quadratic Character

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Thanks to Joe Buhler, Hendrik Lenstra, John Pollard, and Carl Pomerance for their helpful suggestions, and to Andrew Odlyzko for his help with the factorization of 2523 − 1. The first author was supported in part by a National Science Foundation Graduate Fellowship and by Bellcore.

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© 1993 Springer-Verlag

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Bernstein, D.J., Lenstra, A.K. (1993). A general number field sieve implementation. In: Lenstra, A.K., Lenstra, H.W. (eds) The development of the number field sieve. Lecture Notes in Mathematics, vol 1554. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091541

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  • DOI: https://doi.org/10.1007/BFb0091541

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57013-4

  • Online ISBN: 978-3-540-47892-8

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